Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity

Mowffaq Oreijah; Sami Ullah Khan; Muhammad Ijaz Khan; Sarah A. Alsalhi; Faris Alqurashi; Mohamed Kchaou

doi:10.1515/phys-2024-0042

Article Open Access

Thermal analysis of generalized Cattaneo–Christov theories in Burgers nanofluid in the presence of thermo-diffusion effects and variable thermal conductivity

Mowffaq Oreijah , Sami Ullah Khan , Muhammad Ijaz Khan , Sarah A. Alsalhi , Faris Alqurashi and Mohamed Kchaou

Published/Copyright: July 20, 2024

Published by

Become an author with De Gruyter Brill

Submit Manuscript Author Information Explore this Subject

From the journal Open Physics Volume 22 Issue 1

Abstract

The aim of this study is to investigate the heat and mass transfer characteristics of Burgers nanofluid in the presence of thermo-diffusion effects. The analysis considers higher-order slip effects to study the transport phenomena. Additionally, the study examines the impact of thermal radiation and chemical reactions on the flow. Variable thermal conductivity assumptions are made for heat transfer analysis. The Cattaneo–Christov model, an extension of Fourier heat and mass theories, is employed for the analysis. Heat transfer evaluation is conducted using convective thermal constraints, and numerical computations are carried out using the Runge–Kutta method. The study visually represents the impact of flow parameters through graphical analysis. It is suggested that heat transfer can be significantly improved through the interaction of slip effects, and the concentration phenomenon is enhanced by the Soret number.

Keywords: heat and mass transfer; Burgers nanofluid; Cattaneo–Christov model; higher-order slip effects; variable thermal conductivity

Nomenclature

( u , v ): velocity components
T: temperature
C: concentration
T ∞: ambient temperature
C ∞: free stream concentration
T w: surface temperature
C w: surface concentration
( Ω 1 , Ω 2 ): relaxation parameters
Ω 3: retardation constant
A 1: thermal relaxation coefficient
( ρ c ) f: heat capacity
k T: thermal diffusion ratio
K ( T ): variable thermal conductivity
c s: concentration susceptibility
Θ r: Stefan–Boltzmann constant
D T: thermophoresis coefficient
k s: mean absorption coefficient
ω: ratio between nanoparticles’ thermal capacity to fluid capacity
D B: Brownian coefficient
k c: reaction coefficient
D m: molecular diffusivity
c p: specific heat
A 2: concentration relaxation coefficient
D m: molecular diffusivity
T m: mean fluid temperature
k ∞: ambient fluid conductivity
ε: thermal dependence conductivity
( α 1 , α 2 ): Deborah numbers
α 3: retardation time constant
Rd: radiation constant
Pr: Prandtl number
Nb: Brownian parameter
Nt: thermophoresis constant
δ T: thermal relaxation constant
Du: Dufour number
δ c: concentration relaxation parameter
Bi: thermal Biot number
Sc: Schmidt number
kr: chemical reaction parameter
N 1: first-order slip parameter
N 2: second-order slip parameter

1 Introduction

Recent research has shown a growing interest among scholars in the study of nanomaterials. A new avenue of advancement in heat transfer has been identified through the interaction of nanoparticles. Nanofluids, which are a combination of base fluids and metallic particles in the nano-size range, exhibit impressive thermophysical properties and high thermal conductivity. These nanofluids have found various applications in industries such as automotive, electronics cooling and heating, biomedical applications, chemical reactors, and thermal systems. Choi [1] conducted a pioneering analysis on nanofluids highlighting their novel thermal characteristics. Ge-JiLe et al. [2] recommended the analysis of nanofluids for Jeffrey fluids, considering the impact of entropy generation. Acharya [3] discussed the natural convection of nanofluids in thermally stratified flows. Bouselsal et al. [4] explored the significance of heat transfer for aluminum nanoparticles in tube flows and observed the effects in different flow geometries. Ali et al. [5] studied the influence of Lorentz force on the behavior of nanofluids in ciliated regimes. Bafakeeh et al. [6] conducted an analysis on the viscoelastic flow of nanofluid in the presence of thermos-diffusion features. Yang et al. [7] studied the melting impact on nanofluid considering the effects of Brownian motion. Ramesh et al. [8] examined the Carreau nanofluid analysis for radiated flow in microchannels. Alzahrani et al. [9] investigated the Jeffrey nanofluid with distinct thermal conductivity. Dharmaiah et al. [10] conducted a nanofluid analysis based on the Falkner–Skan flow. Jabeen et al. [11] utilized numerical simulations to study the bioconvection flow of Williamson nanofluid. Abbas et al. [12] predicted the flow in curved geometries governed by second-grade nanofluid. Mebarek-Oudina et al. [13] analyzed the flow of magneto-nanoparticles using the Buongiorno model. Mishra and Upreti [14] performed a computational analysis on nanofluid flow around an inclined cylinder considering slip effects. Pandey et al. [15] studied multiple slip features for nanoparticles containing graphene nanoparticles. Pandey and Upreti [16] focused on predicting convective heat transfer based on nanoparticle interactions. Jena et al. [17] numerically explained the effects of non-uniform heat sources on nanofluid flow. Pattnaik et al. [18] investigated the thermal capacitance of three types of nanoparticles: copper, aluminum oxide, and single-walled nanoparticles.

