Heat transfer and entropy generation analysis of non-Newtonian fluid flow through vertical microchannel with convective boundary condition

The entropy generation and heat transfer characteristics of magnetohydrodynamic(MHD) third-grade fluid flow through a vertical porous microchannel with a convective boundary condition are analyzed. Entropy generation due to flow of MHD non-Newtonian third-grade fluid within a microchannel and temperature-dependent viscosity is studied using the entropy generation rate and Vogel's model. The equations describing flow and heat transport along with boundary conditions are first made dimensionless using proper non-dimensional transformations and then solved numerically via the finite element method(FEM). An appropriate comparison is made with the previously published results in the literature as a limiting case of the considered problem.The comparison confirms excellent agreement. The effects of the Grashof number, the Hartmann number, the Biot number, the exponential space-and thermal-dependent heat source(ESHS/THS) parameters, and the viscous dissipation parameter on the temperature and velocity are studied and presented graphically. The entropy generation and the Bejan number are also calculated. From the comprehensive parametric study, it is recognized that the production of entropy can be improved with convective heating and viscous dissipation aspects. It is also found that the ESHS aspect dominates the THS aspect.     

Repercussion of Hall effect and nonlinear radiation on Couette-Poiseuille flow of Casson-Williamson fluid through upright microchannel

The main aim of the present work is to investigate the flow and heat transport properties of non-Newtonian Casson-Williamson fluid through an upright microchannel along with entropy generation analysis, and explore the effects of convective boundary conditions, Couette-Poiseuille flow, and nonlinear radiation. The movement of liquid is scrutinized with the Hall effect and exponential heat source. The rheological characteristics of the Casson-Williamson fluid model are also considered. By considering the desirable similarity variables, the equations of motion are reduced to nonlinear ordinary differential equations. The Runge-Kutta-Fehlberg fourth-fifth order method along with the shooting method is adopted to solve these dimensionless expressions. The detailed investigation is pictorially displayed to show the influence of effective parameters on the entropy generation and the Bejan number. One of the major tasks of the exploration is to compare the Casson fluid and the Williamson fluid. The results show that the rate of heat transfer in the Casson fluid is more remarkable than that in the Williamson fluid.     

Free convection heat and mass transfer with Hall current, Joule heating and thermal diffusion

A boundary layer analysis has been presented to study the combined effects of viscous dissipation, Joule heating, transpiration, heat source, thermal diffusion and Hall current on the hydromagnetic free convection and mass transfer flow of an electrically conducting, viscous, homogeneous, incompressible fluid past an infinite vertical porous plate. The governing partial differential equations of the hydromagnetic free convective boundary layer flow are reduced to non-linear ordinary differential equations and solutions for primary velocity, secondary velocity, temperature and concentration field are obtained for large suction. The expressions for the skin-friction, the heat transfer and the mass transfer are also derived. The results of the study are discussed through graphs and tables for different numerical values of the parameters entered into the equations governing the flow.     

Effect of slip velocity on Casson thin film flow and heat transfer due to unsteady stretching sheet in presence of variable heat flux and viscous dissipation

The aim of the present paper is to study flow and heat transfer characteristics of a viscous Casson thin film flow over an unsteady stretching sheet subject to variable heat flux in the presence of slip velocity condition and viscous dissipation. The governing equations are partial differential equations. They are reduced to a set of highly nonlinear ordinary differential equations by suitable similarity transformations. The resulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are made, and the results are found to be in excellent agreement. In the present work, the effects of the unsteadiness parameter, the Casson parameter, the Eckert number, the slip velocity parameter, and the Prandtl number on flow and heat transfer characteristics are discussed. Also, the local skin-friction coefficient and the local Nusselt number at the stretching sheet are computed and discussed.     

Transient free convection with mass transfer MHD micropolar fluid in a porous plate by the network method

The transient problem of coupled heat and mass transfer of a micropolar fluid in magneto‐hydrodynamic free convection from a vertical infinite porous plate with an exponentially decaying heat generating considering the viscous dissipation and ohmic heating effects is studied. Joule heating must be considered when the viscous dissipation and the Prandtl number are large. The non‐dimensional equations for the conservation of mass, momentum, energy and concentration are solved by means a numerical technique based on electric analogy (network simulation method). This method provides the numerical response of the system by running the network in circuit resolution software with the solution to both transient and steady‐state problems at the same time, and its programming does not require manipulation of the sophisticated mathematical software that is inherent in other numerical methods. The effects of the material parameters, viscous dissipation, internal generation and Joule heating on velocity, angular momentum and temperature fields across the boundary layer are investigated. In addition, the skin‐friction coefficient, couple stress coefficient, Nusselt number and Sherwood number are shown in tabular form. The numerical results for velocity and temperature distributions of micropolar fluids are compared with the corresponding flow problems for a Newtonian fluid. Copyright © 2007 John Wiley & Sons, Ltd.     

