Similarity Solutions for Hydromagnetic Free Convective Heat and Mass Transfer Flow along a Semi-Infinite Permeable Inclined Flat Plate with Heat Generation and Thermophoresis

M S S Alam,M M M Rahman,M A A Sattar

doi:10.15388/na.2007.12.4.14675

Abstract

The problem of steady, two-dimensional, laminar, hydromagnetic flow with heat and mass transfer over a semi-infinite, permeable inclined flat plate in the presence of thermophoresis and heat generation is studied numerically. A similarity transformation is used to reduce the governing non-linear partial differential equations into ordinary ones. The obtained locally similar equations are then solved numerically by applying Nachtsheim-Swigert shooting iteration technique with sixth-order Runge-Kutta integration scheme. Comparisons with previously published work are performed and the results are found to be in very good agreement. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various values of the parameters entering into the problem.

Highlights

Thermophoresis is the term describing the fact that small micron sized particles suspended in a non-isothermal gas will acquire a velocity in the direction of decreasing temperature
Sattar the thermophoretic velocity and the force experienced by the suspended particles due to the temperature gradient is known as the thermophoretic force
Due to free convection problem positive large value of Gr = 6 is taken which correspond to a cooling problem that is generally encountered in nuclear engineering in connection with cooling of reactor

Summary

Introduction

Thermophoresis is the term describing the fact that small micron sized particles suspended in a non-isothermal gas will acquire a velocity in the direction of decreasing temperature. The faster moving molecules collide with the particles more forcefully. This difference in momentum leads to the particle developing a velocity in the direction of the cooler temperature. The magnitudes of the thermophoretic force and velocity are proportional to the temperature gradient and depend on many factors like thermal conductivity of aerosol particles and carrier gas. They depend on the thermophoretic coefficient, the heat capacity of the gas and the Knudsen number.

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