Home Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
Article Open Access

Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio

  • Muthu Rajarathinam , Muhammad Ijaz Khan EMAIL logo , Barno Sayfutdinovna Abdullaeva , Tehseen Abbas , Fuad A. Awwad and Emad A. A. Ismail
Published/Copyright: July 8, 2024
Download Article (PDF)
Open Physics
From the journal Open Physics Volume 22 Issue 1

Abstract

This study examines the influence of wall velocity ratio on mixed convective heat transport in a permeable cavity containing an isothermal solid block at its center. The analysis considers the characteristics of various flow variables, i.e., Darcy number, wall velocity ratio, Richardson number, and volume fraction of suspended nanoparticles, on heat transport and material flow characteristics. The principal equations are solved implementing the semi-implicit method for pressure linked equations algorithm, and the outcomes are compared with existing literature. The study shows that rising estimations of Darcy number, velocity ratio, Richardson number, and nanoparticles volume fraction lead to improved heat transfer rates. For example, at high Richardson number (100) and solid volume fraction (0.05), increasing the velocity ratio from 0.5 to 1.5 results in a 6% (5%) upsurge in heat transport rate. Conversely, at smaller Richardson number (0.01), the heat transport rate upsurges by 29% (28%). Similarly, at high Darcy numbers and low wall velocity ratios, a 3% (4%) escalate in heat transport rate is observed with an increase in nanoparticles concentration from 0 to 0.05, while a 9% (8%) increase in thermal performance is achieved at low Darcy numbers. The study emphasizes the importance of optimizing the combination of nanoparticles volume fraction, Darcy number, velocity ratio, and Richardson number to maximize thermal performance in the porous cavity.

Keywords: porous cavity; nanofluid mixed convection; isothermal block; wall velocity ratio

Nomenclature

c p

specific heat capacity (J kg−1 K−1)

Da

Darcy number

Fc

Forchheimer term

G

acceleration due to gravity ( m s − 2 )

Gr

Grashof number

K

permeability of the medium ( m 2 )

k nf

thermal conductivity ( W m − 1 K 1 )

L

length of the cavity ( m )

Nu

local Nusselt number

p

pressure ( Pa )

P

dimensionless pressure

Pr

Prandtl number

Ra

Rayleigh number

Re

Reynolds number

Ri

Richardson number

Nu ¯

average Nusselt number

U , V

dimensionless velocities

u, v

dimensional velocities

X, Y

dimensionless coordinates

x, y

dimensional coordinate ( m )

Greek symbols

λ

wall velocity ratio

α

thermal diffusivity ( m 2 s − 1 )

τ

dimensionless time

ν

kinematic viscosity ( m 2 s − 1 )

ρ

density (kg m−3)

µ

dynamic viscosity (kg m−1 s−1)

φ

wall velocity ratio

β

coefficient of thermal expansion ( K − 1 )

θ

dimensionless temperature

ε

porosity of the medium

Subscripts

f

base fluid

h

hot

nf

nanofluid

p

nanoparticles

1 Introduction

The presence of an isothermal block within a resonator has attracted attention due to its common occurrence in electronic packages and its various technological applications. As a result, several scientists and examiners have focused on analyzing heat/mass transport in these configurations [1]. Several studies have analyzed the heat transfer performance when an isothermal solid block is present in cavities. For example, Sun et al. [2] investigated natural convective heat transport in closed cavities subject to isothermal solid block at the center. Kalidasan et al. [3] scrutinized the heat transport characteristics of an isothermal solid block in an open-ended cavity using hybrid nanofluids. Mehmood et al. [4] worked on alumina-water based nanoliquids flow with forced convection phenomena and hot iso-thermal block inside a lid-driven cavity considering the characteristics of a applied magnetic field. Their findings showed that the existence of the nano-liquid and mixed convection augmented the heat transport rate. Haq et al. [5] scrutinized the heat transport influence of an isothermal block in a moderately heated rhombus cavity. The research demonstrates that the heat transport and fluid flow behavior were greatly influenced by isothermally heat square block.

In the last couple of decades, there has been a growing curiosity in studying heat transfer in environments where mixed convection occurs and porous walls are present. This research has applied utilizations and application in numerous thermal devices like solar panels, electronic cooling systems, building heating and cooling systems, and the food industry. Kumar et al. [6] focused on a research that represents the characteristics of heat transport in a porous cavity using a multigrid approach. Their findings recommend that the consolidation of shear force and buoyancy effects in mixed convection leads to improved heat propagation. Sivasankaran and Pan [7] scrutinized the characteristics of non-uniform thermal boundary conditions (BC) on mixed convection flow and heat transport in a lid-driven permeable cavity. They observed that non-uniform heating of double side walls resulted in advanced heat transport rates compared to non-uniform heating of a single wall. Moria [8] established a mathematical model to explore natural convective flow using porous medium and solid blocks. Their consequences exhibited an important augmentation in heat transport performance when porous materials were present, especially at high Rayleigh numbers. Colak et al. [9] further investigated a similar problem by incorporating a heated porous block into the mixed convection state. They found that the permeable variable played an important role in improving heat transport by governing vortex formation.

The utilization of nanofluids in electronic devices presents a novel method to enhance heat transfer efficiency [10,11,12]. Various studies have explored the consequences of nanomaterials for cooling performance in lid-driven permeable cavities. Recently, Begum et al. [13] and Hussain et al. [14] conducted numerical simulations and demonstrated that nanofluids can greatly improve cooling rates due to their superior thermal conductivity. Nithyadevi et al. [15] investigated different factors influencing enhanced heat transfer, such as nanofluid char mixed convection, nanofluid properties, and wall speed ratio, highlighting the importance of the wall speed ratio in achieving significant heat transfer enhancement. In a latest research, Alomari et al. [16] inspected heat transport phenomenon in a lid-driven cavity nanofluid flow in the presence of porous layer. Their obtained consequences designated that heat transport rates increase with higher mixed convection and forced convection parameters, nanoparticle concentrations, and porous parameters, with a notable 64% enhancement in heat transport rate at rising Reynolds numbers. Long et al. [17] examined macroscopic and mesoscopic characteristics of sintered silver nanomaterials via crystal plasticity FEM.

Investigating the combined effects of mixed convection, wall velocity ratio and nanomaterials presents motivating exploration query that has not been extensively explored. Heat transport phenomenon in the presence of isothermal solid block is particularly relevant in various industrial utilizations involving porous media. The aim of this exploration work was to address this research gap by examining the impact of an isothermal solid block on thermal behavior and fluid flow, as well as the potential heat transport rate enhancement with the use of Cu-water nanofluids. Additionally, the study will explore the influence of wall velocity ratio on heat transport rate in the presence of the isothermal block and quantify the heat transfer rate increase with the addition of copper nanoparticles. Numerical analysis will be employed to examine the behavior of convective heat transport in a permeable cavity with an isothermal solid block, considering the wall velocity ratio. The findings of this study are expected to provide valuable insights for the design of electronic equipment and contribute to reducing energy ingesting in industrial sceneries.