Non-Newtonian fluids are commonly utilized in a variety of industries such as manufacturing, industrial systems, food production, coatings, oil, and cosmetics. Viscosity plays a significant role in the behavior of different types of non-Newtonian fluids. Due to their unique properties, various classifications of these fluids have been identified. One notable class is the Burgers fluid, which demonstrates distinctive rheological behavior. The Burgers fluid displays a complex relationship between shear force and yield stress. The Burgers fluid model is capable of elucidating the rheological behavior of various viscoelastic materials such as cheese, soil, and food products [19]. Polymer liquids also exhibit similar rheological properties to Burgers fluid. The Burgers fluid model can be used to analyze retardation and relaxation times. Khan et al. [20] studied the impact of induced magnetic forces on Burgers nanofluids. Hassan and Rizwan [21] predicted the thermal behavior of the Burgers model with multi-walled carbon nanotubes. Gangadhar et al. [22] conducted a chemical reactive analysis of Burgers fluid in porous media. Fetecau et al. [23] investigated shear force fluctuations in Burgers fluid. Hejazi et al. [24] explored triple diffusion in Burgers nanofluids. Juhany et al. [25] calculated entropy production in Burgers fluid on a Riga surface. Li et al. [26] studied buoyancy-driven flow in Burgers fluid with an external heat source. Raza et al. [27] examined the role of zeta potential in Burgers fluid flow in cylindrical tubes. Zhao and Yin [28] developed a sub-grid model for turbulent flow of Burgers fluid and utilized an artificial neural network for computations. Khan et al. [29] conducted a thermal analysis of Burgers nanofluids using updated heat flux theories. Khan et al. [30] investigated Burgers nanofluids with variable thermal conductivity.

The current study aims to investigate the impact of Burgers nanofluid on heat and mass transfer phenomena in thermal and industrial systems, particularly focusing on thermo-diffusion effects and higher-order slip effects. The analysis considers the incorporation of Dufour and Soret features in nanofluid flow, which are essential in a wide range of engineered and natural systems. These thermo-diffusion effects play a crucial role in colloidal systems, environmental processes, fuel cells, thermal comfort, chromatography, and the design of efficient chemical processes. The model assumes linear thermal radiation and variable thermal conductivity, and employs the extended heat and mass flux hypothesis. Convective boundary conditions are applied to analyze the thermal outcomes, and a numerical scheme based on the Runge–Kutta (RK) method with high accuracy is utilized. The study is motivated by the potential applications of Burgers nanofluid in various industrial processes such as textile manufacturing, coating, polymers, sterilization, and chemical industries.

2 Flow description

A study was conducted on the steady transport of Burgers nanofluid over a moving surface. The flow is induced by a uniformly stretching surface maintaining a constant velocity u w ( x ) = a x , where a is the stretching coefficient. The fluid model was developed considering the following flow constraints:

A two-dimensional, steady, and incompressible flow of Burgers nanofluid was analyzed to investigate the enhanced heat and mass transfer phenomena.
Slip effects with higher-order relations were taken into account.
Heat and mass transfer analysis was conducted using the well-known Cattaneo–Christov hypothesis.
Thermo-diffusion effects were considered in the problem.
Variable assumptions regarding thermal conductivity were incorporated.

The flow problem was formulated in the Cartesian coordinate system. For the stretched surface, let u be the horizontal velocity component and v be the velocity component in the normal direction. The temperature and concentration fields are represented by T and C , respectively. The thermal flow problem is illustrated in Figure 1. Additionally, T ∞ is linked to the ambient temperature, C ∞ represents the free stream concentration, T w is the surface temperature, and C w denotes the surface concentration.

Figure 1

Flow illustration of the problem.

