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Research Papers: Forced Convection

# Combined Effects of Temperature and Velocity Jump on the Heat Transfer, Fluid Flow, and Entropy Generation Over a Single Rotating Disk

[+] Author and Article Information
A. Arikoglu, A. Y. Gunes

Department of Aeronautical Engineering, Faculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak, TR-34469 Istanbul, Turkey

G. Komurgoz

Department of Electrical Engineering, Faculty of Electrical and Electronic Engineering, Istanbul Technical University, Maslak, TR-34469 Istanbul, Turkey

I. Ozkol

Department of Aeronautical Engineering, Faculty of Aeronautics and Astronautics, Istanbul Technical University, Maslak, TR-34469 Istanbul, Turkeyozkol@itu.edu.tr

J. Heat Transfer 132(11), 111703 (Aug 13, 2010) (10 pages) doi:10.1115/1.4002098 History: Received February 17, 2010; Revised June 10, 2010; Published August 13, 2010; Online August 13, 2010

## Abstract

The present work examines the effects of temperature and velocity jump conditions on heat transfer, fluid flow, and entropy generation. As the physical model, the axially symmetrical steady flow of a Newtonian ambient fluid over a single rotating disk is chosen. The related nonlinear governing equations for flow and thermal fields are reduced to ordinary differential equations by applying so-called classical approach, which was first introduced by von Karman. Instead of a numerical method, a recently developed popular semi numerical-analytical technique; differential transform method is employed to solve the reduced governing equations under the assumptions of velocity and thermal jump conditions on the disk surface. The combined effects of the velocity slip and temperature jump on the thermal and flow fields are investigated in great detail for different values of the nondimensional field parameters. In order to evaluate the efficiency of such rotating fluidic system, the entropy generation equation is derived and nondimensionalized. Additionally, special attention has been given to entropy generation, its characteristic and dependency on various parameters, i.e., group parameter, Kn and Re numbers, etc. It is observed that thermal and velocity jump strongly reduce the magnitude of entropy generation throughout the flow domain. As a result, the efficiency of the related physical system increases. A noticeable objective of this study is to give an open form solution of nonlinear field equations. The reduced recurative form of the governing equations presented gives the reader an opportunity to see the solution in open series form.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

Variation in θ(ζ) with respect to ζ for different values of Re and Kn

Figure 2

Variation in F(ζ) with respect to ζ for different Re and Kn

Figure 3

Variation in G(ζ) with respect to ζ for different Re and Kn

Figure 4

Variation in H(ζ) with respect to ζ for different Re and Kn

Figure 5

Variation in Ng with respect to r¯ and ζ(ψ=10−10)

Figure 6

Variation in Ng with respect to Kn for different ψ and Re (ζ=0 and r¯=1)

Figure 7

Variation in Ng with r¯ for different ψ and Re (ζ=0 and Kn=0.05)

Figure 8

Variation in Ng,av with respect to Kn for different ψ and Re

Figure 9

Variation in Be with respect to r¯ and ζ(ψ=10−10)

Figure 10

Variation in Be with respect to Kn for different ψ and Re (ζ=0 and r¯=1)

Figure 11

Variation in Be with respect to Kn for different Re and r¯ (ψ=10−10 and ζ=0)

Figure 12

Variation in Beav with respect to Kn for different ψ and Re

Figure 13

Variation in Nu with respect to ζ for different Kn and Re

Figure 14

Variation in Nu with respect to Kn and Re on the disk surface (ζ=0)

Figure 15

Variation in δdis and δt with respect to Kn for different Re

## Errata

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