Variable fluid properties and variable heat flux effects on the flow and heat transfer in a non-Newtonian Maxwell fluid over an unsteady stretching sheet with slip velocity

The effects of variable fluid properties and variable heat flux on the flow and heat transfer of a non-Newtonian Maxwell fluid over an unsteady stretching sheet in the presence of slip velocity have been studied. The governing differential equations are transformed into a set of coupled non-linear ordinary differential equations and then solved with a numerical technique using appropriate boundary conditions for various physical parameters. The numerical solution for the governing non-linear boundary value problem is based on applying the fourth-order Runge-Kutta method coupled with the shooting technique over the entire range of physical parameters. The effects of various parameters like the viscosity parameter, thermal conductivity parameter, unsteadiness parameter, slip velocity parameter, the Deborah number, and the Prandtl number on the flow and temperature profiles as well as on the local skin-friction coefficient and the local Nusselt number are presented and discussed. Comparison of numerical results is made with the earlier published results under limiting cases.

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 charac- teristics 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 re- sulting similarity equations are solved numerically with a shooting method. Comparisons with previous works are macle, 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.

Approximate solutions for the problem of liquid film flow over an unsteady stretching sheet with thermal radiation and magnetic field

The proposed method is based on replacement of the unknown function by a truncated series of the shifted Legendre polynomial expansion. An approximate formula of the integer derivative is introduced. Special attention is given to study the convergence analysis and derive an upper bound of the error for the presented approximate formula. The introduced method converts the proposed equation by means of collocation points to a system of algebraic equations with shifted Legendre coefficients. Thus, after solving this system of equations, the shifted Legendre coefficients are obtained. This efficient numerical method is used to solve the system of ordinary differential equations which describe the thin film flow and heat transfer with the effects of the thermal radiation, magnetic field, and slip velocity.

Hydromagnetic Nanofluid Film Flow over a Stretching Sheet with Prescribed Heat Flux and Viscous Dissipation

Thermal radiative heat transfer through a thin horizontal liquid film of a Newtonian nanofluid subjected to a magnetic field is considered.The physical boundary conditions are a variable surface heat flux and a uniform concentration along the sheet.Moreover,viscous dissipation is present and concentration is assumed to be influenced by both thermophoresis and Brownian motion effects.Using a similarity method to turn the underlying Partial differential equations into a set of ordinary differential equations(ODEs)and a shooting technique to solve these equations,the skin-friction coefficient,the Nusselt number,and the Sherwood number are determined.Among other things,it is shown that large values of the thermal radiation heat transfer rate,thermal conductivity parameter,and the Brownian motion parameter can enhance the cooling of the sheet.

Effect of Magnetic Field on the Flow and Heat Transfer in a Casson Thin Film on an Unsteady Stretching Surface in the Presence of Viscous and Internal Heating

The aim of this investigation is to analyze the effectiveness of Lorentz force, viscous dissipation and internal heating on the heat and flow characteristics of a non-Newtonian Casson fluid thin film resting on a stretching surface under the influence of a magnetic field. Employing suitable similarity variables and shooting technique and integrating scheme numerical solutions for velocity and temperature are obtained. The results of this analysis are compared with the published work and are found to be in good agreement. The thickness of the thin film is evaluated and is observed that Lorentz force and the non-Newtonian nature of the fluid have a thinning influence on the film. Velocity and temperature distributions in the thin film are discussed for various flow parameters.

Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux

This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.

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 genera- tion/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. Similar- ity transformation is used to translate the governing partial differential equations into ordinary differential equations. A shooting technique in conjunction with the 4th order Runge-Kutta method is used to solve the transformed equations. Computations are car- ried 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.