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Homotopic simulation for heat transport phenomenon of the Burgers nanofluids flow over a stretching cylinder with thermal convective and zero mass flux conditions

  • Muhammad Ramzan , Ebrahem A. Algehyne , Anwar Saeed EMAIL logo , Abdullah Dawar , Poom Kumam EMAIL logo and Wiboonsak Watthayu
Published/Copyright: April 1, 2022
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 11 Issue 1

Abstract

This study is focused to elaborate on the effect of heat source/sink on the flow of non-Newtonian Burger nanofluid toward the stretching sheet and cylinder. The current flow analysis is designed in the form of higher order nonlinear partial differential equations along with convective heat and zero mass flux conditions. Suitable similarity transformations are used for the conversion of higher order nonlinear partial differential equations into the nonlinear ordinary differential equations. For the computation of graphical and tabular results, the most powerful analytical technique, known as the homotopy analysis method, is applied to the resulting higher order nonlinear ordinary differential equations. The consequence of distinct flow parameters on the Burger nanofluid velocity, temperature, and concentration profiles are determined and debated in a graphical form. The key outcomes of this study are that the Burger nanofluid parameter and Deborah number have reduced the velocity of the Burger nanofluid for both the stretching sheet and cylinder. Also, it is attained that the Burger nanofluid temperature is elevated with the intensifying of thermal Biot number for both stretching sheet and cylinder. The Burger nanofluid concentration becomes higher with the escalating values of Brownian motion parameter and Lewis number for both stretching sheet and cylinder. The Nusselt number of the Burger nanofluid upsurges due to the increment of thermal Biot number for both stretching sheet and cylinder. Also, the different industrial and engineering applications of this study were obtained. The presented model can be used for a variety of industrial and engineering applications such as biotechnology, electrical engineering, cooling of devices, nuclear reactors, mechanical engineering, pharmaceutical science, bioscience, medicine, cancer treatment, industrial-grid engines, automobiles, and many others.

Keywords: Burger nanofluid; heat transfer; stretching cylinder; homotopy analysis method

Nomenclature

( r , θ , z )

cylindrical polar coordinate

( u , 0 , w )

velocity components

l

specific length

T

fluid temperature

C

fluid concentration

T w

surface temperature

T ∞

ambient temperature

C ∞

ambient temperature

λ 1

relaxation time parameter

λ 2

burger fluid material parameter

λ 3

retardation time parameter

α 1

thermal diffusion coefficient

k

thermal conductivity

D B

Brownian diffusivity

ν

kinematics viscosity

Q 0

heat source/sink parameter

ρ

fluid density

C p

specific heat at a constant pressure

D T

thermophoresis coefficient

h f

heat convection coefficient

Dimensionless symbols

γ

fluid curvature parameter

β 1 and β 3

Deborah numbers

Pr

Prandtl number

β 2

Burger fluid parameter

δ

dimensionless heat source/sink parameter

L e

Lewis number

Nt

thermophoresis parameter

Nb

Brownian motion parameter

Re

Reynolds number

Nu z

Nusselt number

Sh z

local Sherwood number

Bi

thermal Biot number

1 Introduction

The non-Newtonian fluid research has become increasingly popular as a result of its importance and wide range of applications in industries and engineering systems like geophysical development, petrochemical advances, process design system, cooling and heating process, biomedical engineering, chemical engineering, metal processing, foodstuff, and oil reservoir engineering. Because of its widespread applications in engineering and industry, researchers and scientists emphasized their research on the non-Newtonian nanofluid problem. Khan et al. [1] addressed the significance of Dufour and Soret parameters on the flow of non-Newtonian micropolar liquid toward the exponential nonlinear stretching cylinder in which they found that Reynolds number diminished the thickness of the micropolar liquid. Bilal et al. [2] explained the performance of activation energy on the flow of non-Newtonian Casson nanoliquid under the rotating thin needle. They inspected that the nanoliquid concentration is enhanced with the increment of activation energy. Ramzan et al. [3] designed the model of non-Newtonian nanoliquid in the existence of entropy and dipole effects on the thin needle. Their conclusions showed that the ferromagnetic parameter enhanced the nanofluid velocity. Alhadihrami et al. [4] considered the study of non-Newtonian Casson liquid through the occurrence of heat transfer and porosity effect in a porous medium. They attained that the transfer of heat is improved when the porosity parameter is higher. Mallawi et al. [5] designated the modeling of non-Newtonian liquid above the Riga plate with the influence of Cattaneo-Christov heat flux. They studied that the thickness of thermal boundary layer of viscoelastic liquid is higher than the second-grade fluid. Dawar et al. [6] examined the impacts of non-isosolutal and non-isothermal conditions over the flow of Williamson nanofluid above the wedge or cone. For the explanation of their problem, they employed the homotopy analysis method (HAM) on the higher order nonlinear ordinary differential equations (ODEs). Reddy et al. [7] explored the consequence of chemical reaction on the three-dimensional magnetohydrodynamic (MHD) flow of non-Newtonian Maxwell nanoliquid through the stretched surface and examined that the radiation parameter weakened the nanoliquid temperature. Qaiser et al. [8] presented the significance of mass transfer and thermal radiation on the non-Newtonian mixed convection flow of Walter-B nanoliquid under the stretchable sheet. Their fallouts show that the Brownian motion parameter improved Sherwood number.