2 Modeling of the problem

In our ongoing research, we have chosen a porous cavity with a size of L as the basis for our study. Inside the cavity, we have introduced a nanofluid consisting of Cu and water (Figure 1). In the graphical abstract, T h and T c, respectively characterize the temperature of left and right vertical walls of the cavity, where T h > T c. Furthermore, the top and bottom walls of the cavity are considered adiabatic. At the center of the cavity, there is a heated square block with an isothermal temperature T h + T c 2 . The size of the block is given by L 4 . Let us assume that the top wall is moved with constant velocity U t = U 0 from left to right. But the bottom wall, can slide with a velocity U b, either in the same direction or opposite direction, where U b = λU 0, and (λ = U b /U 0) stands for variable wall velocity ratio. In this study, we make the following assumptions to model the flow equations:

  • Neglecting induced electric current, viscous dissipation, and Joule heating effects.

  • Assuming negligible radiative heat transport between the cavity walls.

  • Considering the permeable medium to be homogeneous, isotropic, and in thermal equilibrium with the nano-fluid.

  • Assuming the nano-fluid flow to be unsteady, laminar, incompressible, and Newtonian.

  • Treating the nanoliquid as a single-phase system with thermal equilibrium between the nanoparticles and fluid.

  • Given constant physical characteristics of the nanofluid, except for density changes in the buoyancy term using the Boussinesq approximation.

Figure 1 Graphical display of current research.
Figure 1

Graphical display of current research.

In the presence of above assumptions, the principal flow expressions are listed as follows [6,15,18]:

(1) ∂ U ∂ X + ∂ V ∂ Y = 0 ,

(2) 1 ε ∂ U ∂ τ + 1 ε 2 U ∂ U ∂ X + V ∂ U ∂ Y = − ∂ P ∂ X + 1 ε ν nf ν f 1 Re ∇ 2 U − Fc Da U U 2 + V 2 − ν n f ν f 1 Re U Da ,

(3) 1 ε ∂ V ∂ τ + 1 ε 2 U ∂ V ∂ X + V ∂ V ∂ Y = − ∂ P ∂ Y + 1 ε ν nf ν f 1 Re ∇ 2 V − ν nf ν f Re V Da + β nf R i β f θ − Fc Da V U 2 + V 2 ,

(4) ∂ θ ∂ τ + U ∂ θ ∂ X + V ∂ θ ∂ Y = α nf α f 1 Re Pr ∇ 2 θ ,

where Fc = 1.75 150 ε 3 / 2 The list of dimensionless parameters that appeared in the above equations are Ri ( = Gr / Re 2 ) characterizes the Richardson number, Gr = g β f Δ T L 3 ν f 2 is the Grashof number, Da = K L 2 is the Darcy number, Re = U 0 L ν f describes the Reynolds number, and Pr = ν α f is the Prandtl number.

The proposed boundary constraints are [4,19]:

(5) τ = 0 : U = V = 0 , θ = 0 , X , Y ∈ [ 0 , 1 ] τ > 0 : U = V = 0 , θ = 1 , X = 0 , Y ∈ [ 0 , 1 ] , U = 0 , V = 0 , θ = 0 , X = 1 , Y ∈ [ 0 , 1 ] , U = 1 , V = 0 , ∂ θ ∂ Y = 0 , X ∈ [ 0 , 1 ] , Y = 1 , U = λ , V = 0 , ∂ θ ∂ Y = 0 , X ∈ [ 0 , 1 ] , Y = 0 .

At the block surface,

(6) U = 0 , V = 0 , θ = 0.5 .

The mathematical form of the transport units of the nanofluids are [4,17]

(7) ρ nf ρ f = ( 1 − ϕ ) + ϕ ρ p ρ f , α nf = k ρ c p nf , k nf k f = k p ( 1 + 2 ϕ ) + 2 k f ( 1 − ϕ ) k p ( 1 − ϕ ) + k f ( 2 + ϕ ) ( ρ c p ) nf ( ρ c p ) f = ( 1 − ϕ ) + ϕ ( ρ c p ) p ( ρ c p ) f , ( ρ β ) nf ( ρ β ) f = ( 1 − ϕ ) + ϕ ( ρ β ) p ( ρ β ) f .

In the above equation, ρ c p , ρ nf , β nf , k nf , and α nf denote heat capacity, nanofluid density, thermal expansion, thermal conductivity, and thermal diffusivity. Also, f stands for fluid in the subscripts, p denotes the nanoparticles in the subscripts, and ϕ denotes the nanoparticles volume fraction (Table 1).

Table 1

Thermo-physical characteristics of base fluid and nanoparticles [18]

Physical attributes Water Cu
β (1/K) 21 × 10−5 1.67 × 10−5
k (W/m K) 0.613 401
ρ (kg/m3) 997.1 8,933
c p (J/kg K) 4,179 385

2.1 Nusselt number

Mathematically, the Nusselt number for the present flow problem is defined as [4,17]

(8) Nu = − k nf k f ∂ θ ∂ X .

The mathematical expression for the average Nu in the flow of liquid layer adjacent to the hot surface of wall is addressed as [4,17].

(9) Nu ¯ = ∫ 0 1 Nud Y | X = 0 .

3 Scheme procedure, grid independent test and code validation

The finite volume method is utilized to discretize the transport partial differential equations and their boundary condition. However, resolving the momentum equations (ME) is difficult due to their non-linearity and the attendance of an unknown pressure field. The pressure gradient term is included in the ME, but there is no separate equation to regulate the pressure. To tackle these challenges, the semi-implicit method for pressure linked equations algorithm, established by Patankar [20], is employed. The transient terms are handled with a fully implicit scheme, while the convection and diffusion terms are approximated using specific systems. The resultant system of algebraic equations is resolved using the Thomas algorithm with an iterative approach. This process is repeated until a converged solution is attained, with a chosen convergence criterion for the problem (Figures 2–4).

(10) Σ ∣ ϕ i , j n + 1 − ϕ i , j n ∣ Σ ∣ ϕ i , j n + 1 ∣ < 10 − 5 ,

Figure 2 The present outcomes are compared with that in the study by Mehmood et al. [4] between their present findings (bottom) and their previous work at ϕ = 0.2, Re = 100, and Ri = 0.1.
Figure 2

The present outcomes are compared with that in the study by Mehmood et al. [4] between their present findings (bottom) and their previous work at ϕ = 0.2, Re = 100, and Ri = 0.1.

Figure 3 Comparative analysis of present (bottom) with Jmai et al. [19] (top) when Ri = 1.0.
Figure 3

Comparative analysis of present (bottom) with Jmai et al. [19] (top) when Ri = 1.0.

