Search results

The study of instability due to the effects of Maxwell–Cattaneo law and internal heat source/sink on Casson dielectric fluid horizontal layer is an open question. Therefore, in this paper, the impact of internal heat generation/absorption on Rayleigh–Bénard convection in a non-Newtonian dielectric fluid with Maxwell–Cattaneo heat flux is investigated. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary.

The Casson fluid model is utilized to characterize the non-Newtonian fluid behavior. The horizontal layer of the fluid is cooled from the upper boundary, while an isothermal boundary condition is utilized at the lower boundary. The governing equations are non-dimensionalized using appropriate dimensionless variables and the subsequent equations are solved for the critical Rayleigh number using the normal mode technique (NMT).

Results are presented for two different cases namely dielectric Newtonian fluid (DNF) and dielectric non-Newtonian Casson fluid (DNCF). The effects of Cattaneo number, Casson fluid parameter, heat source/sink parameter on critical Rayleigh number and wavenumber are analyzed in detail. It is found that the value Rayleigh number for non-Newtonian fluid is higher than that of Newtonian fluid; also the heat source aspect decreases the magnitude of the Rayleigh number.

The effect of Maxwell–Cattaneo heat flux and internal heat source/sink on Rayleigh-Bénard convection in Casson dielectric fluid is investigated for the first time.

The objectives of present communication are threefolds. First is to model and analyze the two-dimensional Darcy-Forchheimer flow of Maxwell fluid induced by a stretching surface. Temperature-dependent thermal conductivity is taken into account. Second is to examine the heat transfer process through non-classical flux by Cattaneo-Christov theory. Third is to derive convergent homotopic solutions for velocity and temperature distributions. The paper aims to discuss these issues.

The resulting non-linear system is solved through the homotopy analysis method.

An increment in Deborah number β causes a reduction in velocity field f′(η) while opposite behavior is observed for temperature field θ(η). Velocity field f′(η) and thickness of momentum boundary layer are decreased when the authors enhance the values of porosity parameter λ while opposite behavior is noticed for temperature profile θ(η). Temperature field θ(η) is inversely proportional to the thermal relaxation parameter γ. The numerical values of temperature gradient at the sheet − θ′(0) are higher for larger values of thermal relaxation parameter γ.

To the best of author’s knowledge, no such consideration has been given in the literature yet.

This paper aims to present the effect of entropy generation on the unsteady flow of upper-convected Maxwell nanofluid past a wedge embedded in a porous medium in view of buoyancy force. Cattaneo-Christov double diffusion theory simulates the processes of energy phenomenon and mass transfer. Meanwhile, Brownian motion, thermophoresis and convective boundary conditions are discussed to further visualize the heat and mass transfer properties.

Coupled ordinary differential equations are gained by appropriate similar transformations and these equations are manipulated by the Homotopy analysis method.

The result is viewed that velocity distribution is a diminishing function with boosting the value of unsteadiness parameter. Moreover, fluid friction irreversibility is dominant as the enlargement in Brinkman number. Then controlling the temperature and concentration difference parameters can effectively regulate entropy generation.

This paper aims to address the effect of entropy generation on unsteady flow, heat and mass transfer of upper-convected Maxwell nanofluid over a stretched wedge with Cattaneo-Christov double diffusion, which provides a theoretical basis for manufacturing production.

This study presents a mathematical approach and model that can be useful to investigate the thermal performance of fluids with microstructures via hybrid nanoparticles in conventional fluid. It has been found from the extensive literature survey that no study has been conducted to investigate buoyancy effects on the flow of Maxwell fluid comprised of hybrid microstructures and heat generation aspects through the non-Fourier heat flux model.

Non-Fourier heat flux model and non-Newtonian stress–strain rheology with momentum and thermal relaxation phenomena are used to model the transport of heat and momentum in viscoelastic fluid over convectively heated surface. The role of suspension of mono and hybrid nanostructures on an increase in the thermal efficiency of fluid is being used as a medium for transportation of heat energy. The governing mathematical problems with thermo-physical correlations are solved via shooting method.

It is noted from the simulations that rate of heat transfer is much faster in hybrid nanofluid as compare to simple nanofluid with the increasing heat-generation coefficient. Additionally, an increment in the thermal relaxation time leads to decrement in the reduced skin friction coefficient; however, strong behavior of Nusselt number is shown when thermal relaxation time becomes larger for hybrid nanofluid as well as simple nanofluid.