Nanofluids are fluids that contain suspended nanoparticles that are less than a hundred nanometers in size and are used to improve thermal conductivity. The study of nanofluid has attracted the attention of researchers and scientists due to its vast variety of applications in the technical and industrial fields. The industrial and engineering applications of the nanofluid are heat exchangers, vehicle cooling, electronic device cooling, nuclear reactors, transformer cooling, vehicle thermal management, etc. The nanofluid is also used in medical treatments such as wound treatment, resonance imaging, and cancerous and noncancerous tumor treatment. That is why researchers and scientists used nanofluid in their experiments. Hiba et al. [9] computed the mathematical modeling of MHD flow of hybrid nanofluid with Ag–MgO as the nanoparticle and water as the base fluid and adopted the Galerkin finite element method for the numerical solution of their problem. Ouni et al. [10] presented the influence of thermal radiation on the flow of hybrid nanofluid toward the parabolic solar collector in the presence of solar radiation. They examined that hybrid nanofluid temperature is higher for thermal radiation parameters. Khan et al. [11] demonstrated the MHD flow of three-dimensional cross nanofluid by applying Soret and Dufour numbers in which they found that Soret number raised the rate of heat transport. Bejawada et al. [12] explained the problem of MHD flow of nanofluid with the occurrence of viscous dissipation and chemical reaction toward the inclined plate. In this work, it was noted that the concentration of the nanofluid was declined for Schmidt number. Jamshed et al. [13] inspected the consequence of the Joule heating effect on the MHD flow of tangent hyperbolic hybrid nanofluid under the stretching plate. Their problem is simulated numerically with the application of the Keller box scheme. Redouane et al. [14] scrutinized the MHD flow of hybrid nanofluid over the rotating cylinder through the existence of entropic generation. From this examination, it was observed that the entropy generation of the hybrid nanofluid increased with the rising of porosity parameters. Waqas et al. [15] evaluated the consequence of nonlinear thermal radiation over the flow of nanofluid in a permeable cylinder. From this study, they determined that the higher estimation of Reynolds number weakened the velocity of the nanoliquid. Hayat et al. [16] scrutinized the convective flow of Jeffrey nanoliquid through the stretchable cylinder along with heat transport behavior. They examined that Schmidt number diminished the nanofluid concentration. Siddiqui et al. [17] evaluated the problem of boundary layer MHD flow of two-dimensional Maxwell nanoliquid with the incidence of viscous dissipation through the melting surface. From this observation, they noted that the porosity of the nanofluid improved the entropy. Awan et al. [18] computed the mathematical solution of the micropolar nanofluid model with the assistance of the Runge-Kutta method through the presence of Hall current and MHD between the two parallel plates and also discussed some important physical properties of nanofluid. Ramesh et al. [19] reported the consequence of slip and suction/injection effects on the flow of Casson-micropolar nanoliquid under the two-rotating disks in which the reduction in the rate of heat and mass transportation is perceived for the Brownian motion parameter. Lv et al. [20] checked the behavior of entropy and Cattaneo–Christov heat flux over the spinning disk in the flow of bioconvection Reiner–Rivlin nanofluid and their concluding remarks showed that a greater estimation of Lewis and Peclet numbers decrease the motile gyrotactic microorganism profile of the nanoliquid. Waqas et al. [21] detected the movement of heat source/sink on the three-dimensional bioconvection flow of Carreau nanoliquid over the stretchable surface. From this study, they explained that the temperature of the nanofluid is raised for heat source/sink and Biot parameters. Kumar et al. [22] stated the role of Darcy–Forchheimer and heat transport on the flow of stagnation region nanofluid over the flat sheet. Form this study, they noticed the relationship between heat transfer and the Dacry–Forchheimer parameter. Other studies related to the nanofluid flow problem can be found in the references [23–25].

From the last few decades, scientists and researchers have shown a keen interest in studying the MHD flow problems due to its vast array of applications in the arena of engineering and industries. The MHD is a branch of physical science that studies magnetic and electrical fluid behavior such as plasma, liquid metals, electrolytes, and saltwater. In engineering and industry, the MHD has a broad array of applications, especially in the field of biomedical science such as blood flows, tissue temperature, MHD power plants, cell separation, MHD generators, and treatment of tumors. Shah et al. [26] examined the MHD flow of nanofluid along with energy flux due to concentration gradient, mass flux, and temperature gradient toward the horizontal surface and employed the finite difference code (Matlab Function) (bvp4c) technique for the evaluation of the numerical solution of their problem. Wakif et al. [27] presented the MHD mixed convective flow of radiative Walter-B fluid through the inclusion of Fourier’s and Fick’s laws under the linear stretching surface. From this analysis, it is noticed that the amplification in the magnetic field parameter led to the amplification of nanofluid velocity. Shafiq et al. [28] reported the MHD flow of Casson Water/Glycerin nanofluid in the presence of Darcy-Forchheimer over the rotating disk and detected that the skin friction coefficient is enhanced with the increment of the Darcy–Forchheimer parameter. Wakif et al. [29] scrutinized the combined effects of Joule heating and wall suction on the MHD flow of viscous by electrically conducting fluid over the Riga plate. They obtained that the rate of heat transport is augmented with the augmentation of wall suction of the fluid. Wakif et al. [30] inspected the presence of thermal conductivity and temperature-dependent viscosity on the MHD flow of Casson fluid toward the horizontal stretching sheet under the convective conditions. In this inquiry, it is notable that the fluid Casson parameter decayed the surface drag force. Wakif [31] used the spectral local linearization method for the numerical investigation of MHD flow of Walter-B fluid along with the gyrotactic microorganism behavior and attained that the Lorentz force weakened the Nusselt number of the fluid. Khashi’ie et al. [32] observed the Joule heating effect on the MHD boundary layer flow of hybrid nanoliquid above the moving plate. From their numerical result, it was noted that the magnetic and suction parameters augmented the heat rate transport. Krishna et al. [33] explored the mathematical modeling of MHD flow of Ag–Tio/H2O Casson hybrid nanoliquid in a porous medium along with the exponential vertical sheet in which Ag–Tio are the nanoparticles and water was taken as a base liquid. Haider et al. [34] inspected the significance of thermal radiation and activation energy on the unsteady MHD flow of nanoliquid past a stretchable surface. From tthis inquiry, they distinguished that the nanoparticle volume fraction of the nanofluid upsurges with the rise of activation energy. Ahmed et al. [35] explained the computation assessment of thermal conductivity on the MHD flow of Williamson nanoliquid along with the heat transport effect over the exponentially curved surface. They employed the bvp4c technique for the numerical description of the problem. In another study of MHD, Tassaddiq [36] conducted the study of MHD flow of hybrid micropolar nanoliquid with the occurrence of Cattaneo-Christov heat flux and found that the thermal profile of the hybrid nanofluid is raised against micropolar parameter. Qayyum et al. [37] addressed the Newtonian heat and mass conditions on the modeling of MHD flow of Walter-B nanoliquid along the stretched sheet. From this study, they found that the relation between local Nusselt and Sherwood numbers is reverse for thermophoresis parameter. Ghasemi and Hatami [38] scrutinized the presence of solar radiation over the MHD stagnation point flow of nanoliquid under the stretchable surface. From this scrutiny, they observed that the temperature of the nanofluid is higher for the solar radiation parameters. Ramzan et al. [39] reviewed the MHD flow of nanoliquid through the occurrence of homogeneous and heterogeneous reaction effects under the rotating disk. From this study, it was noted that the dimensionless constant of the rotating disk boosted the homogeneous/heterogeneous reactions profile of the nanofluid.

