Exact solution for unsteady free convection flow of Casson fluid in vertical channel

Mohamad Ahmad Qushairi,Ilyas Khan,Zulkhibri Ismail,Jiann Lim Yeou,Sharidan Shafie,Nader Asnafi

doi:10.1051/matecconf/201818901007

Mohamad Ahmad Qushairi, Ilyas Khan + Show 4 more

Open Access

https://doi.org/10.1051/matecconf/201818901007

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Abstract

The influence of free convection flow on unsteady Casson fluid over a vertical channel is studied in this paper. The governing equation consists of partial differential momentum and energy equations have been transformed into non-dimensional equations by using the appropriate nondimensional variables. The expression of exact solutions for nondimensional velocity and temperature profiles are obtained by using the Laplace transform method. The obtained exact solutions are found satisfied all the initial and boundary conditions. The behaviour of velocity and temperature profiles influenced by Casson fluid parameter, Grashof number, Prandtl number and time are plotted graphically and presented in tables. It can be observed that, the velocity profile and boundary layer thickness decrease when the values of Casson fluid parameter and Prandtl number increase. This is due to the increase of viscous force and retard the movement of the velocity. The present result is validated when the obtained exact solution of velocity is compared with published result and found in a good agreement.

Highlights

Heat transfer analysis in vertical channel has been studied by a few researchers due to their applications
In early year of 2000, most of the researchers that dealing with channel problem are using the Laplace transform method, in order to obtain the exact solutions of the problem studied
Paul et al [3] obtained the exact solutions for free convection flow of incompressible viscous fluid in vertical channel with constant heat flux effect whereas Basant [4] solved the problem of free convection flow on magnetic effect in electrically conducting viscous

Summary

Introduction

Heat transfer analysis in vertical channel (two parallel vertical plates) has been studied by a few researchers due to their applications. With the great knowledge of exact solution in vertical channel, once again, Narahari and Vijay [7] published the problem of free convection flow of viscous fluid with the effect of ramped wall temperature. They found that, the velocity and temperature profiles in the case of ramped temperature plate is always less than that of the case of an isothermal plate. Asma et al [16] observed the new problem on unsteady free convection flow of Casson fluid in vertical constant wall temperature They extended their problem by considering the effects of magnetohydrodynamics (MHD) and porous medium [17]. The present work is validated by comparing with published result [6]

Problem formulation

Problem solution

Results and discussion

Conclusion