Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

Ch Ramreddy,D Srinivasacharya,T Pradeepa

doi:10.1155/2015/650813

Abstract

The free convective flow of an incompressible micropolar fluid along permeable vertical plate under the convective boundary condition is investigated. The Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method. A quantitative comparison of the numerical results is made with previously published results for special cases and the results are found to be in good agreement. The results of the physical parameters on the developments of flow, temperature, concentration, skinfriction, wall couple stress, heat transfer, and mass transfer characteristics along vertical plate are given and the salient features are discussed.

Highlights

In the past few decades, most of the researchers considered convective heat transfer problems with either constant wall temperature (CWT), constant heat flux (CHF), or Newtonian heating (NH) in a Newtonian and/or non-Newtonian fluid
A novel mechanism for the heating process has drawn the involvement of many researchers, namely, convective boundary condition (CBC), where the heat is supplied to the convecting fluid through a bounding surface with a finite heat capacity
Aziz [2] reported similarity solution for thermal boundary layer flow over a flat plate in a uniform stream of fluid with the convective boundary condition and he concluded that a similarity solution is possible if the convective heat transfer related to hot fluid on the lower surface of the plate is proportional to the inverse square root of the axial length

Summary

Introduction

In the past few decades, most of the researchers considered convective heat transfer problems with either constant wall temperature (CWT), constant heat flux (CHF), or Newtonian heating (NH) in a Newtonian and/or non-Newtonian fluid. Several researchers are focused on obtaining the similarity solutions of the convective transport phenomena problems arising in fluid dynamics, aerodynamics, plasma physics, meteorology, and some branches of engineering by using different procedures One such procedure is Lie group analysis. It seems that the problem of the free convective heat and mass transport along permeable vertical plate in a micropolar fluid under the convective boundary condition has not been investigated so far Motivated by all these works, this paper attempts to present the new similarity transformations and corresponding similarity solution to investigate the free convection flow of a micropolar fluid under the convective boundary condition using the Lie group transformations. The influence of important parameters, namely, micropolar, suction/injection, and convective heat transfer parameters, on the physical quantities of the flow, heat, and mass transfer rates is analyzed in different flow situations

Mathematical Formulation

Nondimensionalization of the Governing Equations

Similarity Equations via Lie Scaling Group Transformations

Results and Discussions

Conclusions