Heat and mass transport phenomena have recently found an extensive variety of applications in engineering and industry such as industrial equipment, rotating machinery, aerospace, power generation, chemical, and material processes, automotive, food processing, plastics, petrochemical, poultry further processing, rubbers aircraft engine cooling, and environmental control system. Because of the aforementioned applications, scientists and researchers have focused their research on heat and mass transport phenomena. Awais et al. [40] elaborated on the result of gyrotactic microorganisms over the MHD flow of bio nanofluid having the heat and mass transport features. From their outcomes, they detected that the bioconvection Rayleigh number and convection parameter elevated the rate of heat and mass transport. Srinivasulu and Goud [41] described the combined influence of heat and mass transport over the flow of Williamson nanoliquid due to the stretched sheet. They found the aspect of different flow parameters on the nanofluid velocity, temperature, and concentration. Zeeshan et al. [42] elaborated the study of MHD flow of nanoliquid over the vertical wavy sheet with the existence of heat and mass transfer and applied the Keller-box scheme for the numerical evolution of their problem. Punith Gowda et al. [43] explicated the heat and mass transport behavior on the Marangoni driven boundary layer flow of non-Newtonian nanoliquid with chemical reaction along the rectangular surface. In their study, they noticed that the porosity parameter decayed the nanofluid Nusselt number. Shi et al. [44] considered the exponential stretching surface for the explanation of three-dimensional MHD flow of radiative Maxwell nanoliquid along with the occurrence of heat and mass transfer effects. In this study, they discussed that the nanofluid velocity reduces as the rotation parameter upsurges. Zhao et al. [45] talked about the stagnation point flow of a tangent hyperbolic nanoliquid with the assumption of heat and mass transmission and entropy behavior. From this study, they deliberated that the enhancing estimation of the Brownian motion parameter boosted the entropy of the nanofluid. Arif et al. [46] conducted the occurrence of heat and mass transport on the modeling of Casson liquid along with ramped wall temperature in which MoS2–GO are the nanoparticles and engine oil is taken as a base liquid. Rasool et al. [47] reported the flow analysis of convective MHD nanofluid with the perception of heat and mass transfer in a stretchable surface. Their study explained that the concentration of the nanofluid is the growing function of the porosity parameter.

As a result of the above-mentioned literature, it was perceived that no consideration was given to studying the influence of heat source/sink effect on the flow of Burger nanofluid earlier. To fill this gap, the Burger nanofluid along with convective boundary conditions in the presence of Brownian and thermophoresis diffusion was taken into the interpretation. In the current analysis, the physical situation was being modeled in the form of stretching cylinder (see Figure 1). From Figure 1, the present physical situation explained that when curvature parameter ( γ = 0 ) then physically, the current flow problem is for stretching sheet, but when ( γ > 0 ) then the current flow problem is for stretching cylinder. The role of zero mass flux conditions in the Burger nanofluid problem is that there are no mass flux nanoparticles which mean that the nanoparticles’ mass flux is assumed to be zero on the surface, and that is why the current model is taken with zero mass flux condition (see Wakif et al. [48]). This work is very useful in different areas of engineering and industrial fields such as nuclear reactors, cooling of devices, plastics manufacturing, paper production, food processing, glass blowing, and synthetics fibers. The resultant higher orders nonlinear ODEs were resolved by the exploitation of HAM. The consequence of various flow parameters on the velocity, temperature, and concentration of Burger nanofluid was investigated in the graphical form. Also, the Nusselt number of Burger nanofluid was presented in a tabular form and discussed in detail.

Figure 1 Geometry of the flow problem.
Figure 1

Geometry of the flow problem.

2 Problem formulation

Consider the steady and incompressible flow of Burger nanofluid problem over a stretching cylinder with heat source/sink effect. r , θ , and z are the cylindrical coordinates in which u is the velocity component along the r -axis and w is the velocity component along the z - axis. The stretching velocity of the cylinder is w ( z ) = U 0 z l in which z is used as the reference velocity, while l is the specific length. T , T w , and T ∞ are the temperature, temperature at the surface, and ambient temperature, respectively. C and C ∞ are the concentration and ambient concentration, respectively. In addition, the effect of convective heat and zero mass flux conditions were taken. The geometrical representation of the flow problem is displayed in Figure 1. In view of the above assumptions, the leading equations of the current analysis are deliberated as [49–51]:

(1) ∂ u ∂ r + u r + ∂ w ∂ z = 0 ,

(2) u ∂ w ∂ r + w ∂ w ∂ z + λ 1 u 2 ∂ 2 w ∂ r 2 + w 2 ∂ 2 w ∂ z 2 + 2 u w ∂ 2 w ∂ z ∂ r + λ 2 2 u 2 ∂ u ∂ r ∂ 2 w ∂ r 2 + ∂ w ∂ r ∂ 2 w ∂ r ∂ z × u 3 ∂ 3 w ∂ r 3 + w 3 ∂ 3 w ∂ z 3 − u 2 ∂ w ∂ r ∂ 2 u ∂ r 2 + ∂ w ∂ z ∂ 2 w ∂ r 2 + 2 w 2 ∂ u ∂ z ∂ 2 w ∂ r ∂ z + w 2 ∂ w ∂ z ∂ 2 w ∂ z 2 − ∂ w ∂ r ∂ 2 u ∂ z 2 + 3 u w u ∂ 3 w ∂ r 2 ∂ z + w ∂ 3 w ∂ z 2 ∂ r + 2 u w ∂ u ∂ r ∂ 2 w ∂ z ∂ r + ∂ u ∂ z ∂ 2 w ∂ r 2 + ∂ w ∂ r ∂ 2 w ∂ z 2 − ∂ w ∂ r ∂ 2 u ∂ r ∂ z = ν ∂ 2 w ∂ r 2 + 1 r ∂ w ∂ r ν λ 3 u ∂ 3 w ∂ r 3 + w ∂ 3 w ∂ r 2 ∂ z + u r ∂ 2 w ∂ r 2 − ∂ w ∂ r ∂ 2 u ∂ r 2 + w r ∂ 2 w ∂ r ∂ z − 1 r ∂ u ∂ r ∂ w ∂ r − 1 r ∂ w ∂ r ∂ w ∂ z − ∂ w ∂ z ∂ 2 u ∂ r 2 ,

(3) u ∂ T ∂ r + w ∂ T ∂ z = α 1 1 r ∂ ∂ r r ∂ T ∂ r + τ D B δ C ∂ C ∂ r ∂ T ∂ r + D T T ∞ ∂ T ∂ r 2 + Q 0 ( T − T ∞ ) ρ C p ,

(4) u ∂ C ∂ r + w ∂ C ∂ z = D B 1 r ∂ ∂ r r ∂ C ∂ r + δ C D T T ∞ 1 r ∂ ∂ r r ∂ T ∂ r ,

with boundary conditions:

(5) u = 0 , w = U 0 z l , − k ∂ T ∂ r = h f ( T w − T ) , D B δ C ∂ C ∂ r + D T T ∞ ∂ T ∂ r = 0 at r = R , w → 0 , T → T ∞ , C → C ∞ as r → ∞ .

where u and w are the velocity components, λ 1 is the relaxation time, λ 2 is the material parameter of the Burger fluid, λ 3 is the retardation time, T is the temperature of the nanofluid, α 1 = k ρ C p is the thermal diffusion coefficient in which k is the thermal conductivity and ρ C p is the heat capacitance, D B is the diffusion coefficient, ν is the kinematics viscosity, Q 0 the dimensional heat source/sink, the liquid density is ρ , C p is the specific heat, D T is the thermophoresis coefficient, and h f is the coefficient of heat convection.