In view of such constraints, the problem is modeled in terms of following equations [29,30]:

(1) ∂ u ∂ x + ∂ v ∂ y = 0 ,

(2) u ∂ u ∂ x + v ∂ u ∂ y + Ω 1 u 2 ∂ 2 u ∂ x 2 + 2 u v ∂ 2 u ∂ x ∂ y + v 2 ∂ 2 u ∂ y 2 + Ω 2 u 3 ∂ 3 u ∂ x 3 + u 2 2 ∂ v ∂ x ∂ 2 u ∂ x ∂ y + ∂ u ∂ x ∂ 2 u ∂ x 2 − ∂ u ∂ y ∂ 2 v ∂ x 2 + v 3 ∂ 3 u ∂ y 3 + 3 u v u ∂ 3 u ∂ x 2 ∂ y + v ∂ 3 u ∂ y 2 ∂ x 3 v 2 ∂ v ∂ y ∂ 2 u ∂ y 2 + ∂ u ∂ y ∂ 2 u ∂ y ∂ x + 2 u v ∂ v ∂ y ∂ 2 u ∂ y ∂ x + ∂ u ∂ y ∂ 2 u ∂ x 2 − ∂ u ∂ y ∂ 2 v ∂ y ∂ x + ∂ v ∂ x ∂ 2 u ∂ y 2 = v Ω 3 u ∂ 3 u ∂ y 2 ∂ x + v ∂ 3 u ∂ y 3 − ∂ 2 u ∂ y 2 ∂ u ∂ x − ∂ u ∂ y ∂ 2 v ∂ y 2 + ∂ 2 u ∂ y 2 ,

(3) u ∂ T ∂ x + v ∂ T ∂ y + A 1 u ∂ u ∂ x ∂ T ∂ x + v ∂ v ∂ y ∂ T ∂ y + u ∂ v ∂ x ∂ T ∂ y + v ∂ u ∂ y ∂ T ∂ x + 2 u v ∂ 2 T ∂ x ∂ y + u 2 ∂ 2 T ∂ x 2 + v 2 ∂ 2 T ∂ y 2 = 1 ( ρ c ) f ∂ ∂ y K ( T ) ∂ T ∂ y + 16 T ∞ 3 Θ r 3 ( ρ c ) f k s ∂ 2 T ∂ y 2 + ω D B ∂ C ∂ y ∂ T ∂ y + D T T ∞ ∂ T ∂ y 2 + D m k T c s c p ∂ 2 C ∂ y 2 ,

(4) u ∂ C ∂ x + v ∂ C ∂ y + A 2 u ∂ u ∂ x ∂ C ∂ x + v ∂ v ∂ y ∂ C ∂ y + u ∂ v ∂ x ∂ C ∂ y + v ∂ u ∂ y ∂ C ∂ x + 2 uv ∂ 2 C ∂ x ∂ y + u 2 ∂ 2 C ∂ x 2 + v 2 ∂ 2 C ∂ y 2 = D B ∂ 2 C ∂ y 2 + D T T ∞ ∂ 2 T ∂ y 2 + D m k T T m ∂ 2 T ∂ y 2 − k c ( C − C ∞ ) .

The variable thermal conductivity K ( T ) is defined as [30]

(5) K ( T ) = k ∞ 1 + ε T − T ∞ Δ T ,

where Ω 1 and Ω 2 represent the relaxation parameters, Ω 3 denotes the retardation constant, A 1 is the thermal relaxation coefficient, ( ρ c ) f is the heat capacity, k T represents the thermal diffusion ratio, K ( T ) is the variable thermal conductivity, c s is the concentration susceptibility, Θ r is the Stefan–Boltzmann constant, D T is the thermophoresis coefficient, k s is the mean absorption coefficient, ω = ( ( ρ c ) p / ( ρ c ) f ) is the ratio between nanoparticles’ thermal capacity to fluid capacity, D B is the Brownian coefficient, k c is the reaction coefficient, D m is the molecular diffusivity, c p is the specific heat, A 2 is the concentration relaxation coefficient, T m is the mean fluid temperature, k ∞ is the ambient fluid conductivity, and ε is the thermal dependence conductivity.

The flow is prescribed by following conditions [29]:

(6) u = u w ( x ) = ax + u slip , u slip = Λ 1 ∂ u ∂ y + Λ 2 ∂ 2 u ∂ y 2 , v = 0 , − k ∂ T ∂ y = h f ( T f − T ) , C = C w , at y = 0 , u → 0 , T → T ∞ , C → C ∞ , as y → ∞ ,

where Λ 1 and Λ 2 represent the slip coefficient.

Defining the new dimensionless variables [29]:

(7) v = − a ν f ( ξ ) , u = ax f ′ ( ξ ) , θ ( ξ ) = T − T ∞ T f − T ∞ , ξ = a ν y , and ϕ ( ξ ) = C − C ∞ C w − C ∞ .

