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Research Papers: Porous Media

# Effects of Partial Slip on the Analytic Heat and Mass Transfer for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow

[+] Author and Article Information
Mustafa Turkyilmazoglu

Department of Mathematics, Hacettepe University, 06532 Beytepe, Ankara, Turkey e-mail: turkyilm@hacettepe.edu.tr

J. Heat Transfer 133(12), 122602 (Oct 07, 2011) (5 pages) doi:10.1115/1.4004558 History: Received August 30, 2010; Revised July 08, 2011; Published October 07, 2011; Online October 07, 2011

## Abstract

The present paper is concerned with a class of exact solutions to the steady Navier-Stokes equations for the incompressible Newtonian viscous fluid flow motion due to a porous disk rotating with a constant angular speed about its axis. The recent study (Turkyilmazoglu, 2009, “Exact Solutions for the Incompressible Viscous Fluid of a Porous Rotating Disk Flow,” Int. J. Non-Linear Mech., 44, pp. 352–357) is extended to account for the effects of partial flow slip and temperature jump imposed on the wall. The three-dimensional equations of motion are treated analytically yielding derivation of exact solutions for the flow and temperature fields. Explicit expressions representing the flow properties influenced by the slip as well as a uniform suction and injection are extracted, including the velocity, vorticity and temperature fields, shear stresses, flow and thermal layer thicknesses, and Nusselt number. The effects of variation in the slip parameters are better visualized from the formulae obtained.

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## Figures

Figure 1

Schematic description of the flow

Figure 2

Graphs of f and − g are demonstrated. (a) s  = 0 and (b) s  = 2. Curves correspond to the slip parameters, L, of 0, 1, and 10, respectively (from top for f and from bottom for − g).

Figure 3

Variation of the Nusselt number Nu against suction or injection parameter s. Curves correspond to the parameter Γ which is proportional to Eckert number. Solid Γ = − 2, dotted Γ = 0, and dashed Γ  = 2, respectively, for Pr  = 1, 3, and 5 (from bottom to top for all the curves). Temperature slip parameters, κ; (a) κ  = 0 and (b) κ  = 1/5.

Figure 4

Variation of the Nusselt number Nu against suction or injection parameter s. Curves correspond to the parameter Γ which is proportional to Eckert number. Solid Γ = − 2, dotted Γ = 0, and dashed Γ = 2, respectively, for Pr = 1, 3, and 5 (from bottom to top for Γ > 0 and reverse for Γ ≤ 0). Temperature slip parameters, κ; (a) κ = 5 and (b) κ = 15.

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