The similarity transformations in the dimensionless form are [50,51]:

(6) u = − R r U 0 ν l f ( ξ ) , w = U 0 z l f ′ ( ξ ) , θ ( ξ ) = T − T ∞ T w − T ∞ , ϕ ( ξ ) = C − C ∞ C ∞ , ξ = U 0 ν l r 2 − R 2 2 R .

With the implementation of the above similarity variables defined in equation (6), the equation of continuity is satisfied and the dimensionless form of equations (2)–(4) are

(7) ( 1 + 2 γ ξ ) 3 f ‴ + ( 1 + 2 γ ξ ) 2 β 1 [ 2 f f ′ f ″ − f 2 f ‴ ] − ( 1 + 2 γ ξ ) α β 1 f 2 f ″ − 4 γ 2 β 2 f ‴ f ″ − ( 1 + 2 γ ξ ) 2 × β 2 [ 3 f 2 ( f ″ ) 2 + 2 f ( f ′ ) 2 f ″ − f 3 f ′ ‴ ] − 4 γ β 3 ( 1 + 2 γ ξ ) 2 f f ‴ + ( 1 + 2 γ ξ ) γ β 2 [ 3 f 2 f ′ f ″ + f 3 f ‴ ] + ( 1 + 2 γ ξ ) 2 [ 2 γ f ″ + f f ″ − ( f ′ ) 2 ] + ( 1 + 2 γ ξ ) 3 β 3 [ ( f ″ ) 2 − f f ′ ‴ ] = 0 ,

(8) ( 1 + 2 γ ξ ) θ ″ + 2 γ θ ′ + Pr f θ ′ + Pr δ θ + Pr N b ϕ ′ θ ′ ( 1 + 2 γ ξ ) + Pr N t ( θ ′ ) 2 ( 1 + 2 γ ξ ) = 0 ,

(9) ( 1 + 2 γ ξ ) ϕ ″ + 2 γ ϕ ′ + Le Pr f ϕ ′ + ( 1 + 2 γ ξ ) Nt Nb θ ″ + 2 γ Nt Nb θ ′ = 0 ,

The boundary conditions in the dimensionless form are

(10) f ( 0 ) = 0 , f ′ ( 0 ) = 1 , f ′ ( ∞ ) = 0 , θ ′ ( 0 ) = B i ( θ ( 0 ) − 1 ) , θ ( ∞ ) = 0 , Nb ϕ ′ ( 0 ) + Nt θ ′ ( 0 ) = 0 , ϕ ( ∞ ) = 0 . .

In the above equations, γ = 1 R ν l U 0 is the curvature parameter of the fluid, β 1 = λ 1 U 0 l and β 3 = λ 3 U 0 l are Deborah numbers, β 2 = λ 2 U 0 l 2 is the Burger fluid parameter, δ = l Q 0 U 0 ( ρ C p ) is the heat source/sink parameter, Le = α 1 D B is the Lewis number of the nanofluid, Pr = ν α 1 is the Prandtl number, Nt = τ D T ( T w − T ∞ ) ν T ∞ is the thermophoresis parameter, Nb = τ D B C ∞ ν δ c is the Brownian motion parameter, and B i = h f k R r ν l U 0 is the thermal Biot number.

The physical quantities including Nusselt number and local Sherwood number are defined as

(11) Nu z = z q m k ( T w − T ∞ ) , Sh z = z j w D B ( C w − C ∞ ) .

The heat q m and mass flux j w is defined as

(12) q m = − k ∂ T ∂ r r = R , j w = − D B ∂ C ∂ r r = R .

By applying the similarity transformations, the Sherwood number becomes zero and the Nusselt number reduces as

(13) Nu z Re − 1 2 = − θ ′ ( 0 ) ,

where Re = w ( z ) z ν is the local Reynolds number.

3 The solution to the problem

The HAM provides several advantages over other methods. Therefore, the present scheme is very useful for the analytical solution of the higher order nonlinear ODEs along with boundary conditions. The HAM method was used to solve the problem because it offers the following benefits:

  1. Without linearization and discretization of nonlinear differential equations, the proposed technique is simulated for an accurate solution.

  2. It is a more generalized method that works for both weakly and strongly nonlinear problems and is independent of small or large parameters.

  3. The region and the rate of convergence of series solutions are controllable and adjustable with the help of HAM.

  4. The HAM is free from rounding of errors and essay for computation.

That is why the HAM is preferable over other techniques due to the above-mentioned advantages. The linear operator and initial guesses are defined as

(14) f 0 ( η ) = 1 − e − ξ , θ 0 ( η ) = Bi ( 1 + Bi ) e − ξ , ϕ 0 ( η ) = − Nt Nb Bi ( 1 + Bi ) e − ξ , ,

(15) L f = f ‴ − f ′ , L θ = θ ″ − θ , L ϕ = ϕ ″ − ϕ , ,

such that

(16) L f [ C 1 + C 2 exp ( − ξ ) + C 3 exp ( ξ ) ] = 0 , L θ [ C 4 exp ( − ξ ) + C 5 exp ( ξ ) ] = 0 , L ϕ [ C 6 exp ( − ξ ) + C 7 exp ( ξ ) ] = 0 . ,

where C i ( i = 1 − 7 ) are the arbitrary constants.

4 Convergence analysis of the homotopy solution

HAM is used to handle the series solutions of the simulated system of nonlinear differential equations. The auxiliary parameter ℏ is used to manipulate and control the convergence areas of f ″ ( 0 ) , θ ′ ( 0 ) , and ϕ ′ ( 0 ) . Figures 2–4 are drawn to check the convergence region of f ″ ( 0 ) , θ ′ ( 0 ) , and ϕ ′ ( 0 ) . Finally, the convergence region of f ″ ( 0 ) , θ ′ ( 0 ) , and ϕ ′ ( 0 ) are − 1.0 ≤ ℏ f ≤ 1.0 , − 0.8 ≤ ℏ θ ≤ 0.8 , and − 0.75 ≤ ℏ ϕ ≤ 0.75 , respectively.

Figure 2 h -Curve h\text{-Curve} for f ″ ( 0 ) f^{\prime\prime} (0) .
Figure 2

h -Curve for f ″ ( 0 ) .

Figure 3 h -Curve h\text{-Curve} for θ ′ ( 0 ) \theta ^{\prime} (0) .
Figure 3

h -Curve for θ ′ ( 0 ) .