The new developed system is defined by

(8) f ‴ + f f ″ − f ′ 2 + α 1 ( 2 f f ′ f ″ − f 2 f ‴ ) + α 2 ( f 3 f ′ ‴ − 2 f f ″ f ′ 2 − 3 f 2 f ″ 2 ) + α 3 ( f ″ 2 − f f ′ ‴ ) = 0 ,

(9) ( 1 + Rd + ε θ ) θ ″ + ε ( θ ′ ) 2 + Pr [ f θ ′ + Nb θ ′ ϕ ′ + Nt ( θ ′ ) 2 ] − Pr δ T ( f f ′ θ ′ + f 2 θ ″ ) + Du ϕ ″ = 0 ,

(10) ϕ ″ + Sc f ϕ ′ + Nt Nb θ ″ − Sc ( kr ) ϕ + Sr θ ″ − δ c ( f f ′ ϕ ′ + f 2 ϕ ″ ) = 0 ,

where α 1 = Ω 1 a and α 2 = Ω 2 a are the Deborah numbers, α 3 = Ω 3 a is the retardation time constant, Rd = 16 T ∞ 3 Θ r / 3 k ∞ k s is the radiation constant, Pr = ν ( ρ c ) f / k ∞ is the Prandtl number, Nb = ω D b ( C w − C ∞ ) / ν is the Brownian parameter, Nt = ω D T ( T f − T ∞ ) / T ∞ ν is the thermophoresis constant, δ T = A 1 a is the thermal relaxation constant, Du = D m k T ( C w − C ∞ ) / c s c p ν ( T w − T ∞ ) is the Dufour number, δ c = A 2 a is the concentration relaxation parameter, Bi = ( h f / k ) ν / a is the thermal Biot number, Sc = ν / D B is the Schmidt number, and kr = k c / a is the chemical reaction parameter.

The results for viscous fluid are obtained by substituting α 1 = α 2 = α 3 = 0 into Eq. (8).

The simplified boundary conditions are as follows:

(11) f ( 0 ) = 0 , f ′ ( 0 ) = 1 + N 1 f ″ ( 0 ) + N 2 f ‴ ( 0 ) , θ ′ ( 0 ) = − Bi [ 1 − θ ( 0 ) ] , ϕ ( 0 ) = 1 ,

(12) f ′ ( ∞ ) → 0 , θ ( ∞ ) → 0 , ϕ ( ∞ ) → 0 ,

where N 1 = Λ 1 a ν and N 2 = Λ 2 a ν are the first-order and second-order slip parameters, respectively.

3 Numerical simulations

The system of Eqs (8)–(10) is solved numerically using the RK scheme. This scheme is chosen for its higher accuracy in providing an approximate solution through iterative numerical methods. Another benefit of this scheme is that it requires function values at specific points. To implement the RK scheme, the higher-order system is first transformed into a first-order problem by introducing a new variable:

(13) f = Ψ 1 , f ′ = Ψ 2 , f ″ = Ψ 3 , f ‴ = Ψ 4 , f ′ ‴ = Ψ 4 ′ , θ = Ψ 5 , θ ′ = Ψ 6 , θ ″ = Ψ 6 ′ , ϕ = Ψ 7 , ϕ ′ = Ψ 8 , and ϕ ″ = Ψ 8 ′ .

The converted system is expressed as

(14) Ψ 4 ′ = Ψ 4 + Ψ 1 Ψ 3 − ( Ψ 2 ) 2 + α 1 ( 2 Ψ 1 Ψ 2 Ψ 3 − Ψ 1 2 Ψ 4 ) + ( − 2 α 2 Ψ 1 Ψ 3 Ψ 2 2 − 3 α 2 Ψ 1 2 Ψ 3 2 ) + α 3 Ψ 3 2 ( α 3 Ψ 1 − α 2 Ψ 1 3 ) .

(15) Ψ 6 ′ = − ε ( Ψ 6 ) 2 − Pr [ Ψ 1 Ψ 6 + NbΨ 6 Ψ 8 + Nt ( Ψ 6 ) 2 ] + Pr δ T Ψ 1 Ψ 2 Ψ 6 + DuΨ 8 ′ ( 1 + Rd + ε θ − Pr δ T Ψ 1 2 ) ,

(16) Ψ 8 ′ = − ScΨ 1 Ψ 8 − Nt Nb Ψ 6 ′ + Sc ( kr ) Ψ 7 − SrΨ 6 ′ + δ c Ψ 1 Ψ 2 Ψ 8 1 + δ c Ψ 1 2 ,

with

(17) Ψ 1 ( 0 ) = 0 , Ψ 2 ( 0 ) = 1 + N 1 Ψ 3 ( 0 ) + N 2 Ψ 4 ( 0 ) , Ψ 6 ( 0 ) = − Bi [ 1 − Ψ 5 ( 0 ) ] , Ψ 7 ( 0 ) = 1 , Ψ 2 ( ∞ ) → 0 , Ψ 5 ( ∞ ) → 0 , and Ψ 7 ( ∞ ) → 0 .

