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# An Analytical Solution for Boundary Layer Flows Over a Moving-Flat Porous Plate With Viscous Dissipation

[+] Author and Article Information
C. J. Toki

Department of Ecology and Environment,
Technological Educational
Institute of Ionian Islands,
Square of Kalvou, Zakynthos 29100,Greece
e-mail: Christina-toki@yahoo.com

1Corresponding author. Present address: Pediou Volis 32, Stavraki, 453 22, Ioannina, Greece.

Present address: Department of Mechanical Engineering, Curtin University, Sarawak Campus CDT 250, 98009 Miri, Sarawak, Malaysia

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 21, 2012; final manuscript received June 10, 2013; published online November 20, 2013. Assoc. Editor: Sharath S. Girimaji.

J. Fluids Eng 136(2), 024501 (Nov 20, 2013) (5 pages) Paper No: FE-12-1466; doi: 10.1115/1.4025142 History: Received September 21, 2012; Revised June 10, 2013

## Abstract

The problem of boundary layer flow of an incompressible fluid over a moving porous flat plate is investigated, by taking into account the heat due to viscous dissipation. The governing boundary layer equations of this flow field were solved analytically using the Laplace transform technique. These new exact analytical solutions for velocity and temperature were obtained with arbitrary Prandtl number and dissipation parameter (or Eckert number $Ec$). The corresponding solutions for nonporous plate are discussed. Applying numerical values into the analytical expressions of the temperature and heat transfer coefficient, we also discussed the effects of the dissipation parameter in the cases of water, gas, and ammonia flow. We can finally deduce that the fluid temperature of the present problem will increase in the case of viscous dissipation with positive $Ec$, but this temperature will decrease with negative $Ec$.

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## Figures

Fig. 1

Effects of the Eckert number on the temperature profiles of water flows near porous and nonporous flat plate, which is moved with uniform velocity

Fig. 2

Effects of the Eckert number on the temperature profiles of air flows near porous and nonporous flat plate, which is moved with uniform velocity

Fig. 3

Effects of the Eckert number on the temperature profiles of ammonia flows near porous flat plate, which is moved with uniform velocity

Fig. 4

Variation of the heat transfer coefficient as function of the Eckert number in the case of the water flows and air flows near porous and nonporous flat plates, which are moved with uniform velocity

Fig. 5

Variation of the heat transfer coefficient as function of the Eckert number in the case of ammonia near porous and nonporous flat plates, which are moved with uniform velocity

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