Figure 4 h -Curve h\text{-Curve} for ϕ ′ ( 0 ) \phi ^{\prime} (0) .
Figure 4

h -Curve for ϕ ′ ( 0 ) .

5 Validation

A comparison between the present results and the previously published results is demonstrated in Table 1. For the validation of the current problem from Table 1, it was noted that the current findings were in good consistency with previously published findings.

Table 1

Analysis of the present results with previously published results

Pr N u z Re r
Ref. [52] Ref. [53] Ref. [54] Ref. [55] Present results
0.07 0.0665 0.0656 0.0663 0.0656 0.0654
0.20 0.1691 0.1691 0.1691 0.1691 0.1691
0.70 0.4539 0.4539 0.4539 0.4539 0.4539
2.00 0.9114 0.9114 0.9113 0.9115 0.9114

6 Results and discussion

In Section 6, the analytical solution of the Burger nanofluid with convective heat and mass transport phenomena was discussed. For the physical computation of this study, the HAM was employed on the higher order nonlinear ODEs (6–8) along with boundary conditions (9). The significance of distinct flow parameters over the field of velocity, temperature, and concentration of the Burger nanofluid for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) were computed in a graphical form. The ranges of all effective parameters were fixed in a graphical discussion, and only one parameter varies to plot their respective graph. The ranges of distinct flow parameters were β 1 = 0.3, β 2 = 0.2, β 3 = 1.0, δ = 1.3, Bi = 0.3, Pr = 6.0, Le = 1.0, Nb = 0.2, and Nt = 1.0. Also, the Nusselt number Nu z against flow parameters for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) were calculated and discussed in detail.

6.1 Table discussion

Table 2 is made to check the effects of various flow parameters such that Biot number Bi , and heat generation parameter δ on the Nusselt number Nu z Re − 1 2 of the Burger nanofluid for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . It was perceived that the Nusselt number Nu z Re − 1 2 was higher for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) with the improvement of B i . Also, it was observed that the expanding estimation of heat generation parameter δ reduced the Nusselt number for both the stretching sheet ( γ = 0 ) and the stretching cylinder ( γ > 0 ) .

Table 2

Effects of Bi and δ on Nu z Re − 1 2 for γ = 0 and γ > 0

Bi δ Nu z Re − 1 2 for sheet ( γ = 0 ) Nu z Re − 1 2 for cylinder ( γ > 0 )
0.1 0.080030 0.081705
0.2 0.081965 0.083202
0.3 0.148192 0.150276
0.4 0.201516 0.204485
0.2 0.211584 0.212713
0.4 0.207679 0.208807
0.6 0.203774 0.204902
0.8 0.199868 0.200997

6.2 Velocity profile

Figures 5–7 display the effects of the Deborah number β 1 , Burger nanofluid parameter β 2 , and Deborah number β 3 for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . The variation in nanofluid velocity for higher estimation of Deborah number β 1 is described in Figure 5. From Figure 5, it was detected that with the increase of the Deborah number β 1 , the Burger nanofluid velocity was reduced for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . Deborah number was defined as the ratio between the relaxation time parameter and observation time parameter. With the increment of Deborah number, the boundary layer thickness was reduced and the relaxation time parameter of the fluid was enlarged, that’s why the Burger fluid velocity became lower. Also, in the fluid motion, the resistance became higher due to amplification of the relaxation time parameter which led to diminishing Burger fluid velocity. Figure 6 illustrated the consequence of the Burger nanofluid parameter β 2 for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) on the nanofluid velocity. From this study, it was perceived that the velocity of the Burger nanofluid for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) was diminished for the Burger nanofluid parameter β 2 . Similarly, the collision between the fluid particles was raised when the relaxation time parameter in terms of the Burger fluid parameter was intensified. Therefore, the Burger fluid velocity was lower for the Burger fluid parameter β 2 . The graphical relation between Deborah number β 3 and Burger nanofluid velocity for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) was discussed in Figure 7. In this, the increment in Burger nanofluid velocity for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) is noticed against larger values of Deborah number β 3 . The flow’s creep phenomena were manifested by the retardation time. The burger fluid velocity increased due to the retardation time in the fluid motion which was the time required for achieving shear stress. The shear stress of the burger nanofluid is larger with the enchantment of Deborah number β 3 which increased the velocity of the Burger fluid.

Figure 5 Change in nanofluid velocity due to β 1 {\beta }_{1} .
Figure 5

Change in nanofluid velocity due to β 1 .

Figure 6 Change in nanofluid velocity due to β 2 {\beta }_{2} .
Figure 6

Change in nanofluid velocity due to β 2 .

Figure 7 Change in nanofluid velocity due to β 3 {\beta }_{3} .
Figure 7

Change in nanofluid velocity due to β 3 .

6.3 Temperature profile

Figures 8–10 explain the influence of dimensionless heat generation parameter δ , Biot number Bi , and Prandtl number Pr on the Burger nanofluid temperature profile θ ( ξ ) for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . Figure 8 was constructed for the variation of Burger nanofluid temperature against heat generation parameter δ for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . From this investigation, it was clear that the enhancing estimations of heat generation parameter δ amplified the temperature of the Burger nanofluid for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . The reason was that the enhancement in heat generation parameter δ produced an additional amount of heat which augments the heat transmission feature of the flow system. That’s why the Burger fluid temperature becomes higher. Figure 9 explored the variation of Burger nanofluid temperature for growing values of thermal Biot number Bi for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . From this inquiry, it was examined that the temperature of the Burger nanoliquid was improved for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) with the enrichment of Bi . It was noticed that inside the fluid particles, the resistance of heat transport boost-up for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) when the thermal Biot number heightens. Furthermore, at the surface of the body, the rate of heat transport was decayed but the convection coefficient was increased. Then a lot of extra amounts of heat were transferred from the surface of the cylinder to the fluid particles that enhanced the fluid temperature. The change in the temperature of Burger nanofluid for higher estimation of Prandtl number Pr for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) was studied in Figure 10. From this, it was remarked that the decrement in Burger nanofluid temperature was inspected for the rising estimation of Prandtl number for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . Physically, the thermal diffusivity of the fluid was decayed due to the enhancement of Prandtl number because Prandtl number and thermal diffusivity were inversely proportional. That’s why the boundary layer thickness and fluid temperature were weaker.

Figure 8 Change in nanofluid temperature due to δ \delta .
Figure 8

Change in nanofluid temperature due to δ .

Figure 9 Change in nanofluid temperature due to Bi \text{Bi} .
Figure 9

Change in nanofluid temperature due to Bi .

Figure 10 Change in nanofluid temperature due to Pr \Pr .
Figure 10

Change in nanofluid temperature due to Pr .