Figure 4 For Pr = 0.71, Ri = 10−2, ε = 0.9, Da = 10−3, and N = 0, the present outcomes (bottom) is compared with that in the study by Kumar et al. [6].
Figure 4

For Pr = 0.71, Ri = 10−2, ε = 0.9, Da = 10−3, and N = 0, the present outcomes (bottom) is compared with that in the study by Kumar et al. [6].

In Eq. (10), ϕ characterizes θ , U , or V .

To select a better grid size for the present study, grid independent test was performed for different mesh sizes on the average Nusselt number for the hot wall at ϕ = 0.025, Da = 10−3 and Ri = 1.0 which is shown in Table 2. From the table, we observed that extending the grid size from 150 × 150 to 200 × 200 results in the lowest error rate for both λ = −1 and λ = 1. Therefore, to save time, the grid size 150 × 150 is fixed for all simulations in this article. To verify the accuracy of the present in house computational code, the present results are compared with the previous works of Mehmood et al. [4], Jmai et al. [19] and Kumar et al. [6] as shown in Figures 2–4 respectively. These figures qualitatively reflect the comparison results, however a quantitative comparison also being carried out and are presented in Table 3 and Table 4. In these validation, the influence of solid block, wall speed ratio, the porous effect, the mixed convection effect and the presence of nanofluid in porous medium were confronted with the previous ones, and these comparison provides the enough reliability and consistency of the present in house code used here.

Table 2

Analysis of Nu ¯ subject to grid independent approach at ϕ = 0.025, Da = 10−3, and Ri = 1.0

Grid size Nu ¯
λ = 1 Error % λ = −1 Error %
50 × 50 5.912961 3.01 7.227505 1.6
100 × 100 6.096704 0.98 7.345699 0.4
150 × 150 6.157492 0.2 7.381020 0.3
200 × 200 6.170955 7.404594

The bold value indicates that grid size 150 gives the lowest error % and is fixed for the computation of the present analysis.

Table 3

Comparative study of Nu ¯ with Mehmood et al. [4] when ϕ = 0.2 and Re = 100

Richardson number Nu ¯
Present outcomes Mehmood et al. [4] Error %
0.1 7.6998 7.6910 0.1
1.0 8.6051 8.5651 0.5
10 11.3936 11.3558 0.3
Table 4

Comparative scrutiny of Nu ¯ subject to ϕ at ε = 0.4

Ra Da ϕ |ψ| max Nu ¯
[17] Present outcomes Error % [17] Present outcomes Error %
103 10−2 0.0 0.283 0.282 0.35 1.007 1.010 0.29
0.025 0.264 0.263 0.37 1.081 1.090 0.82
0.05 0.246 0.245 0.40 1.160 1.171 0.93

4 Discussion and analysis

In this part of the research study, we have scrutinized the influence of different pertinent flow variables on the isothermal contours, average Nusselt number, and streamlines. The parameters considered are Darcy number, wall velocity ratio, Richardson number and nanoparticles volume fraction. These parameters are varied within a specified range, while other variables, i.e., porosity, Prandtl number and Reynolds number are held constant (0.6, 6.2, 100).

The physical illustration for the behavior of Richardson number and wall velocity ratio on the streamlines is depicted in Figure 5, while the remaining variables are considered constant. The increasing values of wall velocity ratio specifies that both bottom and top walls in the same direct direction, demonstrating conflicting shear and buoyancy forces. When Ri = 0.01, then flow is caused by only forced convection phenomenon, as a result two circular cell formation is obtained. The clockwise cell occupies a larger portion of the cavity than the anticlockwise cell. As the Richardson number rises from 0.01 to 100, the buoyancy force gains more influence compared to the shear force, resulting in a gradual reduction in the size of the counterclockwise cell. Conversely, the clockwise cell expands towards the lower wall as the buoyancy force intensifies. Additionally, increasing the wall velocity ratio enhances the counterclockwise flow in the secondary cell and leads to its gradual enlargement due to increased shear force on the bottom wall.

Figure 5 Physical interpretation of steady state streamlines vs Richardson number and wall speed ratio with fixed ϕ = 0.025 and Da = 10−3.
Figure 5

Physical interpretation of steady state streamlines vs Richardson number and wall speed ratio with fixed ϕ = 0.025 and Da = 10−3.

Figure 6 displays isotherms for various Richardson numbers and wall velocity ratios. Increasing the wall velocity ratio shifts the isotherms near the cold wall towards the left wall through the block’s top surface, causing distortion near the bottom wall due to heightened shear force. A notable temperature gradient is seen near the hot vertical wall. With a higher Richardson number, isotherms tend to cluster near the active wall, indicating a dominant natural convection state. Figure 7 shows the impact of the Darcy number on streamlines, while Figure 8 depicts the effect on isotherms with a fixed Richardson number and nanoparticles volume fraction. The cavity is filled with double circulating cells near the top and bottom walls when Da = 10 − 5 , with the rest remaining stagnant, regardless of the wall velocity ratio.

Figure 6 Physical interpretation of steady state isotherms vs Richardson number and wall speed ratio with fixed ϕ = 0.025 and Da = 10−3.
Figure 6

Physical interpretation of steady state isotherms vs Richardson number and wall speed ratio with fixed ϕ = 0.025 and Da = 10−3.

Figure 7 Demonstration of steady state streamlines subject to velocity wall ratio and Darcy number when ϕ = 0.025 and Ri = 1.0.
Figure 7

Demonstration of steady state streamlines subject to velocity wall ratio and Darcy number when ϕ = 0.025 and Ri = 1.0.

Figure 8 Demonstration of isotherms subject to velocity wall ratio and Darcy number when ϕ = 0.025 and Ri = 1.
Figure 8

Demonstration of isotherms subject to velocity wall ratio and Darcy number when ϕ = 0.025 and Ri = 1.

Increasing the Darcy number in a porous medium enhances its permeability, affecting the size and movement of cells within the medium. Higher Darcy numbers result in larger clockwise cells near the bottom wall and a decrease in counterclockwise cells at higher flow rates. This effect is more pronounced at lower wall speed ratios. For moderate and high wall velocity ratios, increasing the Darcy number intensifies fluid flow, creating eddies near the top and bottom right corners of the cavity. A higher wall velocity ratio leads to a stronger shear force near the moving bottom wall, increasing the size and circulation rate of clockwise cells. The heat transfer process is also influenced by the Darcy number, with higher values indicating stronger convection due to increased buoyancy force. This effect is observed across all wall speed ratios. Additionally, as the wall velocity ratio rises, the isotherms near the bottom position distort and shift towards the top wall.