Steady mixed convection flow of Maxwell fluid over an exponentially stretching vertical surface with magnetic field and viscous dissipation

The steady mixed convection flow and heat transfer from an exponentially stretching vertical surface in a quiescent Maxwell fluid in the presence of magnetic field, viscous dissipation and Joule heating have been studied. The stretching velocity, surface temperature and magnetic field are assumed to have specific exponential function forms for the existence of the local similarity solution. The coupled nonlinear ordinary differential equations governing the local similarity flow and heat transfer have been solved numerically by Chebyshev finite difference method. The influence of the buoyancy parameter, viscous dissipation, relaxation parameter of Maxwell fluid, magnetic field and Prandtl number on the flow and heat transfer has been considered in detail. The Nusselt number increases significantly with the Prandtl number, but the skin friction coefficient decreases. The Nusselt number slightly decreases with increasing viscous dissipation parameter, but the skin friction coefficient slightly increases. Maxwell fluid reduces both skin friction coefficient and Nusselt number, whereas buoyancy force enhances them.     

Entropy analysis in electrical magnetohydrodynamic(MHD) flow of nanofluid with effects of thermal radiation,viscous dissipation,and chemical reaction

The unsteady mixed convection flow of electrical conducting nanofluid and heat transfer due to a permeable linear stretching sheet with the combined effects of an electric field, magnetic field, thermal radiation, viscous dissipation, and chemical reaction have been investigated. A similarity transformation is used to transform the constitutive equations into a system of nonlinear ordinary differential equations.The resultant system of equations is then solved numerically using implicit finite difference method.The velocity, temperature, concentration, entropy generation, and Bejan number are obtained with the dependence of different emerging parameters examined. It is noticed that the velocity is more sensible with high values of electric field and diminished with a magnetic field. The radiative heat transfer and viscous dissipation enhance the heat conduction in the system. Moreover, the impact of mixed convection parameter and Buoyancy ratio parameter on Bejan number profile has reverse effects. A chemical reaction reduced the nanoparticle concentration for higher values.     

Flow of variable thermal conductivity fluid due to inclined stretching cylinder with viscous dissipation and thermal radiation

The aim of the present study is to investigate the flow of the Casson fluid by an inclined stretching cylinder. A heat transfer analysis is carried out in the presence of thermal radiation and viscous dissipation effects. The temperature dependent thermal conductivity of the Casson fluid is considered. The relevant equations are first simplified under usual boundary layer assumptions, and then transformed into ordinary differential equations by suitable transformations. The transformed ordinary differential equations are computed for the series solutions of velocity and temperature. A convergence analysis is shown explicitly. Velocity and temperature fields are discussed for different physical parameters by graphs and numerical values. It is found that the velocity decreases with the increase in the angle of inclination while increases with the increase in the mixed convection parameter. The enhancement in the thermal conductivity and radiation effects corresponds to a higher fluid temperature. It is also found that heat transfer is more pronounced in a cylinder when it is compared with a flat plate. The thermal boundary layer thickness increases with the increase in the Eckert number. The radiation and variable thermal conductivity decreases the heat transfer rate at the surface.     

Radiation effects on combined convection over a vertical flat plate embedded in a porous medium of variable porosity

The present paper is concerned with the study of radiation effects on the combined (forced-free) convection flow of an optically dense viscous incompressible fluid over a vertical surface embedded in a fluid saturated porous medium of variable porosity with heat generation or absorption. The effects of radiation heat transfer from a porous wall on convection flow are very important in high temperature processes. The inclusion of radiation effects in the energy equation leads to a highly non-linear partial differential equations which are transformed to a system of ordinary differential equations using non-similarity transformation. These equations are then solved numerically using implicit finite-difference method subject to appropriate boundary and matching conditions. A parametric study of the physical parameters such as the particle diameter-based Reynolds number, the flow based Reynolds number, the Grashof number, the heat generation or absorption co-efficient and radiation parameter is conducted on temperature distribution. The effects of radiation and other physical parameters on the local skin friction and on local Nusselt number are shown graphically. It is interesting to observe that the momentum and thermal boundary layer thickness increases with the radiation and decrease with increase in the Prandtl number.     

