The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating

A numerical study of heat transfer from boundary layer flow driven by a continuous moving porous plate is proposed. The flow with electrically fluid due to the plate in the presence of a transverse magnetic field and Ohmic heating was molded as a steady, viscous, and incompressible. Both viscosity and thermal conductivity were variable and considered only a function of temperature. Similar analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for momentum and energy and determine the skin-friction coefficient and heat transfer rate. As the magnetic parameter and variable viscosity parameter increase, the fluid temperature and skin-friction coefficient increase and the fluid velocity and heat transfer rate decrease. The fluid temperature increases and heat transfer rate decreases with an increasing Eckert number and thermal conductivity parameter. The skin-friction coefficient and heat transfer rate increase, whereas the fluid velocity and temperature decrease as the wall suction velocity increase.     

The effects of variable fluid properties and thermocapillarity on the flow of a thin film on an unsteady stretching sheet

The effects of variable viscosity, variable thermal conductivity and thermocapillarity on the flow and heat transfer in a laminar liquid film on a horizontal stretching sheet is analyzed. Using a similarity transformation the governing time dependent boundary layer equations for momentum and thermal energy are reduced to a set of coupled ordinary differential equations. The resulting five-parameter problem is solved numerically for some representative value of the parameters. It is shown that the film thickness increases with the increase in viscosity of the fluid. In other words viscosity resists film thinning. Further it is shown that more heat flows out of the liquid through the stretching surface when conductivity increases with temperature than that for the case when conductivity decreases with temperature.     

Flow and heat transfer analysis of MHD third-grade fluid flow through a vertical microchannel subjected to entropy generation

This paper analyses the generation of entropy in an electrically conducting third-grade fluid through a vertical channel considering the variable thermal conductivity. Aspects of radiation, viscous dissipation, porous medium, Joule heating, convective boundary condition, and heat generation are studied. Nonlinear systems of ordinary differential equations are obtained via applying suitable dimensionless variables. After that, the system is solved with the aid of using the Runge–Kutta–Fehlberg method. The numerical solutions are used to characterize the irreversibility and irreversibility ratio. It is established that the entropy is enhanced with accelerating estimations of the third-grade material parameter, Brinkman number, magnetism, Biot number, porous parameter, and the impact is decelerated with elevating values of the radiation. The rate of heat transfer is higher for the Brinkman number, and a similar impact on drag force is noticed for magnetic and Grashof numbers. All the parameters on flow, temperature, fluid irreversibility and irreversibility ratio are discussed through graphical illustration.     

Entropy analysis of unsteady MHD three-dimensional flow of Williamson nanofluid over a convectively heated stretching sheet

This article addresses an investigation of the entropy analysis of Williamson nanofluid flow in the presence of gyrotactic microorganisms by considering variable viscosity and thermal conductivity over a convectively heated bidirectionally stretchable surface. Heat and mass transfer phenomena have been incorporated by taking into account the thermal radiation, heat source or sink, viscous dissipation, Brownian motion, and thermophoretic effects. The representing equations are nonlinear coupled partial differential equations and these equations are shaped into a set of ordinary differential equations via a suitable similarity transformation. The arising set of ordinary differential equations was then worked out by adopting a well-known scheme, namely the shooting method along with the Runge-Kutta-Felberge integration technique. The effects of flow and heat transfer controlling parameters on the solution variables are depicted and analyzed through the graphical presentation. The survey finds that magnifying viscosity parameter, Weissenberg number representing the non-Newtonian Williamson parameter cause to retard the velocity field in both the directions and thermal conductivity parameter causes to reduce fluid temperature. The study also recognizes that enhancing magnetic parameters and thermal conductivity parameters slow down the heat transfer rate. The entropy production of the system is estimated through the Bejan number. It is noticeable that the Bejan number is eminently dependent on the heat generation parameter, thermal radiation parameter, viscosity parameter, thermal conductivity parameter, and Biot number. The skillful accomplishment of the present heat and mass transfer system is achieved through the exteriorized choice of the pertinent parameters.     

Effects of thermal radiation and variable fluid viscosity on free convective flow and heat transfer past a porous stretching surface

Free convective boundary layer flow and heat transfer of a fluid with variable viscosity over a porous stretching vertical surface in presence of thermal radiation is considered. Fluid viscosity is assumed to vary as a linear function of temperature. The symmetry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations viz. scaling group of transformations. A third-order and a second-order coupled ordinary differential equations corresponding to the momentum and the energy equations are obtained. These equations are then solved numerically. It is found that the skin-friction decreases and heat transfer rate increases due to the suction parameter. Opposite nature is noticed in case of blowing. With the increase of temperature-dependent fluid viscosity parameter (i.e. with decreasing viscosity), the fluid velocity increases but the temperature decreases at a particular point of the sheet. Due to suction (injection) fluid velocity decreases (increases) at a particular point of the surface. Effects of increasing Prandtl number as well as radiation parameter on the velocity boundary layer is to suppress the velocity field and the temperature decreases with increasing value of Prandtl number. Due to increase in thermal radiation parameter, temperature at a point of the surface is found to decrease.     