Isotherms contours and streamlines for the escalating estimations of velocity wall ratio ( λ < 0 ) is displayed in Figure 9, when ϕ = 0.025 , Da = 10−3, and Ri = 0.01. A velocity wall ratio ( λ < 0 ) indicates that the top and bottom walls are moving in opposite directions. In this case, the top wall moves steadily to the right with constant velocity ( U 0 = 1 ) , while the bottom wall moves erratically to the left with a variable velocity ( U 0 = − λ ) . In this scenario, a negative λ value indicates that shear and buoyancy forces are working together. When λ = 0.5 , the entire cavity is filled with a single clockwise cell containing multiple structures, resulting in eddies forming near the top and bottom walls. The figure shows that the eddies near the top wall are more concentrated and powerful compared to those near the bottom wall, with the dominant velocity at the top wall being ( U t = 1 ) and at the bottom wall being U b = − 0.5 . As the bottom wall velocity increases towards the left, the eddies near the bottom wall gradually reinforce in both flow rate and size.

Figure 9 Physical interpretation of steady state streamlines and isotherms subject to wall velocity ratio when ϕ = 0.025, Ri = 0.01, and Da = 10−3.
Figure 9

Physical interpretation of steady state streamlines and isotherms subject to wall velocity ratio when ϕ = 0.025, Ri = 0.01, and Da = 10−3.

For a low wall velocity ratio, the distribution of isotherms in the cavity can be observed. Isotherms near the hot wall move right, while those near the cold wall move left due to the opposite motion of the horizontal walls. These isotherms generally follow the path of the bottom wall, and they are more spread out near the bottom wall compared to the top wall. This difference is due to the stronger shear force experienced at the top wall. As the wall velocity ratio increases, leading to higher shear force along the bottom wall, the distribution of isotherms near the bottom wall becomes distorted, as anticipated.

Figure 10 is sketched for both vertical as well as horizontal velocity distributions for the rising estimations of Ri when λ = 1 , Da = 10−3, and ϕ = 0.025 . The velocities of forced and mixed convection regions ( Ri = 0.01 , 1.0 ) , are almost same at the mid-section of the cavity. Nevertheless, the natural convection with a dominant Richardson number of 100 results in the highest velocity at the center plane when compared to Richardson numbers of 0.01 and 1.0. Figure 11 highlights the interpretation of mid-height velocity components for both horizontal and vertical direction for rising values of Darcy number. As the Da values increase, the speed observed also increases, as depicted in Figure 11. The velocity remains relatively constant for Da = 10 − 5 & 10 − 4 in the mid-plane of the cavity. Furthermore, the velocities remain constant at the core for all Da, which is attributed to the solid block’s presence (Tables 2 and 3).

Figure 10 Vertical velocity and mid-height vertical and horizontal velocity profiles subject to Ri when Da = 10−3, ϕ = 0.025, and λ = 1.
Figure 10

Vertical velocity and mid-height vertical and horizontal velocity profiles subject to Ri when Da = 10−3, ϕ = 0.025, and λ = 1.

Figure 11 Vertical velocity and mid-height horizontal velocity against Darcy number when ϕ = 0.025, Ri = 1.0, and λ = 1.
Figure 11

Vertical velocity and mid-height horizontal velocity against Darcy number when ϕ = 0.025, Ri = 1.0, and λ = 1.

Figure 12 illustrates the fields of mid-height velocity components for various wall velocity ratios in both horizontal and vertical directions. The horizontal velocities display an upsurge with higher wall speed ratios. Meanwhile, the V-velocity fields show two separate patterns at the mid-plane of the cavity. On the left side, a low wall speed ratio outcomes in higher V-velocity magnitude, while on the right side, a high wall speed ratio leads to maximum velocity due to augmented shear forces in that direction. In Figure 13(a) and (b), the time history of the average Nusselt number for various Richardson (Ri) and Darcy (Da) numbers is presented. Initially, the average Nusselt number is high and gradually declines over time until reaching a steady state. It is observed that the region dominated by forced convection (Ri = 0.01) and the region dominated by conduction Da = 10 − 5 take the longest time to reach steady state solutions.

Figure 12 Vertical velocity and mid-height horizontal velocity against wall velocity ratio when ϕ = 0.025, Ri = 1.0, and Da = 10−3.
Figure 12

Vertical velocity and mid-height horizontal velocity against wall velocity ratio when ϕ = 0.025, Ri = 1.0, and Da = 10−3.

Figure 13 The time history of average Nusselt number for (a) different Ri with fixed Da = 10−3, ϕ = 0.025 (b) different Da with fixed Ri = 1.0, ϕ = 0.025.
Figure 13

The time history of average Nusselt number for (a) different Ri with fixed Da = 10−3, ϕ = 0.025 (b) different Da with fixed Ri = 1.0, ϕ = 0.025.

Tables 5 and 6 display the dissimilarity average Nusselt number for increasing estimations of Ri , λ , and ϕ when Da = 10 − 3 . From the definition of Richardson number ( Ri = Gr Re 2 ) , we can say that the increase in Ri leads to an augmentation of Gr since Re is fixed and thus enhances the natural convection. For this reason, the heat transport rate upsurges with the increase in the Richardson number. The observation confirmed the augmented rate of heat transport due to the enrichment of the base liquid with Cu nanoparticles. In addition, for all the values of Ri, increasing wall speed ratio either in same direction or opposite direction the heat transport rate is augmented. At high Ri and solid volume fraction ( Ri = 100 , ϕ = 0.05 ) , the significance of heat transport rate is augmented by 6% only with the upsurge of − λ from 0.5 to 1.5; however, there was a 29% increase in the rate of heat transfer when the Richardson number was low ( Ri = 0.01 ) . Similarly, the heat transport rate amplified by only 5% with the upsurge of λ from 0.5 to 1.5 at high Ri , ϕ whereas the rate of heat transfer increases by 28% when the Richardson number is low ( Ri = 0.01 ) . This clearly shows that as the value of λ increases, the forced convection region produces the highest heat transfer rate.

Table 5

Examination of Nu ¯ subject to Richardson number, wall speed ratio ( λ < 0 ) , and ϕ at Da = 10−3

Richardson number Nanoparticles volume fraction Nu ¯
λ
−0.5 −1 −1.5
0.01 0 5.919057 6.947259 7.654598
0.025 6.065295 7.180177 7.947156
0.05 6.206901 7.407756 8.234361
1.0 0 6.214299 7.148318 7.812973
0.025 6.357829 7.381020 8.104932
0.05 6.494800 7.608253 8.392443
100 0 13.38110 13.77049 14.09873
0.025 13.68186 14.10407 14.45983
0.05 13.96672 14.42297 14.80826
Table 6

Examination of Nu ¯ vs Richardson number, wall speed ratio ( λ < 0 ) and ϕ at Da = 10−3

Richardson number Nanoparticles volume fraction Nu ¯
λ
0.5 1 1.5
0.01 0 5.196048 5.978574 6.636054
0.025 5.284909 6.129442 6.797601
0.05 5.371582 6.227012 6.960791
1.0 0 5.376878 6.011653 6.544033
0.025 5.446927 6.157492 6.714101
0.05 5.515021 6.300520 6.884848
100 0 12.71778 13.12886 13.40783
0.025 12.95839 13.37671 13.69086
0.05 13.18089 13.60192 13.95060