MHD natural convection with Joule and viscous heating effects in iso-flux porous medium-filled enclosures

In this study, the magnetohydrodynamics （MHD） natural convection heat transfer with Joule and viscous heating effects inside an iso-flux porous medium-filled inclined rectangular enclosure is studied numerically. An iso-heat flux is applied for heating and cooling the two opposing walls of the enclosure while the other walls are adiabatic. The Forchheimer extension of Darcy-Oberbeck-Boussinesq and energy equations is transformed into a dimensionless form using a set of suitable variables instead of a finite difference scheme. The governing parameters are the magnetic influence number, the modified Rayleigh number, the inclination angle, and the aspect ratio of the enclosure. The results show that viscous and Joule heating effects decrease heat transfer rates.     

Flow and Heat Transfer of Viscous Fluids Saturated in Porous Media over a Permeable Non-isothermal Stretching Sheet

The present paper deals with the flow and heat transfer of a viscous fluid saturated in a porous medium past a permeable and non-isothermal stretching sheet with internal heat generation or absorption and radiation. Closed-form solutions to steady, two dimensional momentum equations with neglecting quadratic inertia terms and heat transfer equation are found using a similarity transformation. Asymptotic expressions of the temperature functions are also presented valid for both very large and very small modified Prandtl numbers. Attention is focused on the effects of porous parameter K, suction parameter R, radiation parameter Nr, viscosity ratio Λ, internal heat parameter α and Prandtl number P to the characteristics of flow and heat transfer.     

Magneto-hydrodynamic mixed convection of a power-law fluid past a stretching surface in the presence of thermal radiation and internal heat generation/absorption

The problem of magneto-hydrodynamic mixed convective flow and heat transfer of an electrically conducting, power-law fluid past a stretching surface in the presence of heat generation/absorption and thermal radiation has been analyzed. After transforming the governing equations with suitable dimensionless variables, numerical solutions are generated by an implicit finite-difference technique for the non-similar, coupled flow. The solution is found to be dependent on the governing parameters including the power-law fluid index, the magnetic field parameter, the modified Richardson number, the radiation parameter, the heat generation parameter, and the generalized Prandtl number. To reveal the tendency of the solutions, typical results for the velocity and temperature profiles, the skin-friction coefficient, and the local Nusselt number are presented for different values of these controlling parameters.     

Effect of viscous dissipation and heat source on flow and heat transfer of dusty fluid over unsteady stretching sheet

This paper investigates the problem of hydrodynamic boundary layer flow and heat transfer of a dusty fluid over an unsteady stretching surface.The study considers the effects of frictional heating(viscous dissipation) and internal heat generation or absorption.The basic equations governing the flow and heat transfer are reduced to a set of non-linear ordinary differential equations by applying suitable similarity transformations.The transformed equations are numerically solved by the Runge-Kutta-Fehlberg-45 order method.An analysis is carried out for two different cases of heating processes,namely,variable wall temperature(VWT) and variable heat flux(VHF).The effects of various physical parameters such as the magnetic parameter,the fluid-particle interaction parameter,the unsteady parameter,the Prandtl number,the Eckert number,the number density of dust particles,and the heat source/sink parameter on velocity and temperature profiles are shown in several plots.The effects of the wall temperature gradient function and the wall temperature function are tabulated and discussed.     

Low-speed peristaltic transport in a vertical channel subject to the Soret and Dufour effects

Simultaneous effects of heat and mass transfer in peristaltic transport of a viscous fluid are considered. Mathematical modeling is provided in the presence of the Joule heating and the Soret and Dufour effects. The analysis is performed using the long wavelength and low Reynolds number considerations. Perturbation solutions are obtained for a small Brinkman number.     

