Heat Transfer in an Upper Convected Maxwell Fluid with Fluid Particle Suspension

An analysis is carried out to study the magnetohydrodynamic (MHD) flow and heat transfer characteristics of an electrically conducting dusty non-Newtonian fluid, namely, the upper convected Maxwell (UCM) fluid over a stretching sheet. The stretching velocity and the temperature at the surface are assumed to vary linearly with the distance from the origin. Using a similarity transformation, the governing nonlinear partial differential equations of the model problem are transformed into coupled non-linear ordinary differential equations and the equations are solved numerically by a second order finite difference implicit method known as the Keller-box method. Comparisons with the available results in the literature are presented as a special case. The effects of the physical parameters on the fluid velocity, the velocity of the dust particle, the density of the dust particle, the fluid temperature, the dust-phase temperature, the skin friction, and the wall-temperature gradient are presented through tables and graphs. It is observed that, Maxwell fluid reduces the wall-shear stress. Also, the fluid particle interaction reduces the fluid temperature in the boundary layer. Furthermore, the results obtained for the flow and heat transfer characteristics reveal many interesting behaviors that warrant further study on the non-Newtonian fluid flow phenomena, especially the dusty UCM fluid flow phenomena

Unsteady flow and heat transfer in a thin film of Ostwald-de Waele liquid over a stretching surface

In this paper, the effects of viscous dissipation and the temperature-dependent thermal conductivity on an unsteady flow and heat transfer in a thin liquid film of a non-Newtonian Ostwald-de Waele fluid over a horizontal porous stretching surface is studied. Using a similarity transformation, the time-dependent boundary-layer equations are reduced to a set of non-linear ordinary differential equations. The resulting five parameter problem is solved by the Keller-Box method. The effects of the unsteady parameter on the film thickness are explored numerically for different values of the power-law index parameter and the injection parameter. Numerical results for the velocity, the temperature, the skin friction and the wall-temperature gradient are presented through graphs and tables for different values of the pertinent parameter. One of the important findings of the study is that the film thickness increases with an increase in the power-law index parameter (as well as the injection parameter). Quite the opposite is true with the unsteady parameter. Furthermore, the wall-temperature gradient decreases with an increase in the Eckert number or the variable thermal conductivity parameter. Furthermore, the surface temperature of a shear thinning fluid is larger compared to the Newtonian and shear thickening fluids. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially the shear-thinning phenomena. © 2012 Elsevier B.V.postprin

Analytical and Numerical Solutions of Nonlinear Differential Equations Arising in Non-Newtonian Fluid Flows

AbstractSolutions for a class of nonlinear second order differential equations, arising in a viscoelastic fluid flow at a rotating cylinder, are obtained. Furthermore, using the Shauder theory and the perturbation technique existence, uniqueness and analyticity results are established. Moreover, the exact analytical solutions (in integral form) are compared with the corresponding numerical ones

Mixed convection heat transfer over a non-linear stretching surface with variable fluid properties

This article presents a numerical solution for the steady two-dimensional mixed convection MHD flow of an electrically conducting viscous fluid over a vertical stretching sheet, in its own plane. The stretching velocity and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent fluid properties, namely, the fluid viscosity and the thermal conductivity are assumed to vary, respectively, as an inverse function of the temperature and a linear function of the temperature. A generalized similarity transformation is introduced to study the influence of temperature dependent fluid properties. The transformed boundary layer equations are solved numerically, using a finite difference scheme known as Keller Box method, for several sets of values of the physical parameters, namely, the stretching parameter, the temperature dependent viscosity parameter, the magnetic parameter, the mixed convection parameter, the temperature dependent thermal conductivity parameter and the Prandtl number. The numerical results thus obtained for the flow and heat transfer characteristics reveal many interesting behaviors. These behaviors warrant further study of the effects of the physical parameters on the flow and heat transfer characteristics. Here it may be noted that, in the case of the classical Navier-Stokes fluid flowing past a horizontal stretching sheet, McLeod and Rajagopal (1987) 42 showed that there exist an unique solution to the problem. This may not be true in the present case. Hence we would like to explore the non-uniqueness of the solution and present the findings in the subsequent paper. © 2009 Elsevier Ltd. All rights reserved

Unsteady convective boundary layer flow of a viscous fluid at a vertical surface with variable fluid properties

In this paper we present numerical solutions to the unsteady convective boundary layer flow of a viscous fluid at a vertical stretching surface with variable transport properties and thermal radiation. Both assisting and opposing buoyant flow situations are considered. Using a similarity transformation, the governing time-dependent partial differential equations are first transformed into coupled, non-linear ordinary differential equations with variable coefficients. Numerical solutions to these equations subject to appropriate boundary conditions are obtained by a second order finite difference scheme known as the Keller-Box method. The numerical results thus obtained are analyzed for the effects of the pertinent parameters namely, the unsteady parameter, the free convection parameter, the suction/injection parameter, the Prandtl number, the thermal conductivity parameter and the thermal radiation parameter on the flow and heat transfer characteristics. It is worth mentioning that the momentum and thermal boundary layer thicknesses decrease with an increase in the unsteady parameter. © 2012 Published by Elsevier Ltd