Tables 7 and 8 are sketched to determine how some variables, i.e., Da, λ , and ϕ influence the Nusselt number when Ri is constant. Looking at the figures, a better heat flow (Nusselt number or heat transfer coefficient) can be seen if Da, ϕ , and | λ | are assigned larger values. Examination of the tables shows a better heat transfer rates for negative λ values compared to positive λ values. This result shows that the opposite moving walls generate the effective cooling system than the same direction of moving walls. In addition to that the increasing percentage of heat transport rate is sufficiently large by upsurge of wall speed ratio than the rising of solid volume fraction. At the moderate value of Da (10−4), the heat transport rate is improved by 46% with the enhancement of | λ | from 0.5 to 1.5 than the remaining values of Da ( 10 − 5 , 10 − 3 ) . At higher Darcy number ( Da = 10 − 3 ) and low wall velocity ratio λ = 0.5 ( − 0.5 ) , the heat transport rate is enhanced by only 3% (4%) with the enhancement of nanoparticles concentration from 0 to 0.05 whereas it is increased to about 9% (8%) at low ( Da = 10 − 5 ) . However, the opposite behavior was found at high wall velocity ratio λ = 1.5 ( − 1.5 ) . This indicates that the influence of nanoparticle concentration is more efficient in the conduction conquered region ( Da = 10 − 5 ) when low value of wall velocity is very low, whereas the convection conquered region ( Da = 10 − 3 ) is more efficient for high value of wall velocity ratio.

Table 7

Examination of Nu ¯ vs Darcy number, wall speed ratio ( λ < 0 ) and ϕ at Ri = 1.0

Darcy number Nanoparticles volume fraction Nu ¯
λ
−0.5 −1 −1.5
10−5 0 1.880017 2.101634 2.363503
0.025 1.947787 2.161028 2.415158
0.05 2.021530 2.226617 2.473001
10−4 0 3.612986 4.512475 5.260185
0.025 3.649016 4.561086 5.338616
0.05 3.687500 4.608705 5.412831
10−3 0 6.214299 7.148318 7.812973
0.025 6.357829 7.381020 8.104932
0.05 6.494800 7.608253 8.392443
Table 8

Examination of Nu ¯ vs Da, wall speed ratio ( λ < 0 ) and ϕ at Ri = 1.0

Darcy number ϕ Nu ¯
λ
0.5 1 1.5
10−5 0 1.732055 1.841868 2.007792
0.025 1.802991 1.903395 2.059767
0.05 1.880220 1.971709 2.119037
10−4 0 3.133966 3.852411 4.444283
0.025 3.154937 3.862300 4.464971
0.05 3.181067 3.874341 4.484497
10−3 0 5.376878 6.011653 6.544033
0.025 5.446927 6.157492 6.714101
0.05 5.515021 6.300520 6.884848

5 Final remarks

In this research attempt, we have investigated the issue of mixed convective heat transport of nanofluids in a permeable cavity with an isothermal solid block, using numerical analysis. We have varied the wall speed ratio and concluded the following findings from our research:

  • The non-dimensional parameters, i.e., Ri, Da, and λ have a significant impact on both the flow and thermal fields.

  • The heat transport rate is enhanced for the higher values of Ri, Da, φ, and |λ|.

  • A faster rate of heat transport is noticed when the wall velocity ratio λ < 0 compared to λ > 0. This indicates that supremum heat transport occurs when the lids move in opposite directions rather than in the same direction.

  • At high Ri = 100 and ϕ = 0.05, the heat transport rate enhanced by only 6% (5%) when the parameter −λ (λ) was increased from 0.5 to 1.5. In contrast, at Ri = 0.01, the heat transport rate enhanced by 29% (28%).

  • At higher (Da = 10−3) and low wall velocity ratio λ = 0.5(−0.5), the heat transfer rate increased by only 3% (4%) when the nanoparticle concentration was increased from 0 to 0.05. However, at lower (Da = 10−5), the heat transport rate enhanced by approximately 9% (8%).

  • After taking into account all the elements that improve the transfer of heat, it was determined that the best rate of heat transfer in the existing system is attained with the specific combination of parameters (Ri, Da, φ, and |λ|) = (100, 10−3, 0.05, and 1.5).

  • For future research, it is recommended to inspect the consequence of a magnetic field on heat transport, as well as study the inspiration of the location and size of the isothermal solid block.

Acknowledgments

Researchers Supporting Project number (RSPD2024R576), King Saud University, Riyadh, Saudi Arabia.

  1. Funding information: Researchers Supporting Project number (RSPD2024R576), King Saud University, Riyadh, Saudi Arabia.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Conflict of interest: The authors state no conflict of interest.

References

[1] Javed T, Siddiqui MA. Effect of MHD on heat transfer through ferrofluid inside a square cavity containing obstacle/heat source. Int J Therm Sci. 2018;125:419–27.10.1016/j.ijthermalsci.2017.12.009Search in Google Scholar

[2] Sun H, Chnier E, Lauriat G. Effect of surface radiation on the breakdown of steady natural convectionflows in a square, air-filled cavity containing a centered inner body. Appl Therm Eng. 2011;31:1252–62.10.1016/j.applthermaleng.2010.12.028Search in Google Scholar

[3] Kalidasan K, Velkennedy R, RajeshKanna P. Laminar natural convection of Copper - Titania/Water hybrid nanofluid in an open ended C-shaped enclosure with an isothermal block. J Mol Liq. 2017;246:251–8.10.1016/j.molliq.2017.09.071Search in Google Scholar

[4] Mehmood K, Hussain S, Sagheer M. Mixed convection in alumina-water nanofluid filled lid-driven square cavity with an isothermally heated square blockage inside with magnetic field effect: Introduction. Int J Heat Mass Transf. 2017;109:397–409.10.1016/j.ijheatmasstransfer.2017.01.117Search in Google Scholar

[5] Haq RU, Soomro FA, Hammouch Z. Heat transfer analysis of CuO-water enclosed in a partially heated rhombus with heated square obstacle. Int J Heat Mass Transf. 2018;118:773–84.10.1016/j.ijheatmasstransfer.2017.11.043Search in Google Scholar

[6] Kumar DS, Dass AK, Dewan A. Analysis of non-Darcy models for mixed convection in a porous cavity using multigrid approach. Numer Heat Transf Part A. 2009;56:685–708.10.1080/10407780903424674Search in Google Scholar

[7] Sivasankaran S, Pan KL. Numerical simulation on mixed convection in a porous lid-driven cavity with nonuniform heating on both side walls. Numer Heat Transf Part A. 2012;61:101–21.10.1080/10407782.2011.643741Search in Google Scholar

