Effect of non-uniform slot injection (suction) on a forced flow over a slender cylinder

An analysis is performed to obtain the non-similar solution of a steady laminar forced convection boundary layer flow over a horizontal slender cylinder including the effect of non-uniform slot injection (suction). The effects of transverse curvature and viscous dissipation are also included in the analysis. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form using suitable transformations and the resulting system of nonlinear coupled partial differential equations is then solved by an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results for the effect of non-uniform slot injection (suction) on skin friction coefficient and heat transfer rate are presented. The effects of transverse curvature, viscous dissipation and Prandtl number on velocity and temperature profiles and skin friction and heat transfer coefficients are also reported.     

Heat transfer in a liquid film over an unsteady stretching sheet

The effects of viscous dissipation, non-uniform heat source/sink, magnetic field, and thermal radiation on heat transfer characteristics of a thin liquid film flow over an unsteady stretching sheet are analyzed. A similarity transformation is used to reduce the governing time dependent momentum and energy equations into non-linear ordinary differential equations. The resulting differential equations with the appropriate boundary conditions are solved by an efficient shooting algorithm with fourth order Runge–Kutta technique. The effects of the physical parameters on the flow and heat transfer characteristics are presented through graphs and analyzed. The numerical results for the wall temperature gradient (Nusselt number) are calculated and presented through tables. Also, the effects of the physical parameters on the heat transfer characteristics are brought out: suggestions are made for efficient cooling. Furthermore, the limiting cases are obtained and are found to be in good agreement with the previously published results.     

Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source

In this paper, visco-elastic boundary layer flow and heat transfer over a stretching sheet in presence of viscous dissipation and non-uniform heat source have been discussed. Analytical solutions of highly non-linear momentum equation and confluent hypergeometric similarity solution of heat transfer equations are obtained. Here two types of different heating processes are considered namely (i) prescribed surface temperature (PST) and (ii) prescribed wall heat flux (PHF). The effect of various parameters like visco-elastic parameter, Eckert number, Prandtl number, and non-uniform heat source/sink parameter on temperature distribution are analyzed and effect of all these parameters on wall temperature gradient and wall temperature are tabulated and 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.     

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.     

Numerical study of Williamson fluid flow and heat transfer over a permeable stretching cylinder with the effects of Joule heating and heat generation/absorption

The present study aims to discuss the Williamson fluid flow and heat transfer across a permeable stretching cylinder with heat generation/absorption effects. The effects of viscous dissipation, Joule heating, and magnetic field are also taken into account. The BVP-4C numerical solver in MATLAB is adopted for all the numerical simulations in the present study. For this, the modeled partial differential equations are translated into dimensionless ordinary differential equations using some well-developed similarity transformations. A good agreement between the numerical results of the present study and existing literature is exhibited. The dimensionless physical parameters being investigated are Reynolds number, magnetic field parameter, suction parameter, heat source/sink parameter, Williamson fluid parameter, and mixed convection parameter. The numerical calculations are also performed for the skin friction coefficient and local Nusselt number to get an understanding of the shear stress rate and heat transfer rate, respectively. Furthermore, the impact of all these physical parameters on the velocity and temperature profiles is investigated and represented throughout the literature.     

Non-uniform double slot injection (suction) on a forced flow over a slender cylinder

A general analysis has been developed to investigate the influence of non-uniform double slot injection (suction) on the steady non-similar incompressible laminar boundary layer flow over a slender cylinder, where the slender cylinder is inline with the flow. Non-similar solutions are obtained starting from the origin of the stream-wise coordinate along the stream-wise direction by using an implicit finite difference scheme in combination with the quasilinearization technique. Numerical results are reported to display the effects of non-uniform double slot injection/suction on skin friction coefficient and heat transfer rate at the wall. Further, the effects of viscous dissipation and Prandtl number on velocity and temperature profile, and skin friction and heat transfer co-efficients are also presented in this paper.     

MHD non-Darcian mixed convection heat and mass transfer over a non-linear stretching sheet with Soret-Dufour effects and chemical reaction

A study has been carried out to analyze the effects of variable thermal conductivity, Soret (thermal-diffusion) and Dufour (diffusion-thermo) on MHD non-Darcy mixed convection heat and mass transfer over a non-linear stretching sheet embedded in a saturated porous medium in the presence of thermal radiation, viscous dissipation, non-uniform heat source/sink and first-order chemical reaction. The governing differential equations transform into a set of non-linear coupled ordinary differential equations using similarity analysis. Similarity equations are then solved numerically using shooting algorithm with Runge-Kutta Fehlberg integration scheme over the entire range of physical parameters. A comparison with previously published work has been carried out and the results are found to be in good agreement. Graphical presentation of the local skin-friction coefficient, the local Nusselt number and the local Sherwood number as well as the temperature profiles show interesting features of the physical parameters.     

Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity

In this paper we have analyzed the combined effects of magnetic field and convective diffusion of species through a non-Darcy porous medium over a vertical stretching sheet with temperature dependent viscosity and non-uniform heat source/sink. The boundary layer equations are transformed into ordinary differential equations using self-similarity transformation which are then solved numerically using fifth-order Runge–Kutta Fehlberg method with shooting technique for various values of the governing parameters. The effects of electric field parameter, non-uniform heat source/sink parameters and Schmidt number on concentration profiles are analyzed and discussed graphically. Favorable comparisons with previously published work on various special cases of the problem are obtained.     

Heat and mass transfer flow over a stretching surface with Ohmic heating and chemical reaction

The present study analyzes the effect of chemical reaction on an unsteady magnetohydrodynamic boundary layer viscous fluid over a stretching surface embedded in a porous medium with a uniform transverse magnetic field. A Darcy‐Forchheimer drag force model is employed to simulate the effect of second‐order porous resistance. Dissipative heat energy based on both viscous and Joule dissipation along with a heat source/sink is considered to enhance the energy equation. Similarity analysis is imposed to transform the governing differential equations into a set of nonlinear coupled ordinary differential equations. These sets of equations are solved numerically using the Runge‐Kutta fourth‐order scheme followed by the shooting algorithm. The effects of physical parameters such as magnetic field, Prandtl number, Eckert number, Schmidt number, unsteadiness parameter, and chemical reaction parameters have been discussed on velocity, temperature, and concentration fields. Computation for the coefficient of skin friction, rate of heat and mass transfer is done and presented in a table for validation of the present outcomes.     

Effect of Viscous Dissipation and Internal Heat Generation/Absorption on Heat Transfer Flow Over a Moving Wedge With Convective Boundary Condition

In this study, the effects of viscous dissipation and internal heat generation/absorption on heat transfer viscous flow over a moving wedge in the presence of suction or injection with a convective boundary condition have been carried out numerically for various values of dimensionless parameters. With the help of similarity transformation, the momentum and energy equations are reduced to a set of coupled non‐linear ordinary differential equations. These equations are solved using the Runge–Kutta fourth‐order method with a shooting technique. The variation in the dimensionless temperature, velocity, heat transfer coefficient, and shear stress have been presented in tabular as well as in graphical form for a range of controlling parameters. It is shown that the dimensionless heat transfer rate is a strong function of viscous dissipation and convective parameters and heat transfer shows an enhanced behavior with the stretching parameter for both the favorable and unfavorable regimes. It is also shown that in the presence of a heat source, the dimensionless temperature and its gradients in thermal boundary layers are found to be high for a high value of the convection parameter. The comparison of present results with the available data shows a good agreement. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 42(7): 589–602, 2013; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21055     

Nonlinear convective boundary layer flow of micropolar‐couple stress nanofluids past permeable stretching sheet using Cattaneo‐Christov heat and mass flux model

The present work aims to examine the effects of viscous dissipation and unsteadiness parameters on nonlinear convective laminar boundary layer flow of micropolar‐couple stress nanofluid past a permeable stretching sheet with non‐Fourier heat flux model in the presence of suction/injection variable. The unsteadiness in the flow, temperature, and concentration profile is caused by the time‐dependence of the stretching velocity, surface temperature, and surface concentration of the boundary layer flow. Similarity transformation is applied to transform the time‐dependent boundary layer flow equations into the corresponding highly nonlinear coupled ordinary differential equations with appropriate boundary conditions. The robust numerical technique called Galerkin finite element method is used to solve the obtained dimensionless governing equations of the flow. The effects of Eckert number, unsteadiness parameter, suction/injection parameter, mixed convection parameter, material parameter, Schmidt number, and couple stress parameter on linear velocity, angular velocity, temperature, concentration, local skin friction coefficient, local wall couple stress, local Nusselt number, and local Sherwood number is analyzed with the help of graphical and tabular form. Under special conditions, the present result is compared with the existing literature and revealed good agreement. Our result shows that as unsteadiness parameter boost, both heat and mass transfer rate rises. The present study has a significant application in material processing technology.     

Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet

The article examines the hydromagnetic laminar boundary layer flow and heat transfer in a power law fluid over a stretching surface. The flow is influenced by linear stretching of the sheet. Also the energy equation with temperature-dependent thermal conductivity, thermal radiation, work done by stress, viscous dissipation and internal heat generation is considered. The governing partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by Keller–Box method. The effects of various physical parameters on the flow and heat transfer characteristics are presented graphically and discussed.     

Unsteady mixed convection flow over a vertical wedge

The behavior of unsteady mixed convection flow of an incompressible viscous fluid over a vertical wedge with constant suction/injection have been investigated. The unsteadiness is due to the time-dependent free stream velocity. The governing boundary layer equations along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then resulting system of coupled non-linear partial differential equations is solved by an implicit finite-difference scheme in combination with the quasi-linearization technique. Numerical results for the effects of various parameters on velocity, temperature and concentration profiles and on their gradient at the wall are reported in the present study. The buoyancy force causes considerable velocity overshoot for low Prandtl number (Pr) fluids. Skin friction coefficient, heat and concentration transfer rates are found to alter significantly due to injection/suction for both accelerating and decelerating flow.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Heat transfer over a nonlinearly stretching sheet with non-uniform heat source and variable wall temperature

In this paper we study the flow and heat transfer characteristics of a viscous fluid over a nonlinearly stretching sheet in the presence of non-uniform heat source and variable wall temperature. A similarity transformation is used to transform the governing partial differential equations to a system of nonlinear ordinary differential equations. An efficient numerical shooting technique with a fourth-order Runge–Kutta scheme is used to obtain the solution of the boundary value problem. The effects of various parameters (such as the power law index n, the Prandtl number Pr, the wall temperature parameter λ, the space dependent heat source parameter A¹ and the temperature dependent heat source parameter B¹) on the heat transfer characteristics are analyzed. The numerical results for the heat transfer coefficient (the Nusselt number) are presented for several sets of values of the parameters and are discussed. The results reveal many interesting behaviors that warrant further study on the effects of non-uniform heat source and the variable wall temperature on the heat transfer phenomena at the nonlinear stretching sheet.     

Symmetry analysis of MHD Casson fluid flow for heat and mass transfer near a stagnation point over a linearly stretching sheet with variable viscosity and thermal conductivity

In this article, the impacts of variable viscosity and thermal conductivity on magnetohydrodynamic, heat transfer, and mass transfer flow of a Casson fluid are analyzed on a linearly stretching sheet inserted in a permeable medium along with heat source/sink and viscous dissipation. To reduce the ascendant partial differential equations into ordinary differential equations, Lie group transformation is utilized. Further, the fourth-order Runge–Kutta strategy is utilized to solve the ordinary differential equations numerically. The numerical results obtained for various parameters by employing coding in MATLAB programming are investigated and considered through graphical representation and tables. We anatomize the impacts of distinctive parameters on velocity, temperature, and concentration distributions.     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Effect of heat source/sink on MHD flow due to porous rotating disk with variable thickness in the presence of cross diffusion

An analysis of steady magnetohydrodynamic axisymmetric flow of a viscous incompressible electrically conducting fluid due to porous rotating disk with variable thickness in the presence of heat source/sink is presented. Soret and Dufour effects (cross‐diffusion) are also considered. The governing partial differential equations are transformed into a system of nonlinear ordinary differential equations. The homotopy analysis method is used to solve the resulting coupled nonlinear equations under appropriate transformed boundary conditions. A parametric study of the physical parameters is made and results are presented through graphs and tables. The results indicate that the thermal boundary layer is thicker for the flow problems having a heat source when compared with that of the problems without a heat source. It is also found that thickness of the disk is having a high impact on fluid velocity, temperature, and concentration.     

Flow and heat transfer over an unsteady stretching surface with non-uniform heat source

The non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity is studied. The boundary layer equations are transformed by using similarity analysis to be a set of ordinary differential equations containing three parameters: unsteadiness parameter (S), space-dependent parameter (A?) and temperature-dependent parameter (B?) for heat source/sink. The velocity and temperature fields are solved using the Chebyshev finite difference method (ChFD). Results showed that the heat transfer rate, − θ′(0) and the skin friction, − f″(0) increase as the unsteadiness parameter increases whereas decrease as the space-dependent and temperature-dependent parameters for heat source/sink increase.