Effect of internal heat generation on free convective power-law variable temperature past a vertical plate considering exponential variable viscosity and thermal conductivity

M Ferdows,Md Shamshuddin,M G Murtaza

doi:10.1186/s42787-019-0062-5

Abstract

The aim of this paper is to study the free convection boundary-layer flow with heat generation and variable fluid properties past a vertical plate. We incorporated the heat generation and variable viscosity are the exponential decay form and thermal conductivity is the linear form in the governing equation. Using similarity transformations, the governing coupled non-linear partial differential equations are transformed into a system of coupled non-linear ordinary differential equations and then solved using Maple symbolic software to execute the computations via dsolve. The effects of the temperature-dependent viscosity, the wall velocity power index, the thermal conductivity, the wall temperature parameter, and the Prandtl number on the flow and temperature fields are presented. The skin friction and the wall temperature gradient are also presented for different values of the physical parameters.

Highlights

For a long time, a vital subject in fluid dynamics is the problem of steady and unsteady laminar flow over a permeable surface because of its worth from both theoretical and viable point of view and has been studied in detail
The heat transfer mechanisms with non-uniform heat source/sink are an important topic for current researchers due to its comprehensive applications in the fields of physics and engineering
To the best knowledge of the authors, not many studies have been conducted on the flow of these fluids by considering the impacts of non-uniform heat source/sink, exponential variable viscosity, and thermal conductivity in mathematical model with a Lie group transformation approach

Summary

Introduction

A vital subject in fluid dynamics is the problem of steady and unsteady laminar flow over a permeable surface because of its worth from both theoretical and viable point of view and has been studied in detail. To the best knowledge of the authors, not many studies have been conducted on the flow of these fluids by considering the impacts of non-uniform heat source/sink, exponential variable viscosity, and thermal conductivity in mathematical model with a Lie group transformation approach. Influenced by the abovementioned literature, the objective of our study is to explore the effects of internal heat generation on steady, free convective and variable fluid properties past a vertical plate.

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Results

Conclusion