6.4 Concentration profile

The consequence of Lewis number Le , Brownian motion parameter Nb , and thermophoresis parameter Nt on the concentration profile ϕ ( ξ ) for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) is elaborated in Figures 11–13. The significance of Lewis number Le for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) on the concentration of Burger nanofluid was intended in Figure 11. From this review, it was detected that the elevation in the concentration of Burger nanofluid was observed for increasing values of Lewis number Le for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . The graph of Burger nanofluid concentration for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) against the rising estimation of Nb was deliberated in Figure 12. The heightening impact of the concentration of Burger nanofluid for both stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) was distinguished for intensifying the estimation Nb . Figure 13 explained the significance of Nt on the concentration of Burger nanofluid for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) . From this, it was clear that the Burger nanofluid concentration decayed for both the stretching sheet ( γ = 0 ) and cylinder ( γ > 0 ) for escalating values of the thermophoresis parameter Nt .

Figure 11 Change in nanofluid concentration due to Le \text{Le} .
Figure 11

Change in nanofluid concentration due to Le .

Figure 12 Change in nanofluid concentration due to Nb \text{Nb} .
Figure 12

Change in nanofluid concentration due to Nb .

Figure 13 Change in nanofluid concentration due to Nt \text{Nt} .
Figure 13

Change in nanofluid concentration due to Nt .

7 Conclusion

In this study, the Burger nanofluid problem in the presence of convective heat and mass transport phenomena for both stretching sheet and cylinder was addressed. The heat source/sink effects were applied in the temperature equation for the investigation of the temperature field of the Burger nanofluid. By applying the HAM on the higher order nonlinear ODEs, the analytical resolution of this study was attained. Finally, the outcomes of numerous flow parameters were calculated and debated in detail. The key findings of the present analysis were

  • The Nusselt number was enhanced for both the stretching sheet and cylinder with the augmentation of the Biot number.

  • The declining performance in the Nusselt number was observed for intensifying the estimation of heat generation parameters for both the stretching sheet and cylinder.

  • The Burger nanofluid velocity was amplified for both stretching sheet and cylinder with the heightening of Deborah number.

  • For both the stretching sheet and cylinder, the higher estimation of heat generation parameter, Biot number, and Prandtl number enhanced the temperature of the Burger nanofluid.

  • Intensification in Burger nanofluid concentration is noted against the expanding values of Lewis number and Brownian motion parameter for both stretching sheet and cylinder.

  • For both stretching sheet and cylinder, the Burger fluid concentration is lower for thermophoresis parameter.

  1. Funding information: The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2022 (FF65).

  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.

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Received: 2022-01-11
Revised: 2022-02-15
Accepted: 2022-03-15
Published Online: 2022-04-01