Thermal analysis in swirl motion of Maxwell nanofluid over a rotating circular cylinder

In this paper, the mechanism of thermal energy transport in swirling flow of the Maxwell nanofluid induced by a stretchable rotating cylinder is studied. The rotation of the cylinder is kept constant in order to avoid the induced axially secondary flow. Further, the novel features of heat generation/absorption, thermal radiation, and Joule heating are studied to control the rate of heat transfer. The effects of Brownian and thermophoretic forces exerted by the Maxwell nanofluid to the transport of thermal energy are investigated by utilizing an effective model for the nanofluid proposed by Buongiorno. The whole physical problem of fluid flow and thermal energy transport is modelled in the form of partial differential equations(PDEs) and transformed into nonlinear ordinary differential equations(ODEs) with the help of the suitable flow ansatz.Numerically acquired results through the technique bvp4c are reported graphically with physical explanation. Graphical analysis reveals that there is higher transport of heat energy in the Maxwell nanoliquid for a constant wall temperature(CWT) as compared with the prescribed surface temperature(PST). Both thermophoretic and Brownian forces enhance the thermal energy transport in the flowing Maxwell nanofluid. Moreover, the temperature distribution increases with increasing values of the radiation parameter and the Eckert number. It is also noted that an increase in Reynolds number reduces the penetration depth, and as a result the flow and transport of energy occur only near the surface of the cylinder.     

Hydromagnetic thin film flow of Casson fluid in non-Darcy porous medium with Joule dissipation and Navier's partial slip

In this paper, the effects of viscous and Ohmic heating and heat generation/absorption on magnetohydrodynamic flow of an electrically conducting Casson thin film fluid over an unsteady horizontal stretching sheet in a non-Darcy porous medium are investigated. The fluid is assumed to slip along the boundary of the sheet. Similarity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4 th order Runge-Kutta method is used to solve the transformed equations. Computations are carried out for velocity and temperature of the fluid thin film along with local skin friction coefficient and local Nusselt number for a range of values of pertinent flow parameters. It is observed that the Casson parameter has the ability to enhance free surface velocity and film thickness, whereas the Forchheimer parameter, which is responsible for the inertial drag has an adverse effect on the fluid velocity inside the film. The velocity slip along the boundary tends to decrease the fluid velocity. This investigation has various applications in engineering and in practical problems such as very large scale integration(VLSI) of electronic chips and film coating.     

Effects of thermophoresis particle deposition and of the thermal conductivity in a porous plate with dissipative heat and mass transfer

Network simulation method(NSM) is used to solve the laminar heat and mass transfer of an electricallyconducting,heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule heating problem. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations,in a single independent variable,η. The resulting coupled,nonlinear equations are solved under appropriate transformed boundary conditions. Computations are performed for a wide range of the governing flow parameters,viz Prandtl number,thermophoretic coeffcient(a function of Knudsen number),thermal conductivity parameter,wall transpiration parameter and Schmidt number. The numerical details are discussed with relevant applications. The present problem finds applications in optical fiber fabrication,aerosol filter precipitators,particle deposition on hydronautical blades,semiconductor wafer design,thermo-electronics and problems including nuclear reactor safety.     

Darcy-Forchheimer flow with nonlinear mixed convection

An analysis of the mixed convective flow of viscous fluids induced by a nonlinear inclined stretching surface is addressed. Heat and mass transfer phenomena are analyzed with additional effects of heat generation/absorption and activation energy, respectively. The nonlinear Darcy-Forchheimer relation is deliberated. The dimensionless problem is obtained through appropriate transformations. Convergent series solutions are obtained by utilizing an optimal homotopic analysis method (OHAM). Graphs depicting the consequence of influential variables on physical quantities are presented. Enhancement in the velocity is observed through the local mixed convection parameter while an opposite trend of the concentration field is noted for the chemical reaction rate parameter.     

Viscous Dissipation and Thermal Radiation Effects on Mixed Convection from a Vertical Plate in a Non-Darcy Porous Medium

The paper presents an investigation of the influence of thermal radiation and viscous dissipation on the mixed convective flow due to a vertical plate immersed in a non-Darcy porous medium saturated with a Newtonian fluid. The physical properties of the fluid are assumed to be constant. The Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing partial differential equations are transformed into a system of ordinary differential equations and solved numerically using a shooting method. The results are analyzed for the effects of various physical parameters such as viscous dissipation, thermal radiation, mixed convection parameters, and the modified Reynolds number on dynamics. The heat transfer coefficient is also tabulated for different values of the physical parameters.     

Entropy generation effects in a hydromagnetic free convection flow past a vertical oscillating plate

An unsteady free convective flow of a viscous fluid past an oscillating plate is considered, and the effects of entropy generation are investigated. The governing partial differential equations are normalized by using suitable transformations, and an exact solution of the problem is obtained by using the Laplace transformation technique. The expressions for the velocity and temperature are then used to compute the skin friction, Nusselt number, local entropy generation number, and Bejan number.