Effects of variable thermophysical properties on mixed convection slip flow over a wedge

This paper reveals the characteristics of mixed convection slip flow of an electrically conducting fluid over a wedge subject to temperature dependent viscosity and thermal conductivity variations. The system of dimensionless nonsimilar governing equations has been solved by an implicit finite difference method. We also use stream‐function formulation to reduce the governing equations into a convenient form, which are valid for small and large time regimes. These are solved employing the perturbation method for small time and the asymptotic method for large time. Numerical solutions yield a good agreement with the series solutions. Because of the increase in the mixed convection parameter, the peak of the velocity profile increases whereas the maximum temperature decreases. In contrast, the local skin‐friction coefficient and local Nusselt number are found to increase with the mixed convection parameter. For higher values of the velocity slip and temperature jump conditions, the local skin‐friction coefficient and the local Nusselt number are found to increase. The viscosity parameter enhances the local skin friction and the local Nusselt number. But the converse characteristic is observed for the thermal conductivity parameter. The results could be used in microelectromechanical systems, fabrication, melting of polymers, polishing of artificial heart valves, etc.     

Combined influence of cross-diffusion and variable fluid properties on free convection flow past a vertical cone

The free convective flow of an incompressible viscous fluid over an isothermal vertical cone with variable viscosity and variable thermal conductivity is examined in the presence of the Soret and Dufour effects. As thermal and solutal boundary conditions at the cone's surface, the constant temperature and concentration (WTC) and constant heat and mass flux (HMF) cases are taken into account. The successive linearization method is applied to linearize a system of nonlinear differential equations that describes the flow under investigation. The numerical solution for the resulting linear equations is attained by means of the Chebyshev spectral method. The obtained numerical results are compared and found to be in good agreement with previously published results. The impact of significant parameters on the heat and mass transfer rates is evaluated and presented graphically for the WTC and HMF situations. In both cases, the Soret number increases the skin friction coefficient and rate of heat transfer while decreasing the Sherwood number. With an increase in the Dufour parameter, the coefficient of skin friction and Sherwood numbers increase while the heat transmission rate decreases.     

The eventuality of diffusiophoresis and chemical reaction in a flow with variable fluid properties through an upright channel

The quintessence of this article encompasses the effect of diffusiophoresis, chemical reaction, and varying viscosity as well as thermal conductivity on a fully developed dissipative flow through an upright channel. The fluid is electrically conducting undergoing mixed convection. The governing equations, after transfiguring into dimensionless formation, are solved through a numerical procedure for boundary value problems incorporating MATLAB solver. Imperative scrutiny is made to visualize associative impacts of flow parameters, namely, magnetic parameter, the Brinkmann number, the Schmidt number, variable viscosity parameter, variable thermal conductivity parameter, chemical reaction parameter, diffusiophoretic parameter, and particle diffusion parameter, on the flow. The velocity field, the temperature field, the solute concentration field, the particle concentration field, the skin friction, the Nusselt number, the Sherwood number, and the particle concentration gradient are assessed in view of alteration of the aforesaid parameters with the help of visual illustrations in graphical form and tabular form. Solute mass transposition and colloidal particle locomotion are the fresh inclusions to the scrutiny of upright channel flow in light of solving scheme of bvp4c. Chemical reaction engulfs both solute and particle concentration. Growing viscosity hinders the fluid velocity and heats up the flow encouraging interlayer friction.     

Thermochemistry and viscous heat dissipative effects on unsteady upper-convected Maxwell fluid flow past a stretching vertical plate with thermophysical variables

In this paper, unsteady upper-convected Maxwell fluid flow with variability in viscosity, thermal conductivity, and mass diffusivity is presented. The effects of chemical reaction, internal heat generation, and viscous dissipation with respect to variability properties were explored. The governing partial differential equations were transformed with the appropriate similarity transformation variables into nonlinear coupled ordinary differential equations. The spectral collocation method was used to solve the resulting ordinary differential equations. Hence, the effects of various parameters such as temperature-dependent viscosity and thermal conductivity, mass diffusivity parameters among others on velocity, temperature, concentration, skin friction, local heat and mass transfers were presented in graphs and tables. It is seen that heat and molecules of the fluid disperse faster as a result of destructive chemical reaction, while, the temperature-dependent viscosity and thermal conductivity gave increasing profiles of the momentum and thermal boundary layer. The viscous dissipative parameter generates heat and yields a buoyancy force in consequence.     