The solution is ensured with an accuracy of 10⁻⁶.

4 Validation of numerical results

The validation of calculated numerical outcomes is warranted. The outcomes are juxtaposed in Table 1 with the analysis conducted by Makinde and Aziz [31]. Both investigations demonstrate a high level of precision in the results.

Table 1

Comparative analysis for − θ ′ ( 0 ) with investigation of Makinde and Aziz [31]

Pr	Makinde and Aziz [31]	Present results
0.07	0.0663	0.06638
0.2	0.6191	0.61912
0.7	0.4539	0.45391

5 Discussion

The physical problem is described in terms of relevant flow parameters. A mathematical model is formulated based on certain theoretical flow assumptions, with fixed numerical values assigned to all flow parameters such as α 1 = 0.2 , α 2 = 0.3 , α 3 = 0.5 , Rd = 0.5 , Pr = 0.7 , Nb = 0.3 , Nt = 0.2 , δ T = 0.4 , Du = 0.3 , δ c = 0.2 , Bi = 0.4 , Sc = 0.5 , N 1 = 0.4 , N 2 = 0.4 , and kr = 0.2 . Figure 2(a–d) shows the analysis for velocity f ′ due to a variation of Deborah number α 1 , retardation parameter α 3 , first-order slip parameter N 1 and second-order slip constant N 2 . Figure 2(a) claims the role of Deborah number α 1 in assessment of velocity f ′ . A lower fluctuation in the f ′ is inspected for large variation α 1 . Physically, the change in α 1 is associated with the moving fluid to retain its original position. Figure 2(b) signifies the effects of retardation parameter α 3 on f ′ . An increasing role of α 3 on f ′ has been visualized. The interaction of first-order slip coefficient N 1 and second-order slip constant N 2 on f ′ is justified in Figure 2(c) and (d), respectively. Both parameters effectively control the velocity of fluid. The slower velocity rate is more prominent with interaction of slip parameters. The role of slip phenomenon associated with the heat transfer systems is important in surface coating, microfluidic, oil recovery, heat exchangers, etc.

$Figure 2 (a–d) Profile of f ′ f^{\prime} subject to variation of (a) α 1 {\alpha }_{1} , (b) α 3 {\alpha }_{3} , (c) N 1 {N}_{1} , and (d) N 2 {N}_{2} .$

Figure 2

(a–d) Profile of f ′ subject to variation of (a) α 1 , (b) α 3 , (c) N 1 , and (d) N 2 .

Figure 3(a–g) expresses the thermal investigation associated under the prominent role of fluid parameters. Figure 3(a) analyzes the effects of variable thermal conductivity parameter ε on temperature profile θ . The improved rate of heat transfer is executed with ε . It is noted that in many thermal systems, the thermal conductivity cannot be treated constant as it fluctuates with different physical sources. The consideration of variable thermal conductivity is more effective to improve the heat transfer in any engineering or thermal systems. Figure 3(b) presents the observations for change in θ in view of Dufour number Du fluctuation. The summarized results convey that an enriched change in θ is prescribed by varying Du . Physically, Du presents a ratio between thermal diffusion and mass diffusion. By increasing Du , the heat transport enhances, which leads to an increment in θ . The prediction for θ due to radiation parameter R is examined by plotting Figure 3(c). As expected, the boosted effects of R on θ are noted. The radiated phenomenon is based on transfer of energy via electromagnetic source. In contrast to convection and conduction, the radiation phenomenon does not require any medium for transport process. The electromagnetic waves containing the oscillatory magnetic and electric fields can move with speed of light. Figure 3(d) reflects that θ is lower by enlarging thermal relaxation parameter δ T . The role of δ T specifies that the measurement of fluid materials changes with temperature gradient. The effect of thermal Biot number β i on θ is defined in Figure 2(e). The increasing visualization of θ is governed by enriching β i . Physically, the thermal Biot number conveys a direct association with the heat transfer coefficient, which leads to an increment in θ . Figure 3(f–g) pronounces the role of important slip parameters N 1 and N 2 on θ . Here, assigning change to both slip parameters leads to an improvement in θ . The heat transfer can be updated by utilizing the role of slip phenomenon. Such observations play a novel role in heat exchangers and petroleum industry.