Axisymmetric magneto-hydrodynamic (MHD) flow and heat transfer at a non-isothermal stretching cylinder

An investigation is made to study the effects of transverse curvature and the temperature dependent thermal conductivity on the magneto-hydrodynamic (MHD) axisymmetric flow and heat transfer characteristics of a viscous incompressible fluid induced by a non-isothermal stretching cylinder in the presence of internal heat generation/absorption. It is assumed that the cylinder is stretched in the axial direction with a linear velocity and the surface temperature of the cylinder is subjected to vary non-isothermally. Here the thermal conductivity is assumed to vary linearly with temperature. Using a similarity transformation, the governing system of partial differential equations is first transformed into coupled non-linear ordinary differential equations with variable coefficients. The resulting intricate non-linear boundary value problem is solved numerically by a second order finite difference scheme for different values of the pertinent parameters for two cases: (i) the prescribed surface temperature (PST case) and (ii) the prescribed heat flux (PHF case). Numerical results are obtained for two different cases namely, zero and non-zero values of the curvature parameter to get the effects on the velocity and temperature fields. The combined effects of the curvature parameter and the thermal conductivity parameter are examined. The physical significances of the numerical results are presented for several limiting cases. © 2012 Elsevier Inc. All rights reserved

Hall current, Newtonian heating and second-order slip effects on convective magneto-micropolar fluid flow over a sheet

© 2018 World Scientific Publishing Company. This research deals with an analysis of the Hall current effect on the mixed convective magneto-micropolar fluid flow over a permeable stretching/shrinking sheet. Impact of the Newtonian heating parameter is analyzed in the slip flow regime. The nonlinear equations of the fluid flow are derived with the help of a similarity transform and its solutions are obtained by Optimal Homotopy Analysis Method (OHAM). For limiting cases, obtained results are in excellent agreement with the available exact and numerical results in the literature. The graphical and tabular representations of the obtained results show significant effects of the physical parameters on the magneto-micropolar fluid flow and heat transfer characteristics. In particular, it is observed that, as the sheet stretches, a change in the Hall current parameter yields a higher horizontal velocity component for the lower value of the magnetic field parameter; while it produces a higher and shorter transverse velocity profile at high intensity of the magnetic field. In Magnetohydrodynamics (MHD) generators, Hall effects are an important consideration to analyze the heat transfer phenomenon with high temperature conducting fluids

Diffusion of a chemically reactive species of a power-law fluid past a stretching surface

A numerical solution for the steady magnetohydrodynamic (MHD) non-Newtonian power-law fluid flow over a continuously moving surface with species concentration and chemical reaction has been obtained. The viscous flow is driven solely by the linearly stretching sheet, and the reactive species emitted from this sheet undergoes an isothermal and homogeneous one-stage reaction as it diffuses into the surrounding fluid. Using a similarity transformation, the governing non-linear partial differential equations are transformed into coupled nonlinear ordinary differential equations. The governing equations of the mathematical model show that the flow and mass transfer characteristics depend on six parameters, namely, the power-law index, the magnetic parameter, the local Grashof number with respect to species diffusion, the modified Schmidt number, the reaction rate parameter, and the wall concentration parameter. Numerical solutions for these coupled equations are obtained by the KellerBox method, and the solutions obtained are presented through graphs and tables. The numerical results obtained reveal that the magnetic field significantly increases the magnitude of the skin friction, but slightly reduces the mass transfer rate. However, the surface mass transfer strongly depends on the modified Schmidt number and the reaction rate parameter; it increases with increasing values of these parameters. The results obtained reveal many interesting behaviors that warrant further study of the equations related to non-Newtonian fluid phenomena, especially shear-thinning phenomena. Shear thinning reduces the wall shear stress. © 2011 Elsevier Ltd. All rights reserved

Fourier–Galerkin domain truncation method for Stokes’ first problem with Oldroyd four-constant liquid

AbstractUsing the Fourier–Galerkin method with domain truncation strategy, Stokes’ first problem for Oldroyd four-constant liquid on a semi-infinite interval is studied. It is shown that the Fourier–Galerkin approximations are convergent on the bounded interval. Moreover, an efficient and accurate algorithm based on the Fourier–Galerkin approximations is developed and implemented in solving the differential equations related to the present problem. Also, the effects of non-Newtonian parameters on the flow characteristics are obtained and analyzed. The method developed here is so general that it can be used to study the mathematical models that involve the flow of viscous fluids with shear rate-dependent properties: For example, models dealing with polymer processing, tribology & lubrication, and food processing

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 A* and the temperature dependent heat source parameter B*) 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. © 2011 Elsevier Ltd. All rights reserved.postprin