Entropy generation analysis for a non axisymmetric flow over a rotating porous disk assignment

M. Baghban", J. A. Esfahani, and Z. Shams.

Abstract: In the present study, entropy generation in a non-axisymmetric steady-state incompress- ible viscous flow over a single rotating porous disk is investigated analytically. The dimensionless form of the local and total entropy generation caused by frictional and thermal effects are derived. The effects of the injection rate and Brinkman number on the entropy generation are revealed. It is found that there exists an optimal injection rate for each Brinkman number, which minimizes the total entropy generation.
Keywords: rotating disk, injection rate, Brinkman number, entropy generation, Bejan number.

INTRODUCTION

The fluid flow and heat transfer over rotating bodies find special places in many science and engineering ap- plications, for instance, in turbo-machinery, meteorology, computer disk drives, geophysical fluid dynamics, gaseous and nuclear reactors, and so on. In recent years, investigations on the hydrodynamic flow due to an infinite rotating disk have gained considerable attention. Originally von Kármán [1] discussed a steady flow of a Newtonian fluid over a rotating disk and introduced a useful transformation that enabled the Navier-Stokes equations for an isother- mal impermeable rotating disk to be reduced to a system of coupled ordinary differential equations. Berker [2] represented a solution for the flow of a fluid contained between parallel plates rotating about the same axis. The usual solution for the flow due to rotation of disks is assumed to have axial symmetry [1, 2]. However, as shown by Parter and Rajagopal [3] and Lai et al. [4], a non-axisymmetric solution is more reliable for practical cases. Turkyilmazoglu [5] represented exact solutions for a non-axisymmetric incompressible electrically conducting fluid flow due to an infinite porous disk and studied the flow and heat transfer.

Awareness of the limits of energy resources causes great attention on conservation of useful energy. The entropy generation is the measure of destruction of the available work of the system. Hence, minimization of the entropy generation provides a useful tool to determine optimized operation conditions.

Bejan [6, 7] presented the second-law analysis in heat transfer and thermal design. He established the concept of the entropy generation number, irreversibility distribution ratio, and introduced the basic steps for the procedure of entropy generation minimization at the system component level.

Arikoglu et al. [8] investigated the effect of slip on the entropy generation due to the fluid flow and heat transfer over a free rotating disk. The entropy generation analysis for an axisymmetric laminar flow over a freerotating disk was studied numerically by Shanbghazani et al. [9]. They found that an increase in the rotational Reynolds number increases the local entropy generation rate and irreversibility rate. Rashidi et al. [10] studied the entropy generation of a rotating porous disk in the presence of a magnetic field with temperature-dependent thermophysical properties.

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