According to the literature survey, no investigation has been made on buoyancy effects of Maxwell fluid flow with hybrid microstructures and heat generation aspects through non-Fourier heat flux model. The authors confirm that this work is original, and it has neither been published elsewhere nor is it currently under consideration for publication elsewhere.

This paper aims to describe the laminar flow of Maxwell fluid past a non-isothermal rigid plate with a stream wise pressure gradient. Heat transfer mechanism is analyzed in the context of non-Fourier heat conduction featuring thermal relaxation effects.

Flow field is permeated to uniform transverse magnetic field. The governing transport equations are changed to globally similar ordinary differential equations, which are tackled analytically by homotopy analysis technique. Homotopy analysis method-Padè approach is used to accelerate the convergence of homotopy solutions. Also, numerical approximations are made by means of shooting method coupled with fifth-order Runge-Kutta method.

The solutions predict that fluid relaxation time has a tendency to suppress the hydrodynamic boundary layer. Also, heat penetration depth reduces for increasing values of thermal relaxation time. The general trend of wall temperature gradient appears to be similar in Fourier and Cattaneo–Christov models.

An important implication of current research is that the thermal relaxation time considerably alters the temperature and surface heat flux.

Current problem even in case of Newtonian fluid has not been attempted previously.

The purpose of this paper is to introduce the Cattaneo-Christov heat flux model for an Oldroyd-B fluid.

Cattaneo-Christov heat flux model is utilized for the heat transfer analysis instead of Fourier’s law of heat conduction. Analytical solutions of nonlinear problems are computed.

The authors found that the temperature is decreased with an increase in relaxation time of heat flux but temperature gradient is enhanced.

No such analysis exists in the literature yet.

The purpose of this paper is to investigate the two-dimensional stagnation-point flow, heat and mass transfer of an incompressible upper-convected Oldroyd-B MHD nanofluid over a stretching surface with convective heat transfer boundary condition in the presence of thermal radiation, Brownian motion, thermophoresis and chemical reaction. The process of heat and mass transfer based on Cattaneo–Christov double-diffusion model is studied, which can characterize the features of thermal and concentration relaxations factors.

The governing equations are developed and similarly transformed into a set of ordinary differential equations, which are solved by a newly approximate analytical method combining the double-parameter transformation expansion method with the base function method (DPTEM-BF).

An interesting phenomenon can be found that all the velocity profiles first enhance up to a maximal value and then gradually drop to the value of the stagnation parameter, which indicates the viscoelastic memory characteristic of Oldroyd-B fluid. Moreover, it is revealed that the thickness of the thermal and mass boundary layer is increasing with larger values of thermal and concentration relaxation parameters, which indicates that Cattaneo–Christov double-diffusion model restricts the heat and mass transfer comparing with classical Fourier’s law and Fick’s law.

This paper focuses on stagnation-point flow, heat and mass transfer combining the constitutive relation of upper-convected Oldroyd-B fluid and Cattaneo–Christov double diffusion model.

The purpose of current flow configuration is to spotlights the thermophysical aspects of magnetohydrodynamics (MHD) viscoinelastic fluid flow over a stretching surface.

The fluid momentum problem is mathematically formulated by using the Prandtl–Eyring constitutive law. Also, the non-Fourier heat flux model is considered to disclose the heat transfer characteristics. The governing problem contains the nonlinear partial differential equations with appropriate boundary conditions. To facilitate the computation process, the governing problem is transmuted into dimensionless form via appropriate group of scaling transforms. The numerical technique shooting method is used to solve dimensionless boundary value problem.

The expressions for dimensionless velocity and temperature are found and investigated under different parametric conditions. The important features of fluid flow near the wall, i.e. wall friction factor and wall heat flux, are deliberated by altering the pertinent parameters. The impacts of governing parameters are highlighted in graphical as well as tabular manner against focused physical quantities (velocity, temperature, wall friction factor and wall heat flux). A comparison is presented to justify the computed results, it can be noticed that present results have quite resemblance with previous literature which led to confidence on the present computations.

The computed results are quite useful for researchers working in theoretical physics. Additionally, computed results are very useful in industry and daily-use processes.

The purpose of this paper is to focus on MHD unsteady flow of Carreau fluid over a variable thickness melting surface in the presence of chemical reaction and non-uniform heat sink/source.

The flow governing partial differential equations are transformed into ordinary ones with the help of similarity transformations. The set of ODEs are solved by a shooting technique together with the R.K.–Fehlberg method. Further, the graphs are depicted to scrutinize the velocity, concentration and temperature fields of the Carreau fluid flow. The numerical values of friction factor, heat and mass transfer rates are tabulated.