$Figure 3 (a–g) Profile of θ \theta subject to variation of (a) ε \varepsilon , (b) Du \text{Du} , (c) R R , (d) δ T {\delta }_{\text{T}} , (e) β i {\beta }_{i} , (f) N 1 {N}_{1} , and (g) N 2 {N}_{2} .$

Figure 3

(a–g) Profile of θ subject to variation of (a) ε , (b) Du , (c) R , (d) δ T , (e) β i , (f) N 1 , and (g) N 2 .

Figure 4(a) aims to investigate the observations for concentration field ϕ by interpreting the role of Soret number Sr . An increasing reflection in profile of ϕ is announced under the effective values of Sr . Physically, the Soret number defines the heat and mass transfer analysis with association of mass gradient with thermal gradient ratio. The mass gradient enhances due to larger Sr , which improved the concentration of nanofluid. Figure 4(b) claims the results for thermophoresis parameter Nt on ϕ . The thermophoresis parameter predicts increasing outcomes for ϕ . Physical aspects of such increasing declaration is due to thermo-diffusion phenomenon. In thermo-diffusion, the increment in concentration of nanofluid is exhibited due to the collection of heat particles in cooler region. The thermo-diffusion phenomenon is novel in the aerosol technology, combustion process, environmental engineering, etc. In Figure 3(c) the simulations are determined for ϕ with a variation of α 1 . An improved change in ϕ is noted due to α 1 . Figure 3(d) exposes the influence of reaction parameter kr on ϕ . The chemical reaction parameter reduces the concentration. Figure 3(e) exhibits the analysis for ϕ against concentration relaxation parameter δ c . A decreasing effects are deduced for ϕ by assigning change to δ c . Figure 3(e) visualizes the effects of Schmidt number Sc on ϕ . The increment in Sc leads to low mass diffusivity, which results in a decrement in ϕ .

$Figure 4 (a–f) Profile of ϕ \phi subject to variation of (a) Sr \text{Sr} , (b) Nt \text{Nt} , (c) α 1 {\alpha }_{1} , (d) kr \text{kr} , (e) δ c {\delta }_{\text{c}} , and (f) Sc \text{Sc} .$

Figure 4

(a–f) Profile of ϕ subject to variation of (a) Sr , (b) Nt , (c) α 1 , (d) kr , (e) δ c , and (f) Sc .

6 Conclusions

A theoretical framework is proposed to examine the heat and mass transfer in a Burgers nanofluid considering the influence of Soret and Dufour effects. The Cattaneo–Christov theory is employed to describe heat transfer phenomena. The problem is tackled using the RK numerical method. The outcomes exhibit high precision compared to existing research in special scenarios. Key discoveries include:

The interaction of slip parameters presents a reduction in the velocity.
The velocity profile enhances with retardation time parameter.
The heat transfer boosted due to Dufour number and thermal Biot number.
The presence of slip parameters enhances the heat transfer phenomenon.
With increasing thermal relaxation time parameter, a reduction in temperature is examined.
Increasing effects of Soret number are claimed for nanofluid concentration.
The change in chemical reaction and concentration relaxation constant leads to a decrement in the concentration.
With a variation of relaxation constant, the concentration profile improved.
The simulated results may find applications in the heat transfer enhancement, chemical processes, nuclear systems, heat transfer devices, thermal engineering, manufacturing processes, aerospace technology, extrusion systems, etc.

Acknowledgments

The authors are thankful to the Deanship of Graduate Studies and Scientific Research at University of Bisha for supporting this work through the Fast-Track Research Support Program.

Funding information: The authors are thankful to the Deanship of Graduate Studies and Scientific Research at University of Bisha for supporting this work through the Fast-Track Research Support Program.
Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.
Conflict of interest: The authors state no conflict of interest.
Data availability statement: The datasets generated and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

[1] Choi SUS. Enhancing thermal conductivity of fluids with nanoparticles. In: Proceedings of the ASME International Mechanical Engineering Congress and Exposition. San Francisco, CA, USA; 1995. p. 99–105.Search in Google Scholar

[2] Ge-JiLe H, Qayyum S, Shah F, Khan MI, Khan SU. Slip flow of Jeffrey nanofluid with activation energy and entropy generation applications. Adv Mech Eng. 2021;13(3):1–9.10.1177/16878140211006578Search in Google Scholar

[3] Acharya S. Effect of cavity undulations and thermal boundary conditions on natural convection and entropy generation in CuO-water/Al2O3-water nanofluid. J Nanofluids. 2023;12(3):687–98.10.1166/jon.2023.1956Search in Google Scholar