© 2022 Muhammad Ramzan et al., published by De Gruyter

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

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  73. Design of thin-film configuration of SnO2–Ag2O composites for NO2 gas-sensing applications
  74. Study on stress distribution of SiC/Al composites based on microstructure models with microns and nanoparticles
  75. PVDF green nanofibers as potential carriers for improving self-healing and mechanical properties of carbon fiber/epoxy prepregs
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  78. Preparation and bonding mechanisms of polymer/metal hybrid composite by nano molding technology
  79. Damage self-sensing and strain monitoring of glass-reinforced epoxy composite impregnated with graphene nanoplatelet and multiwalled carbon nanotubes
  80. Thermal analysis characterisation of solar-powered ship using Oldroyd hybrid nanofluids in parabolic trough solar collector: An optimal thermal application
  81. Pyrene-functionalized halloysite nanotubes for simultaneously detecting and separating Hg(ii) in aqueous media: A comprehensive comparison on interparticle and intraparticle excimers
  82. Fabrication of self-assembly CNT flexible film and its piezoresistive sensing behaviors
  83. Thermal valuation and entropy inspection of second-grade nanoscale fluid flow over a stretching surface by applying Koo–Kleinstreuer–Li relation
  84. Mechanical properties and microstructure of nano-SiO2 and basalt-fiber-reinforced recycled aggregate concrete
  85. Characterization and tribology performance of polyaniline-coated nanodiamond lubricant additives
  86. Combined impact of Marangoni convection and thermophoretic particle deposition on chemically reactive transport of nanofluid flow over a stretching surface
  87. Spark plasma extrusion of binder free hydroxyapatite powder
  88. An investigation on thermo-mechanical performance of graphene-oxide-reinforced shape memory polymer
  89. Effect of nanoadditives on the novel leather fiber/recycled poly(ethylene-vinyl-acetate) polymer composites for multifunctional applications: Fabrication, characterizations, and multiobjective optimization using central composite design
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  92. Green synthesis of spinel copper ferrite (CuFe2O4) nanoparticles and their toxicity
  93. The effect of TaC and NbC hybrid and mono-nanoparticles on AA2024 nanocomposites: Microstructure, strengthening, and artificial aging
  94. Excited-state geometry relaxation of pyrene-modified cellulose nanocrystals under UV-light excitation for detecting Fe3+
  95. Effect of CNTs and MEA on the creep of face-slab concrete at an early age
  96. Effect of deformation conditions on compression phase transformation of AZ31
  97. Application of MXene as a new generation of highly conductive coating materials for electromembrane-surrounded solid-phase microextraction
  98. A comparative study of the elasto-plastic properties for ceramic nanocomposites filled by graphene or graphene oxide nanoplates
  99. Encapsulation strategies for improving the biological behavior of CdS@ZIF-8 nanocomposites
  100. Biosynthesis of ZnO NPs from pumpkin seeds’ extract and elucidation of its anticancer potential against breast cancer
  101. Preliminary trials of the gold nanoparticles conjugated chrysin: An assessment of anti-oxidant, anti-microbial, and in vitro cytotoxic activities of a nanoformulated flavonoid
  102. Effect of micron-scale pores increased by nano-SiO2 sol modification on the strength of cement mortar
  103. Fractional simulations for thermal flow of hybrid nanofluid with aluminum oxide and titanium oxide nanoparticles with water and blood base fluids
  104. The effect of graphene nano-powder on the viscosity of water: An experimental study and artificial neural network modeling
  105. Development of a novel heat- and shear-resistant nano-silica gelling agent
  106. Characterization, biocompatibility and in vivo of nominal MnO2-containing wollastonite glass-ceramic
  107. Entropy production simulation of second-grade magnetic nanomaterials flowing across an expanding surface with viscidness dissipative flux
  108. Enhancement in structural, morphological, and optical properties of copper oxide for optoelectronic device applications
  109. Aptamer-functionalized chitosan-coated gold nanoparticle complex as a suitable targeted drug carrier for improved breast cancer treatment
  110. Performance and overall evaluation of nano-alumina-modified asphalt mixture
  111. Analysis of pure nanofluid (GO/engine oil) and hybrid nanofluid (GO–Fe3O4/engine oil): Novel thermal and magnetic features
  112. Synthesis of Ag@AgCl modified anatase/rutile/brookite mixed phase TiO2 and their photocatalytic property
  113. Mechanisms and influential variables on the abrasion resistance hydraulic concrete
  114. Synergistic reinforcement mechanism of basalt fiber/cellulose nanocrystals/polypropylene composites
  115. Achieving excellent oxidation resistance and mechanical properties of TiB2–B4C/carbon aerogel composites by quick-gelation and mechanical mixing
  116. Microwave-assisted sol–gel template-free synthesis and characterization of silica nanoparticles obtained from South African coal fly ash
  117. Pulsed laser-assisted synthesis of nano nickel(ii) oxide-anchored graphitic carbon nitride: Characterizations and their potential antibacterial/anti-biofilm applications
  118. Effects of nano-ZrSi2 on thermal stability of phenolic resin and thermal reusability of quartz–phenolic composites
  119. Benzaldehyde derivatives on tin electroplating as corrosion resistance for fabricating copper circuit
  120. Mechanical and heat transfer properties of 4D-printed shape memory graphene oxide/epoxy acrylate composites
  121. Coupling the vanadium-induced amorphous/crystalline NiFe2O4 with phosphide heterojunction toward active oxygen evolution reaction catalysts
  122. Graphene-oxide-reinforced cement composites mechanical and microstructural characteristics at elevated temperatures
  123. Gray correlation analysis of factors influencing compressive strength and durability of nano-SiO2 and PVA fiber reinforced geopolymer mortar
  124. Preparation of layered gradient Cu–Cr–Ti alloy with excellent mechanical properties, thermal stability, and electrical conductivity
  125. Recovery of Cr from chrome-containing leather wastes to develop aluminum-based composite material along with Al2O3 ceramic particles: An ingenious approach
  126. Mechanisms of the improved stiffness of flexible polymers under impact loading
  127. Anticancer potential of gold nanoparticles (AuNPs) using a battery of in vitro tests
  128. Review Articles
  129. Proposed approaches for coronaviruses elimination from wastewater: Membrane techniques and nanotechnology solutions
  130. Application of Pickering emulsion in oil drilling and production
  131. The contribution of microfluidics to the fight against tuberculosis
  132. Graphene-based biosensors for disease theranostics: Development, applications, and recent advancements
  133. Synthesis and encapsulation of iron oxide nanorods for application in magnetic hyperthermia and photothermal therapy
  134. Contemporary nano-architectured drugs and leads for ανβ3 integrin-based chemotherapy: Rationale and retrospect
  135. State-of-the-art review of fabrication, application, and mechanical properties of functionally graded porous nanocomposite materials
  136. Insights on magnetic spinel ferrites for targeted drug delivery and hyperthermia applications
  137. A review on heterogeneous oxidation of acetaminophen based on micro and nanoparticles catalyzed by different activators
  138. Early diagnosis of lung cancer using magnetic nanoparticles-integrated systems
  139. Advances in ZnO: Manipulation of defects for enhancing their technological potentials
  140. Efficacious nanomedicine track toward combating COVID-19
  141. A review of the design, processes, and properties of Mg-based composites
  142. Green synthesis of nanoparticles for varied applications: Green renewable resources and energy-efficient synthetic routes
  143. Two-dimensional nanomaterial-based polymer composites: Fundamentals and applications
  144. Recent progress and challenges in plasmonic nanomaterials
  145. Apoptotic cell-derived micro/nanosized extracellular vesicles in tissue regeneration
  146. Electronic noses based on metal oxide nanowires: A review
  147. Framework materials for supercapacitors
  148. An overview on the reproductive toxicity of graphene derivatives: Highlighting the importance
  149. Antibacterial nanomaterials: Upcoming hope to overcome antibiotic resistance crisis
  150. Research progress of carbon materials in the field of three-dimensional printing polymer nanocomposites
  151. A review of atomic layer deposition modelling and simulation methodologies: Density functional theory and molecular dynamics
  152. Recent advances in the preparation of PVDF-based piezoelectric materials
  153. Recent developments in tensile properties of friction welding of carbon fiber-reinforced composite: A review
  154. Comprehensive review of the properties of fly ash-based geopolymer with additive of nano-SiO2
  155. Perspectives in biopolymer/graphene-based composite application: Advances, challenges, and recommendations
  156. Graphene-based nanocomposite using new modeling molecular dynamic simulations for proposed neutralizing mechanism and real-time sensing of COVID-19
  157. Nanotechnology application on bamboo materials: A review
  158. Recent developments and future perspectives of biorenewable nanocomposites for advanced applications
  159. Nanostructured lipid carrier system: A compendium of their formulation development approaches, optimization strategies by quality by design, and recent applications in drug delivery
  160. 3D printing customized design of human bone tissue implant and its application
  161. Design, preparation, and functionalization of nanobiomaterials for enhanced efficacy in current and future biomedical applications
  162. A brief review of nanoparticles-doped PEDOT:PSS nanocomposite for OLED and OPV
  163. Nanotechnology interventions as a putative tool for the treatment of dental afflictions
  164. Recent advancements in metal–organic frameworks integrating quantum dots (QDs@MOF) and their potential applications
  165. A focused review of short electrospun nanofiber preparation techniques for composite reinforcement
  166. Microstructural characteristics and nano-modification of interfacial transition zone in concrete: A review
  167. Latest developments in the upconversion nanotechnology for the rapid detection of food safety: A review
  168. Strategic applications of nano-fertilizers for sustainable agriculture: Benefits and bottlenecks
  169. Molecular dynamics application of cocrystal energetic materials: A review
  170. Synthesis and application of nanometer hydroxyapatite in biomedicine
  171. Cutting-edge development in waste-recycled nanomaterials for energy storage and conversion applications
  172. Biological applications of ternary quantum dots: A review
  173. Nanotherapeutics for hydrogen sulfide-involved treatment: An emerging approach for cancer therapy
  174. Application of antibacterial nanoparticles in orthodontic materials
  175. Effect of natural-based biological hydrogels combined with growth factors on skin wound healing
  176. Nanozymes – A route to overcome microbial resistance: A viewpoint
  177. Recent developments and applications of smart nanoparticles in biomedicine
  178. Contemporary review on carbon nanotube (CNT) composites and their impact on multifarious applications
  179. Interfacial interactions and reinforcing mechanisms of cellulose and chitin nanomaterials and starch derivatives for cement and concrete strength and durability enhancement: A review
  180. Diamond-like carbon films for tribological modification of rubber
  181. Layered double hydroxides (LDHs) modified cement-based materials: A systematic review
  182. Recent research progress and advanced applications of silica/polymer nanocomposites
  183. Modeling of supramolecular biopolymers: Leading the in silico revolution of tissue engineering and nanomedicine
  184. Recent advances in perovskites-based optoelectronics
  185. Biogenic synthesis of palladium nanoparticles: New production methods and applications
  186. A comprehensive review of nanofluids with fractional derivatives: Modeling and application
  187. Electrospinning of marine polysaccharides: Processing and chemical aspects, challenges, and future prospects
  188. Electrohydrodynamic printing for demanding devices: A review of processing and applications
  189. Rapid Communications
  190. Structural material with designed thermal twist for a simple actuation
  191. Recent advances in photothermal materials for solar-driven crude oil adsorption
https://doi.org/10.1515/ntrev-2022-0089
Keywords for this article
Burger nanofluid; heat transfer; stretching cylinder; homotopy analysis method
Creative Commons
BY 4.0