The results are presented for both Newtonian and non-Newtonian fluid flow cases. The authors conclude that the nature of three typical fields and the physical quantities are alike in both cases. An increase in melting parameter slows down the velocity field and enhances the temperature and concentration fields. But an opposite outcome is noticed with thermal relaxation parameter. Also the elevating values of thermal relaxation parameter/ wall thickness parameter/Prandtl number inflate the mass and heat transfer rates.

This is a new research article in the field of heat and mass transfer in fluid flows. Cattaneo–Christov heat flux model is used. The surface of the flow is assumed to be melting.

The purpose of this paper is to explore the novel aspects of activation energy in the nonlinearly convective flow of Walter-B nanofluid in view of Cattaneo–Christov double-diffusion model over a permeable stretched sheet. Features of nonlinear thermal radiation, dual stratification, non-uniform heat generation/absorption, MHD and binary chemical reaction are also evaluated for present flow problem. Walter-B nanomaterial model is employed to describe the significant slip mechanism of Brownian and thermophoresis diffusions. Generalized Fourier’s and Fick’s laws are examined through Cattaneo–Christov double-diffusion model. Modified Arrhenius formula for activation energy is also implemented.

Several techniques are employed for solving nonlinear differential equations. The authors have used a homotopy technique (HAM) for our nonlinear problem to get convergent solutions. The homotopy analysis method (HAM) is a semi-analytical technique to solve nonlinear coupled ordinary/partial differential equations. The capability of the HAM to naturally display convergence of the series solution is unusual in analytical and semi-analytic approaches to nonlinear partial differential equations. This analytical method has the following great advantages over other techniques:

• It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

• It guarantees the convergence of series solutions for nonlinear problems.

• It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

It provides a series solution without depending upon small/large physical parameters and applicable for not only weakly but also strongly nonlinear problems.

It guarantees the convergence of series solutions for nonlinear problems.

It provides us a great choice to select the base function of the required solution and the corresponding auxiliary linear operator of the homotopy.

Brief mathematical description of HAM technique (Liao, 2012; Mabood et al., 2016) is as follows. For a general nonlinear equation:

where N denotes a nonlinear operator, x the independent variables and u(x) is an unknown function, respectively. By means of generalizing the traditional homotopy method, Liao (1992) creates the so-called zero-order deformation equation:

here q∈[0, 1] is the embedding parameter, H(x) ≠ 0 is an auxiliary function, h(≠ 0) is a nonzero parameter, L is an auxiliary linear operator, u_o(x) is an initial guess of u(x) and u ˆ ( x ; q ) is an unknown function, respectively. It is significant that one has great freedom to choose auxiliary things in HAM. Noticeably, when q=0 and q=1, following holds:

Expanding u ˆ ( x ; q ) in Taylor series with respect to (q), we have:

If the initial guess, the auxiliary linear operator, the auxiliary h and the auxiliary function are selected properly, then the series (4) converges at q=1, then we have:

By defining a vector u → = ( u o ( x ) , u 1 ( x ) , u 2 ( x ) , … , u n ( x ) ) , and differentiating Equation (2) m-times with respect to (q) and then setting q=0, we obtain the mth-order deformation equation:

where:

Applying L⁻¹ on both sides of Equation (6), we get:

In this way, we obtain u_m for m ⩾ 1, at mth-order, we have:

It is evident from obtained results that the nanoparticle concentration field is directly proportional to the chemical reaction with activation energy. Additionally, both temperature and concentration distributions are declining functions of thermal and solutal stratification parameters (P₁) and (P₂), respectively. Moreover, temperature Θ(Ω₁) enhances for greater values of Brownian motion parameter (N_b), non-uniform heat source/sink parameter (B₁) and thermophoresis factor (N_t). Reverse behavior of concentration ϒ(Ω₁) field is remarked in view of (N_b) and (N_t). Graphs and tables are also constructed to analyze the effect of different flow parameters on skin friction coefficient, local Nusselt number, Sherwood numbers, velocity, temperature and concentration fields.

The novelty of the present problem is to inspect the Arrhenius activation energy phenomena for viscoelastic Walter-B nanofluid model with additional features of nonlinear thermal radiation, non-uniform heat generation/absorption, nonlinear mixed convection, thermal and solutal stratification. The novel aspect of binary chemical reaction is analyzed to characterize the impact of activation energy in the presence of Cattaneo–Christov double-diffusion model. The mathematical model of Buongiorno is employed to incorporate Brownian motion and thermophoresis effects due to nanoparticles.