[8] Moria H. Natural convection in an L-shape cavity equipped with heating blocks and porous layers. Int Commun Heat Mass Transf. 2021;126:105375.10.1016/j.icheatmasstransfer.2021.105375Search in Google Scholar

[9] Colak E, Ekici O, Oztop HF. Mixed convection in a lid-driven cavity with partially heated porous block. Int Commun Heat Mass Transf. 2021;126:105450.10.1016/j.icheatmasstransfer.2021.105450Search in Google Scholar

[10] Fu Y, Bian B, Liu Y, Zhang L, Li M, Wen J, et al. Airside heat transfer analysis using Wilson plot method of three analogous serpentine tube heat exchangers for aero-engine cooling. Appl Therm Eng. 2024;248:123238.10.1016/j.applthermaleng.2024.123238Search in Google Scholar

[11] Xiao D, Xiao H, Song W, Li G, Zhang J, Deng H, et al. Utilization method of low-grade thermal energy during drilling based on insulated drill pipe. Renew Energy. 2024;225:120363.10.1016/j.renene.2024.120363Search in Google Scholar

[12] Hou Y, Cheng M, Sheng Z, Wang J. Unsteady conjugate heat transfer simulation of wall heat loads for rotating detonation combustor. Int J Heat Mass Transf. 2024;221:125081.10.1016/j.ijheatmasstransfer.2023.125081Search in Google Scholar

[13] Begum AS, Nithyadevi N, Oztop HF, Al-Salem K. Numerical simulation of MHD mixed convection in a nanofluid filled non-Darcy porous enclosure. Int J Mech Sci. 2017;130:154–66.10.1016/j.ijmecsci.2017.06.008Search in Google Scholar

[14] Hussain S, Mehmooda K, Sagheera M, Farooqa A. Entropy generation analysis of mixed convective flow in an inclined channel with cavity with Al2O3-water nanofluid in porous medium. Int Commun Heat Mass Transf. 2017;89:1054–66.10.1016/j.icheatmasstransfer.2017.10.009Search in Google Scholar

[15] Nithyadevi N, Begum AS, Oztop HF, Abu-Hamdeh N. Mixed convection analysis in heat transfer enhancement of a nanofluid filled porous enclosure with various wall speed ratios. Int J Heat Mass Transf. 2017;113:716–29.10.1016/j.ijheatmasstransfer.2017.05.134Search in Google Scholar

[16] Alomari MA, Al-Farhany K, Al-Salami QH, Al-Jaburi K, Alyousuf FQA, Ali IR, et al. Magnetohydrodynamic mixed convection in lid-driven curvilinear enclosure with nanofluid and partial porous layer. J Magn Magn Mater. 2023;582:170952.10.1016/j.jmmm.2023.170952Search in Google Scholar

[17] Long X, Chong K, Su Y, Du L, Zhang G. Connecting the macroscopic and mesoscopic properties of sintered silver nanoparticles by crystal plasticity finite element method. Eng Fract Mech. 2023;281:109137.10.1016/j.engfracmech.2023.109137Search in Google Scholar

[18] Nguyen MT, Aly AM, Lee SW. Natural convection in a non-Darcy porous cavity filled with Cu-water nanofluid using the characteristic-based split procedure in finite element method. Numer Heat Transf Part A. 2015;67:224–47.10.1080/10407782.2014.923225Search in Google Scholar

[19] Jmai R, Ben-Beya B, Lili T. Numerical analysis of mixed convection at various wall speed ratios in two sided lid-driven cavity partially heated and filled with nanofluid. J Mol Liq. 2016;221:691–713.10.1016/j.molliq.2016.05.076Search in Google Scholar

[20] Patankar SV. Numerical heat transfer and fluid flow. Washington: Hemisphere Publishing Corporation; 1980.Search in Google Scholar
Received: 2023-08-22
Revised: 2023-10-06
Accepted: 2024-03-07
Published Online: 2024-07-08

© 2024 the author(s), published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

  1. Regular Articles
  2. Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
  3. Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
  4. High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
  5. Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
  6. Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
  7. Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
  8. The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
  9. Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
  10. A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
  11. Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
  12. Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
  13. Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
  14. Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
  15. Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
  16. Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
  17. Chaotic control problem of BEC system based on Hartree–Fock mean field theory
  18. Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
  19. Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
  20. Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
  21. Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
  22. Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
  23. Model of conversion of flow from confined to unconfined aquifers with stochastic approach
  24. Study of fractional variable-order lymphatic filariasis infection model
  25. Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
  26. Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
  27. Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
  28. Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
  29. Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
  30. Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
  31. Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
  32. A two-stage framework for predicting the remaining useful life of bearings
  33. Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
  34. Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
  35. Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
  36. In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
  37. Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
  38. Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
  39. A comparative analysis of shielding effectiveness in glass and concrete containers
  40. Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
  41. Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
  42. Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
  43. Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
  44. Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
  45. Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
  49. Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
  55. Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
  56. An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
  57. CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
  58. Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
  59. A short report on a probability-based interpretation of quantum mechanics
  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
  62. Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
  64. A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
  65. Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
  66. Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
  67. Thermal analysis of extended surfaces using deep neural networks
  68. Steady-state thermodynamic process in multilayered heterogeneous cylinder
  69. Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
  70. Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
  71. Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
  72. The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
  74. Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
  77. Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
  79. Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
  81. New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
  82. Physical aspects of quantile residual lifetime sequence
  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
  91. New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
  93. Inflation and the principle of equivalence
  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
  97. Photon balance in the fiber laser model
  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
https://doi.org/10.1515/phys-2024-0003
Keywords for this article
porous cavity; nanofluid mixed convection; isothermal block; wall velocity ratio
Creative Commons
BY 4.0

