Flow and heat transfer in a Maxwell liquid film over an unsteady stretching sheet in a porous medium with radiation.

Shimaa E Waheed

doi:10.1186/s40064-016-2655-x

Abstract

A problem of flow and heat transfer in a non-Newtonian Maxwell liquid film over an unsteady stretching sheet embedded in a porous medium in the presence of a thermal radiation is investigated. The unsteady boundary layer equations describing the problem are transformed to a system of non-linear ordinary differential equations which is solved numerically using the shooting method. The effects of various parameters like the Darcy parameter, the radiation 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. It is observed that increasing values of the Darcy parameter and the Deborah number cause an increase of the local skin-friction coefficient values and decrease in the values of the local Nusselt number. Also, it is noticed that the local Nusselt number increases as the Prandtl number increases and it decreases with increasing the radiation parameter. However, it is found that the free surface temperature increases by increasing the Darcy parameter, the radiation parameter and the Deborah number whereas it decreases by increasing the Prandtl number.

Highlights

The flow and heat transfer within a thin liquid film due to the stretching surface in otherwise quiescent fluid are important because of their wide applications in a number of industrial engineering processes
The problem of the flow and heat transfer in a thin film of power-law fluid on an unsteady stretching surface has been investigated by Chen (2003, 2006) where he studied the effect of viscous dissipation on heat transfer in a non-Newtonian thin liquid film over an unsteady stretching sheet
A theoretical analysis is performed to study thermal radiation effects on flow and heat transfer in an upper convected Maxwell liquid film on an unsteady stretching sheet embedded in a porous medium

Summary

Introduction

The flow and heat transfer within a thin liquid film due to the stretching surface in otherwise quiescent fluid are important because of their wide applications in a number of industrial engineering processes. The problem of the flow and heat transfer in a thin film of power-law fluid on an unsteady stretching surface has been investigated by Chen (2003, 2006) where he studied the effect of viscous dissipation on heat transfer in a non-Newtonian thin liquid film over an unsteady stretching sheet. The flow and heat transfer problem of a second grade fluid film over an unsteady stretching sheet has been presented by Hayat et al (2008). Mahmoud and Megahed (2009) investigated the effects of variable viscosity and thermal conductivity on the flow and heat transfer of an electrically conducting non-Newtonian power-law fluid within a thin liquid film over an unsteady stretching sheet in the presence of a transverse magnetic field Sajid et al (2009) presented exact solutions for thin film flows of a micropolar fluid down an inclined plane on moving belt and down a vertical cylinder. Mahmoud and Megahed (2009) investigated the effects of variable viscosity and thermal conductivity on the flow and heat transfer of an electrically conducting non-Newtonian power-law fluid within a thin liquid film over an unsteady stretching sheet in the presence of a transverse magnetic field

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