The effects of variable fluid properties on the hydro-magnetic flow and heat transfer over a non-linearly stretching sheet

The influence of temperature-dependent fluid properties on the hydro-magnetic flow and heat transfer over a stretching surface is studied. The stretching velocity and the transverse magnetic field are assumed to vary as a power of the distance from the origin. It is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. Using the similarity transformation, the governing coupled non-linear partial differential equations are transformed into coupled non-linear ordinary differential equations and are solved numerically by the Keller–Box method. The governing equations of the problem show that the flow and heat transfer characteristics depend on five parameters, namely the stretching parameter, viscosity parameter, magnetic parameter, variable thermal conductivity parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, skin friction, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are discussed.     

On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation,internal heat source and thermal radiation

In this paper we study the magneto-hydrodynamic flow and heat transfer of an electrically conducting, viscoelastic fluid past a stretching surface, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation. Closed-form solutions for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walters’ liquid B fluids. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with the existing literature. The effects of various physical parameters, such as viscoelasticity, magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail.     

Natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium

This work studies the natural convection heat transfer from an inclined wavy plate in a bidisperse porous medium with uniform wall temperature. The two-velocity two-temperature formulation is used to derive the governing equations of this system. The Prandtl coordinate transformation is used to transform the wavy surface into a regular plane, and the obtained equations are then simplified further by the order-of-magnitude analysis to give the boundary layer equations. The cubic spline collocation method is used to solve the boundary layer governing equations. The effects of dimensionless amplitude, angle of inclination, inter-phase heat transfer parameter, modified thermal conductivity ratio, and permeability ratio on the heat transfer and flow characteristics are studied. Increasing the modified thermal conductivity ratio and the permeability ratio can effectively enhance the natural convection heat transfer of the inclined plate in bidisperse porous media. Moreover, the thermal non-equilibrium effects are significant for low values of the inter-phase heat transfer parameter. As the dimensionless amplitude increases, both the fluctuations of the local Nusselt number for the f-phase and the p-phase with the streamwise coordinate are enhanced.     

Numerical study of fluid flow and heat transfer in microchannel cooling passages

Numerical investigation was conducted for fluid flow and heat transfer in microchannel cooling passages. Effects of viscosity and thermal conductivity variations on characteristics of fluid flow and heat transfer were taken into account in theoretical modeling. Two-dimensional simulation was performed for low Reynolds number flow of liquid water in a 100 μm single channel subjected to localized heat flux boundary conditions. The velocity field was highly coupled with temperature distribution and distorted through the variations of viscosity and thermal conductivity. The induced cross-flow velocity had a marked contribution to the convection. The heat transfer enhancement due to viscosity-variation was pronounced, though the axial conduction introduced by thermal-conductivity-variation was insignificant unless for the cases with very low Reynolds numbers.     

Natural convection boundary layer flow of a micropolar fluid over a vertical permeable cone with variable wall temperature

This work studies the natural convection boundary layer flow of a micropolar fluid near a vertical permeable cone with variable wall temperature. The transformed boundary layer governing equations are solved by the cubic spline collocation method. The local Nusselt numbers are presented as functions of suction variables for different values of vortex viscosity parameter, surface temperature exponent, and Prandtl number. Results show that the heat transfer rates of the permeable cones with higher suction variables are higher than those with lower suction variables. Moreover, the heat transfer rate from a vertical permeable cone in Newtonian fluids is higher than that in micropolar fluids.     

Flow and heat transfer in a power-law fluid over a stretching sheet with variable thermal conductivity and non-uniform heat source

In this paper the flow of a power-law fluid due to a linearly stretching sheet and heat transfer characteristics using variable thermal conductivity is studied in the presence of a non-uniform heat source/sink. The thermal conductivity is assumed to vary as a linear function of temperature. The similarity transformation is used to convert the governing partial differential equations of flow and heat transfer into a set of non-linear ordinary differential equations. The Keller box method is used to find the solution of the boundary value problem. The effect of power-law index, Chandrasekhar number, Prandtl number, non-uniform heat source/sink parameters and variable thermal conductivity parameter on the dynamics is analyzed. The skin friction and heat transfer coefficients are tabulated for a range of values of said parameters.     