Articles in the same Issue

  1. Regular Articles
  2. Numerical study of flow and heat transfer in the channel of panel-type radiator with semi-detached inclined trapezoidal wing vortex generators
  3. Homogeneous–heterogeneous reactions in the colloidal investigation of Casson fluid
  4. High-speed mid-infrared Mach–Zehnder electro-optical modulators in lithium niobate thin film on sapphire
  5. Numerical analysis of dengue transmission model using Caputo–Fabrizio fractional derivative
  6. Mononuclear nanofluids undergoing convective heating across a stretching sheet and undergoing MHD flow in three dimensions: Potential industrial applications
  7. Heat transfer characteristics of cobalt ferrite nanoparticles scattered in sodium alginate-based non-Newtonian nanofluid over a stretching/shrinking horizontal plane surface
  8. The electrically conducting water-based nanofluid flow containing titanium and aluminum alloys over a rotating disk surface with nonlinear thermal radiation: A numerical analysis
  9. Growth, characterization, and anti-bacterial activity of l-methionine supplemented with sulphamic acid single crystals
  10. A numerical analysis of the blood-based Casson hybrid nanofluid flow past a convectively heated surface embedded in a porous medium
  11. Optoelectronic–thermomagnetic effect of a microelongated non-local rotating semiconductor heated by pulsed laser with varying thermal conductivity
  12. Thermal proficiency of magnetized and radiative cross-ternary hybrid nanofluid flow induced by a vertical cylinder
  13. Enhanced heat transfer and fluid motion in 3D nanofluid with anisotropic slip and magnetic field
  14. Numerical analysis of thermophoretic particle deposition on 3D Casson nanofluid: Artificial neural networks-based Levenberg–Marquardt algorithm
  15. Analyzing fuzzy fractional Degasperis–Procesi and Camassa–Holm equations with the Atangana–Baleanu operator
  16. Bayesian estimation of equipment reliability with normal-type life distribution based on multiple batch tests
  17. Chaotic control problem of BEC system based on Hartree–Fock mean field theory
  18. Optimized framework numerical solution for swirling hybrid nanofluid flow with silver/gold nanoparticles on a stretching cylinder with heat source/sink and reactive agents
  19. Stability analysis and numerical results for some schemes discretising 2D nonconstant coefficient advection–diffusion equations
  20. Convective flow of a magnetohydrodynamic second-grade fluid past a stretching surface with Cattaneo–Christov heat and mass flux model
  21. Analysis of the heat transfer enhancement in water-based micropolar hybrid nanofluid flow over a vertical flat surface
  22. Microscopic seepage simulation of gas and water in shale pores and slits based on VOF
  23. Model of conversion of flow from confined to unconfined aquifers with stochastic approach
  24. Study of fractional variable-order lymphatic filariasis infection model
  25. Soliton, quasi-soliton, and their interaction solutions of a nonlinear (2 + 1)-dimensional ZK–mZK–BBM equation for gravity waves
  26. Application of conserved quantities using the formal Lagrangian of a nonlinear integro partial differential equation through optimal system of one-dimensional subalgebras in physics and engineering
  27. Nonlinear fractional-order differential equations: New closed-form traveling-wave solutions
  28. Sixth-kind Chebyshev polynomials technique to numerically treat the dissipative viscoelastic fluid flow in the rheology of Cattaneo–Christov model
  29. Some transforms, Riemann–Liouville fractional operators, and applications of newly extended M–L (p, s, k) function
  30. Magnetohydrodynamic water-based hybrid nanofluid flow comprising diamond and copper nanoparticles on a stretching sheet with slips constraints
  31. Super-resolution reconstruction method of the optical synthetic aperture image using generative adversarial network
  32. A two-stage framework for predicting the remaining useful life of bearings
  33. Influence of variable fluid properties on mixed convective Darcy–Forchheimer flow relation over a surface with Soret and Dufour spectacle
  34. Inclined surface mixed convection flow of viscous fluid with porous medium and Soret effects
  35. Exact solutions to vorticity of the fractional nonuniform Poiseuille flows
  36. In silico modified UV spectrophotometric approaches to resolve overlapped spectra for quality control of rosuvastatin and teneligliptin formulation
  37. Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems
  38. Substituent effect on the electronic and optical properties of newly designed pyrrole derivatives using density functional theory
  39. A comparative analysis of shielding effectiveness in glass and concrete containers
  40. Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation
  41. Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena
  42. Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials
  43. Analysis of nonlinear fractional-order Fisher equation using two reliable techniques
  44. Comparison of plan quality and robustness using VMAT and IMRT for breast cancer
  45. Radiative nanofluid flow over a slender stretching Riga plate under the impact of exponential heat source/sink
  46. Numerical investigation of acoustic streaming vortices in cylindrical tube arrays
  47. Numerical study of blood-based MHD tangent hyperbolic hybrid nanofluid flow over a permeable stretching sheet with variable thermal conductivity and cross-diffusion
  48. Fractional view analytical analysis of generalized regularized long wave equation
  49. Dynamic simulation of non-Newtonian boundary layer flow: An enhanced exponential time integrator approach with spatially and temporally variable heat sources
  50. Inclined magnetized infinite shear rate viscosity of non-Newtonian tetra hybrid nanofluid in stenosed artery with non-uniform heat sink/source
  51. Estimation of monotone α-quantile of past lifetime function with application
  52. Numerical simulation for the slip impacts on the radiative nanofluid flow over a stretched surface with nonuniform heat generation and viscous dissipation
  53. Study of fractional telegraph equation via Shehu homotopy perturbation method
  54. An investigation into the impact of thermal radiation and chemical reactions on the flow through porous media of a Casson hybrid nanofluid including unstable mixed convection with stretched sheet in the presence of thermophoresis and Brownian motion
  55. Establishing breather and N-soliton solutions for conformable Klein–Gordon equation
  56. An electro-optic half subtractor from a silicon-based hybrid surface plasmon polariton waveguide
  57. CFD analysis of particle shape and Reynolds number on heat transfer characteristics of nanofluid in heated tube
  58. Abundant exact traveling wave solutions and modulation instability analysis to the generalized Hirota–Satsuma–Ito equation
  59. A short report on a probability-based interpretation of quantum mechanics
  60. Study on cavitation and pulsation characteristics of a novel rotor-radial groove hydrodynamic cavitation reactor
  61. Optimizing heat transport in a permeable cavity with an isothermal solid block: Influence of nanoparticles volume fraction and wall velocity ratio
  62. Linear instability of the vertical throughflow in a porous layer saturated by a power-law fluid with variable gravity effect
  63. Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity
  64. A new benchmark for camouflaged object detection: RGB-D camouflaged object detection dataset
  65. Effect of electron temperature and concentration on production of hydroxyl radical and nitric oxide in atmospheric pressure low-temperature helium plasma jet: Swarm analysis and global model investigation
  66. Double diffusion convection of Maxwell–Cattaneo fluids in a vertical slot
  67. Thermal analysis of extended surfaces using deep neural networks
  68. Steady-state thermodynamic process in multilayered heterogeneous cylinder
  69. Multiresponse optimisation and process capability analysis of chemical vapour jet machining for the acrylonitrile butadiene styrene polymer: Unveiling the morphology
  70. Modeling monkeypox virus transmission: Stability analysis and comparison of analytical techniques
  71. Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain
  72. The chaotic behavior and traveling wave solutions of the conformable extended Korteweg–de-Vries model
  73. Research on optimization of combustor liner structure based on arc-shaped slot hole