[4] Bouselsal M, Mebarek-Oudina F, Biswas N, Ismail AA. Heat transfer enhancement using Al2O3-MWCNT hybrid-nanofluid inside a tube/shell heat exchanger with different tube shapes. Micromachines. 2023;14(5):1072.10.3390/mi14051072Search in Google Scholar PubMed PubMed Central

[5] Ali A, Mebarek-Oudina F, Barman A, Das S, Ismail AI. Peristaltic transportation of hybrid nano-blood through a ciliated micro-vessel subject to heat source and Lorentz force. J Therm Anal Calorim. 2023;148:7059–83.10.1007/s10973-023-12217-xSearch in Google Scholar

[6] Bafakeeh OT, Al-Khaled K, Khan SU, Abbasi A, Ganteda C, Khan MI, et al. On the bioconvective aspect of viscoelastic micropolar nanofluid referring to variable thermal conductivity and thermo-diffusion characteristics. Bioengineering. 2023;10(1):73.10.3390/bioengineering10010073Search in Google Scholar PubMed PubMed Central

[7] Yang H, Majeed A, Al-Khaled K, Abbas T, Naeem M, Khan SU, et al. Significance of melting heat transfer and Brownian motion on flow of power-Eyring fluid conveying nano-sized particles with improved energy systems. Lubricants. 2023;11(1):32.10.3390/lubricants11010032Search in Google Scholar

[8] Ramesh K, Mebarek-Oudina F, Ismail AI, Jaiswal BR, Warke AS, Lodhi RK, et al. Computational analysis on radiative non-Newtonian Carreau nanofluid flow in a microchannel under the magnetic properties. Sciencia Iran. 2023;30(2):376–90.10.24200/sci.2022.58629.5822Search in Google Scholar

[9] Alzahrani J, Aziz S, Hamoudi MR, Sadon SH, Le QH, Khan SU, et al. Evaluation of bioconvection for sinusoidally moving Jeffrey nanoparticles in view of temperature dependent thermal conductivity and Cattaneo-Christov heat diffusion model. Ain Shams Eng J. September 2023;14(9):102124.10.1016/j.asej.2023.102124Search in Google Scholar

[10] Dharmaiah G, Mebarek-Oudina F, Kumar MS, Kala KC. Nuclear reactor application on Jeffrey fluid flow with Falkner-skan factor, Brownian and thermophoresis, non linear thermal radiation impacts past a wedge. J Indian Chem Soc. 2023;100(2):100907.10.1016/j.jics.2023.100907Search in Google Scholar

[11] Jabeen K, Mushtaq M, Mushtaq T, Muntazir RM. A numerical study of boundary layer flow of Williamson nanofluid in the presence of viscous dissipation, bioconvection, and activation energy. Numer Heat Transfer Part A: Appl. 2024;85(3):378–99.10.1080/10407782.2023.2187494Search in Google Scholar

[12] Abbas N, Ali M, Shatanawi W. Chemical reactive second-grade nanofluid flow past an exponential curved stretching surface: Numerically. Int J Mod Phys B. 2024;38(2):2450026.10.1142/S0217979224500267Search in Google Scholar

[13] Mebarek-Oudina F, Preeti, Sabu AS, Vaidya H, Lewis RW, Areekara S, et al. Hydromagnetic flow of magnetite-water nano-fluid utilizing adapted Buongiorno model. Int J Mod Phys B. 2023;38(1):2450003.10.1142/S0217979224500036Search in Google Scholar

[14] Mishra A, Upreti H. Computational analysis of radiative nanofluid flow past an inclined cylinder with slip effects using the Yamada–Ota model. Numer Heat Transfer Part A: Appl. 2023;1–19.10.1080/10407782.2023.2258556Search in Google Scholar

[15] Pandey AK, Upreti H, Joshi N, Uddin Z. Effect of natural convection on 3D MHD flow of MoS2–GO/H2O via porous surface due to multiple slip mechanisms. J Taibah Univ Sci. 2022;16(1):749–62.10.1080/16583655.2022.2113729Search in Google Scholar

[16] Pandey AK, Upreti H. Heat and mass transfer in convective flow of nanofluid. In: Advances in mathematical and computational modeling of engineering systems. CRC Press; 2023. p. 295–313.10.1201/9781003367420-14Search in Google Scholar

[17] Jena S, Mishra SR, Pattnaik PK. Development in the heat transfer properties of nanofluid due to the interaction of inclined magnetic field and non-uniform heat source. J Nanofluids. 2020;9(3):143–51.10.1166/jon.2020.1749Search in Google Scholar