A boundary layer analysis of heat transfer by free convection from permeable horizontal cylinders of elliptic cross-section in porous media using a thermal non-equilibrium model

This work uses a thermal non-equilibrium model to study the free convection boundary layer flow driven by temperature gradients near a permeable horizontal cylinder of elliptic cross-section with constant wall temperature in a fluid-saturated porous medium. A coordinate transformation is used to obtain the nonsimilar boundary layer equations. The transformed boundary layer equations are then solved by the cubic spline collocation method. Results for the local Nusselt numbers are presented as functions of the porosity scaled thermal conductivity ratio, the heat transfer coefficient between solid and fluid phases, the transpiration parameter, and the aspect ratio when the major axis of the elliptical cylinder is vertical (slender orientation) and horizontal (blunt orientation). An increase in the porosity scaled thermal conductivity ratio or the heat transfer coefficient between the solid and fluid phases increases the heat transfer rates. Moreover, the use of suction (positive transpiration parameter) tends to increase the heat transfer rates between the porous medium and the surface.     

A Thermal Nonequilibrium Approach to Natural Convection in a Square Enclosure Due to the Partially Cooled Sidewalls of the Enclosure

This article presents a numerical investigation of steady non-Darcy natural convection heat transfer in a square cavity filled with a heat-generating porous medium with partial cooling using a local thermal nonequilibrium (LTNE) model. Five different partial cooling boundary conditions and the fully cooled boundary condition are investigated under LTNE and local thermal equilibrium (LTE). The cooling portions of the left and the right sidewalls of the cavity are maintained at temperature T ₀ while the enclosure's top and bottom walls, as well as the inactive parts of its sidewalls, are kept insulated. The simulation results show that the placement order of wall cooling has a significant effect on the flow pattern and heat transfer rate. Compared with the fully cooled wall, the partially cooled wall of the cavity yielded a higher local Nusselt number for both fluid and solid phases. Under the same boundary conditions, the LTNE and LTE models can demonstrate significant differences in flow patterns and temperature fields. The total heat transfer rate increases with both Darcy number and Rayleigh number. Enhancement of interphase heat transfer coefficient (H) reduces the impact of Darcy number on the heat transfer rate of a porous cavity. Also, the total heat transfer rate of the porous medium decreases steadily with thermal conductivity ratio γ and interphase heat transfer coefficient H.     

Effects of variable electric conductivity and non-uniform heat source (or sink)on convective micropolar fluid flow along an inclined flat plate with surfaceheat flux

Numerical simulations have been carried out to investigate the effects of the fluid electric conductivity and non-uniform heat source (or sink) on two-dimensional steady hydromagnetic convective flow of a micropolar fluid (in comparison with the Newtonian fluid) flowing along an inclined flat plate with a uniform surface heat flux. The local similarity solutions are presented for the non-dimensional velocity distribution, microrotation, and temperature profiles in the boundary layer. The significance of the physical parameters on the flow field is discussed in detail. The results show that the values of the skin-friction coefficient and the Nusselt number are higher for the case of constant fluid electric conductivity compared with those for the variable fluid electric conductivity. The effect of temperature dependent heat generation is much stronger than the effect of surface dependent heat generation. The results also show that effects of the fluid electric conductivity and non-uniform heat generation in a micropolar fluid are less pronounced than that in a Newtonian fluid.     

Buoyancy and wall conduction effects on forced convection of micropolar fluid flow along a vertical slender hollow circular cylinder

This paper presents a numerical analysis of the flow and heat transfer characteristics of forced convection in a micropolar fluid flowing along a vertical slender hollow circular cylinder with wall conduction and buoyancy effects. The non-linear formulation governing equations and their associated boundary conditions are solved using the cubic spline collocation method and the finite difference scheme with a local non-similar transformation. This study investigates the effects of the conjugate heat transfer parameter, the Richardson number, the micropolar parameter, and the Prandtl number on the flow and the thermal fields. The effect of wall conduction on the thermal and the flow fields are found to be more pronounced in a system with a greater buoyancy effect or Prandtl number but is less sensitive with a greater micropolar material parameter. Compared to the case of pure forced convection, buoyancy effect is found to result in a lower interfacial temperature but higher the local heat transfer rate and the skin friction factor. Finally, compared to Newtonian fluid, an increase in the interfacial temperature, a reduction in the skin friction factor, and a reduction in the local heat transfer rate are identified in the current micropolar fluid case.     

Lie group analysis of hyperbolic tangent fluid flow in the presence of thermal radiation

The present study is devoted to the flow and heat transfer analysis of the hyperbolic tangent fluid through a stretching sheet by considering the effect of thermal radiation in addition to an applied transverse magnetic field, as well as thermal and velocity slip conditions. The Lie group analysis technique has been utilized for establishing similarity transformations, which effectively transform the governing equations to a system of nonlinear ordinary differential equations (ODEs). These ODEs are numerically solved by utilizing the shooting method. The heat transfer properties and flow features under the influence of various physical parameters are also studied. We noted that by increasing the thermal radiation parameter, the temperature profile increases and also the thermal boundary layer thickens. Furthermore, it is deduced that rising the thermal radiation parameter reduces the local Nusselt number. Moreover, the numerical results obtained are in agreement with the existing results in the literature.