  74. Construction of M-shaped solitons for a modified regularized long-wave equation via Hirota's bilinear method
  75. Effectiveness of microwave ablation using two simultaneous antennas for liver malignancy treatment
  76. Discussion on optical solitons, sensitivity and qualitative analysis to a fractional model of ion sound and Langmuir waves with Atangana Baleanu derivatives
  77. Reliability of two-dimensional steady magnetized Jeffery fluid over shrinking sheet with chemical effect
  78. Generalized model of thermoelasticity associated with fractional time-derivative operators and its applications to non-simple elastic materials
  79. Migration of two rigid spheres translating within an infinite couple stress fluid under the impact of magnetic field
  80. A comparative investigation of neutron and gamma radiation interaction properties of zircaloy-2 and zircaloy-4 with consideration of mechanical properties
  81. New optical stochastic solutions for the Schrödinger equation with multiplicative Wiener process/random variable coefficients using two different methods
  82. Physical aspects of quantile residual lifetime sequence
  83. Synthesis, structure, I–V characteristics, and optical properties of chromium oxide thin films for optoelectronic applications
  84. Smart mathematically filtered UV spectroscopic methods for quality assurance of rosuvastatin and valsartan from formulation
  85. A novel investigation into time-fractional multi-dimensional Navier–Stokes equations within Aboodh transform
  86. Homotopic dynamic solution of hydrodynamic nonlinear natural convection containing superhydrophobicity and isothermally heated parallel plate with hybrid nanoparticles
  87. A novel tetra hybrid bio-nanofluid model with stenosed artery
  88. Propagation of traveling wave solution of the strain wave equation in microcrystalline materials
  89. Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method
  90. A new investigation of the extended Sakovich equation for abundant soliton solution in industrial engineering via two efficient techniques
  91. New soliton solutions of the conformable time fractional Drinfel'd–Sokolov–Wilson equation based on the complete discriminant system method
  92. Irradiation of hydrophilic acrylic intraocular lenses by a 365 nm UV lamp
  93. Inflation and the principle of equivalence
  94. The use of a supercontinuum light source for the characterization of passive fiber optic components
  95. Optical solitons to the fractional Kundu–Mukherjee–Naskar equation with time-dependent coefficients
  96. A promising photocathode for green hydrogen generation from sanitation water without external sacrificing agent: silver-silver oxide/poly(1H-pyrrole) dendritic nanocomposite seeded on poly-1H pyrrole film
  97. Photon balance in the fiber laser model
  98. Propagation of optical spatial solitons in nematic liquid crystals with quadruple power law of nonlinearity appears in fluid mechanics
  99. Theoretical investigation and sensitivity analysis of non-Newtonian fluid during roll coating process by response surface methodology
  100. Utilizing slip conditions on transport phenomena of heat energy with dust and tiny nanoparticles over a wedge
  101. Bismuthyl chloride/poly(m-toluidine) nanocomposite seeded on poly-1H pyrrole: Photocathode for green hydrogen generation
  102. Infrared thermography based fault diagnosis of diesel engines using convolutional neural network and image enhancement
  103. On some solitary wave solutions of the Estevez--Mansfield--Clarkson equation with conformable fractional derivatives in time
  104. Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres
  105. Review Article
  106. Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey
  107. Special Issue on Predicting pattern alterations in nature - Part II
  108. A comparative study of Bagley–Torvik equation under nonsingular kernel derivatives using Weeks method
  109. On the existence and numerical simulation of Cholera epidemic model
  110. Numerical solutions of generalized Atangana–Baleanu time-fractional FitzHugh–Nagumo equation using cubic B-spline functions
  111. Dynamic properties of the multimalware attacks in wireless sensor networks: Fractional derivative analysis of wireless sensor networks
  112. Prediction of COVID-19 spread with models in different patterns: A case study of Russia
  113. Study of chronic myeloid leukemia with T-cell under fractal-fractional order model
  114. Accumulation process in the environment for a generalized mass transport system
  115. Analysis of a generalized proportional fractional stochastic differential equation incorporating Carathéodory's approximation and applications
  116. Special Issue on Nanomaterial utilization and structural optimization - Part II
  117. Numerical study on flow and heat transfer performance of a spiral-wound heat exchanger for natural gas
  118. Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt
  119. Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger
  120. Improving heat transfer efficiency via optimization and sensitivity assessment in hybrid nanofluid flow with variable magnetism using the Yamada–Ota model
  121. Special Issue on Nanofluids: Synthesis, Characterization, and Applications
  122. Exact solutions of a class of generalized nanofluidic models
  123. Stability enhancement of Al2O3, ZnO, and TiO2 binary nanofluids for heat transfer applications
  124. Thermal transport energy performance on tangent hyperbolic hybrid nanofluids and their implementation in concentrated solar aircraft wings
  125. Studying nonlinear vibration analysis of nanoelectro-mechanical resonators via analytical computational method
  126. Numerical analysis of non-linear radiative Casson fluids containing CNTs having length and radius over permeable moving plate
  127. Two-phase numerical simulation of thermal and solutal transport exploration of a non-Newtonian nanomaterial flow past a stretching surface with chemical reaction
  128. Natural convection and flow patterns of Cu–water nanofluids in hexagonal cavity: A novel thermal case study
  129. Solitonic solutions and study of nonlinear wave dynamics in a Murnaghan hyperelastic circular pipe
  130. Comparative study of couple stress fluid flow using OHAM and NIM
  131. Utilization of OHAM to investigate entropy generation with a temperature-dependent thermal conductivity model in hybrid nanofluid using the radiation phenomenon
  132. Slip effects on magnetized radiatively hybridized ferrofluid flow with acute magnetic force over shrinking/stretching surface
  133. Significance of 3D rectangular closed domain filled with charged particles and nanoparticles engaging finite element methodology
  134. Robustness and dynamical features of fractional difference spacecraft model with Mittag–Leffler stability
  135. Characterizing magnetohydrodynamic effects on developed nanofluid flow in an obstructed vertical duct under constant pressure gradient
  136. Study on dynamic and static tensile and puncture-resistant mechanical properties of impregnated STF multi-dimensional structure Kevlar fiber reinforced composites
  137. Thermosolutal Marangoni convective flow of MHD tangent hyperbolic hybrid nanofluids with elastic deformation and heat source
  138. Investigation of convective heat transport in a Carreau hybrid nanofluid between two stretchable rotatory disks
  139. Single-channel cooling system design by using perforated porous insert and modeling with POD for double conductive panel
  140. Special Issue on Fundamental Physics from Atoms to Cosmos - Part I
  141. Pulsed excitation of a quantum oscillator: A model accounting for damping
  142. Review of recent analytical advances in the spectroscopy of hydrogenic lines in plasmas
  143. Heavy mesons mass spectroscopy under a spin-dependent Cornell potential within the framework of the spinless Salpeter equation
  144. Coherent manipulation of bright and dark solitons of reflection and transmission pulses through sodium atomic medium
  145. Effect of the gravitational field strength on the rate of chemical reactions
  146. The kinetic relativity theory – hiding in plain sight
  147. Special Issue on Advanced Energy Materials - Part III
  148. Eco-friendly graphitic carbon nitride–poly(1H pyrrole) nanocomposite: A photocathode for green hydrogen production, paving the way for commercial applications
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 7.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/phys-2024-0003/html
Scroll to top button