[18] Pattnaik PK, Parida SK, Mishra SR, Ali Abbas M, Bhatti MM. Analysis of metallic nanoparticles (Cu, Al2O3, and SWCNTs) on magnetohydrodynamics water-based nanofluid through a porous medium. J Math. 2022;2022:1–12.10.1155/2022/3237815Search in Google Scholar

[19] Krishnan JM, Rajagopal KR. Review of the uses and modeling of bitumen from and ancient to modern times. Appl Mech Rev. 2003;56:149–214.10.1115/1.1529658Search in Google Scholar

[20] Khan MN, Nadeem S, Abbas N, Zidan AM. Heat and mass transfer investigation of a chemically reactive Burgers nanofluid with an induced magnetic field over an exponentially stretching surface. Proc Inst Mech Eng Part E: J Process Mech Eng. 2021;235(6):2189–200.10.1177/09544089211034941Search in Google Scholar

[21] Hassan M, Rizwan M. Mathematical modeling and flow behavior of homogenous complex MWCNT/PEG nanofluids through Burger model with Maxwell representation. J Therm Anal Calorim. 2023;148(14):7383–94.10.1007/s10973-023-12192-3Search in Google Scholar

[22] Gangadhar K, Kumari MA, Wajdi K, Omer AS, Rao MV, Khan I, et al. Heat transport magnetization for Burgers fluid in a porous medium with convective heating and heterogeneous-homogeneous response. Case Stud Therm Eng. 2023;48:103087.10.1016/j.csite.2023.103087Search in Google Scholar

[23] Fetecau C, Moroşanu C, Akhtar S. A strange result regarding some MHD motions of generalized burgers’ fluids with a differential expression of shear stress on the boundary. AppliedMath. 2024;4(1):289–304.10.3390/appliedmath4010015Search in Google Scholar

[24] Hejazi HA, Khan SU, Ijaz Khan M, Khan I. Enhancement of heat transfer due to nonlinear radiative Burgers nanofluid with triple diffusion and heat source effects. Int J Comput Mater Sci Eng. 2024;2450010.10.1142/S2047684124500106Search in Google Scholar

[25] Juhany KA, Shahzad F, Alzhrani S, Pasha AA, Jamshed W, Islam N, et al. Finite element mechanism and quadratic regression of magnetized mixed convective Burgers’ nanofluid flow with applying entropy generation along the riga surface. Int Commun Heat Mass Transf. 2023;142:106631.10.1016/j.icheatmasstransfer.2023.106631Search in Google Scholar

[26] Li S, Abbas T, Al-Khaled K, Khan SU, Ul Haq E, Abdullaev SS, et al. Insight into the heat transfer across the dynamics of Burger fluid due to stretching and buoyancy forces when thermal radiation and heat source are significant. Pramana. 2023;97(4):196.10.1007/s12043-023-02678-ySearch in Google Scholar

[27] Raza N, Khan AK, Awan AU, Abro KA. Dynamical aspects of transient electro-osmotic flow of Burgers’ fluid with zeta potential in cylindrical tube. Nonlinear Eng. 2023;12(1):20220256.10.1515/nleng-2022-0256Search in Google Scholar

[28] Zhao X, Yin K. A sub-grid scale model for Burgers turbulence based on the artificial neural network method. Theor Appl Mech Lett. 2024;14:100519.10.1016/j.taml.2024.100519Search in Google Scholar

[29] Khan SU, Al-Khaled K, Gasmi H, Hamdi E, Ouazir A, Ghazouani N. Significance of variable thermal conductivity and non-uniform heating source for Burgers nanofluid flow subject to modified thermal laws. Int J Mod Phys B. 2023;37(1):2350005.10.1142/S0217979223500054Search in Google Scholar

[30] Khan M, Iqbal Z, Ahmed A. Energy transport analysis in the flow of burgers nanofluid inspired by variable thermal conductivity. Pramana. 2021;95(2):74.10.1007/s12043-021-02097-xSearch in Google Scholar

[31] Makinde OD, Aziz A. Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition. Int J Therm Sci. 2011;50:1326–32.10.1016/j.ijthermalsci.2011.02.019Search in Google Scholar

Received: 2023-12-12

Revised: 2024-04-26

Accepted: 2024-05-17

Published Online: 2024-07-20

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

Articles in the same Issue

https://doi.org/10.1515/phys-2024-0042

Keywords for this article

heat and mass transfer; Burgers nanofluid; Cattaneo–Christov model; higher-order slip effects; variable thermal conductivity

Creative Commons

BY 4.0