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  111. Analysis of pure nanofluid (GO/engine oil) and hybrid nanofluid (GO–Fe3O4/engine oil): Novel thermal and magnetic features
  112. Synthesis of Ag@AgCl modified anatase/rutile/brookite mixed phase TiO2 and their photocatalytic property
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  116. Microwave-assisted sol–gel template-free synthesis and characterization of silica nanoparticles obtained from South African coal fly ash
  117. Pulsed laser-assisted synthesis of nano nickel(ii) oxide-anchored graphitic carbon nitride: Characterizations and their potential antibacterial/anti-biofilm applications
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  119. Benzaldehyde derivatives on tin electroplating as corrosion resistance for fabricating copper circuit
  120. Mechanical and heat transfer properties of 4D-printed shape memory graphene oxide/epoxy acrylate composites
  121. Coupling the vanadium-induced amorphous/crystalline NiFe2O4 with phosphide heterojunction toward active oxygen evolution reaction catalysts
  122. Graphene-oxide-reinforced cement composites mechanical and microstructural characteristics at elevated temperatures
  123. Gray correlation analysis of factors influencing compressive strength and durability of nano-SiO2 and PVA fiber reinforced geopolymer mortar
  124. Preparation of layered gradient Cu–Cr–Ti alloy with excellent mechanical properties, thermal stability, and electrical conductivity
  125. Recovery of Cr from chrome-containing leather wastes to develop aluminum-based composite material along with Al2O3 ceramic particles: An ingenious approach
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  127. Anticancer potential of gold nanoparticles (AuNPs) using a battery of in vitro tests
  128. Review Articles
  129. Proposed approaches for coronaviruses elimination from wastewater: Membrane techniques and nanotechnology solutions
  130. Application of Pickering emulsion in oil drilling and production
  131. The contribution of microfluidics to the fight against tuberculosis
  132. Graphene-based biosensors for disease theranostics: Development, applications, and recent advancements
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  137. A review on heterogeneous oxidation of acetaminophen based on micro and nanoparticles catalyzed by different activators
  138. Early diagnosis of lung cancer using magnetic nanoparticles-integrated systems
  139. Advances in ZnO: Manipulation of defects for enhancing their technological potentials
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  141. A review of the design, processes, and properties of Mg-based composites
  142. Green synthesis of nanoparticles for varied applications: Green renewable resources and energy-efficient synthetic routes
  143. Two-dimensional nanomaterial-based polymer composites: Fundamentals and applications
  144. Recent progress and challenges in plasmonic nanomaterials
  145. Apoptotic cell-derived micro/nanosized extracellular vesicles in tissue regeneration
  146. Electronic noses based on metal oxide nanowires: A review
  147. Framework materials for supercapacitors
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  149. Antibacterial nanomaterials: Upcoming hope to overcome antibiotic resistance crisis
  150. Research progress of carbon materials in the field of three-dimensional printing polymer nanocomposites
  151. A review of atomic layer deposition modelling and simulation methodologies: Density functional theory and molecular dynamics
  152. Recent advances in the preparation of PVDF-based piezoelectric materials
  153. Recent developments in tensile properties of friction welding of carbon fiber-reinforced composite: A review
  154. Comprehensive review of the properties of fly ash-based geopolymer with additive of nano-SiO2
  155. Perspectives in biopolymer/graphene-based composite application: Advances, challenges, and recommendations
  156. Graphene-based nanocomposite using new modeling molecular dynamic simulations for proposed neutralizing mechanism and real-time sensing of COVID-19
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  158. Recent developments and future perspectives of biorenewable nanocomposites for advanced applications
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  160. 3D printing customized design of human bone tissue implant and its application
  161. Design, preparation, and functionalization of nanobiomaterials for enhanced efficacy in current and future biomedical applications
  162. A brief review of nanoparticles-doped PEDOT:PSS nanocomposite for OLED and OPV
  163. Nanotechnology interventions as a putative tool for the treatment of dental afflictions
  164. Recent advancements in metal–organic frameworks integrating quantum dots (QDs@MOF) and their potential applications
  165. A focused review of short electrospun nanofiber preparation techniques for composite reinforcement
  166. Microstructural characteristics and nano-modification of interfacial transition zone in concrete: A review
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  168. Strategic applications of nano-fertilizers for sustainable agriculture: Benefits and bottlenecks
  169. Molecular dynamics application of cocrystal energetic materials: A review
  170. Synthesis and application of nanometer hydroxyapatite in biomedicine
  171. Cutting-edge development in waste-recycled nanomaterials for energy storage and conversion applications
  172. Biological applications of ternary quantum dots: A review
  173. Nanotherapeutics for hydrogen sulfide-involved treatment: An emerging approach for cancer therapy
  174. Application of antibacterial nanoparticles in orthodontic materials
  175. Effect of natural-based biological hydrogels combined with growth factors on skin wound healing
  176. Nanozymes – A route to overcome microbial resistance: A viewpoint
  177. Recent developments and applications of smart nanoparticles in biomedicine
  178. Contemporary review on carbon nanotube (CNT) composites and their impact on multifarious applications
  179. Interfacial interactions and reinforcing mechanisms of cellulose and chitin nanomaterials and starch derivatives for cement and concrete strength and durability enhancement: A review
  180. Diamond-like carbon films for tribological modification of rubber
  181. Layered double hydroxides (LDHs) modified cement-based materials: A systematic review
  182. Recent research progress and advanced applications of silica/polymer nanocomposites
  183. Modeling of supramolecular biopolymers: Leading the in silico revolution of tissue engineering and nanomedicine
  184. Recent advances in perovskites-based optoelectronics
  185. Biogenic synthesis of palladium nanoparticles: New production methods and applications
  186. A comprehensive review of nanofluids with fractional derivatives: Modeling and application
  187. Electrospinning of marine polysaccharides: Processing and chemical aspects, challenges, and future prospects
  188. Electrohydrodynamic printing for demanding devices: A review of processing and applications
  189. Rapid Communications
  190. Structural material with designed thermal twist for a simple actuation
  191. Recent advances in photothermal materials for solar-driven crude oil adsorption
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