Effects of Thermocapillarity and Thermal Radiation on Flow and Heat Transfer in a Thin Liquid Film on an Unsteady Stretching Sheet

R C Aziz,S Abbasbandy,I Hashim

doi:10.1155/2012/127320

Abstract

This paper examines the effects of thermocapillarity and thermal radiation on the boundary layer flow and heat transfer in a thin film on an unsteady stretching sheet with nonuniform heat source/sink. The governing partial differential equations are converted into ordinary differential equations by a similarity transformation and then are solved by using the homotopy analysis method (HAM). The effects of the radiation parameter, the thermocapillarity number, and the temperature‐dependent parameter in this study are discussed and presented graphically via velocity and temperature profiles.

Highlights

The analysis of heat transfer of boundary layer flow with thermal radiation is important in electrical power generation, astrophysical flows, solar power technology, space vehicle reentry, and other industrial engineering processes.Wang 1 was the pioneer in investigating the hydrodynamics of a flow in a thin liquid film on an unsteady stretching surface
Andersson et al 2 studied the heat transfer characteristics of the hydrodynamical problem solved by Wang 1
Wang 4 investigated the same problem of Andersson et al 2, presenting analytic solutions

Summary

Introduction

The analysis of heat transfer of boundary layer flow with thermal radiation is important in electrical power generation, astrophysical flows, solar power technology, space vehicle reentry, and other industrial engineering processes. Wang 1 was the pioneer in investigating the hydrodynamics of a flow in a thin liquid film on an unsteady stretching surface. Wang 4 was probably the first to analyze the flow and heat transfer in a thin liquid film on an unsteady stretching surface using the homotopy analysis method HAM. Studies by Dandapat et al 10, 11 reported that thermocapillarity generates surface-tension gradients along the horizontal interface between the passive gas and the liquid film. Both Abd El-Aziz and Mahmoud have studied the influence of thermal radiation on the flow and heat transfer on an unsteady stretching sheet. The solutions reached using HAM are presented and implications discussed

Problem Formulation

Solution Approach

Convergence of the HAM Solution

Results and Discussion

Concluding Remarks