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Research Papers: Forced Convection

# Flow and Heat Transfer Over a Stretched Microsurface

[+] Author and Article Information
Suhil Kiwan1

Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid, 22110, Jordankiwan@just.edu.jo

M. A. Al-Nimr

Department of Mechanical Engineering, Jordan University of Science and Technology, P.O. Box 3030, Irbid, 22110, Jordan

1

Corresponding author.

J. Heat Transfer 131(6), 061703 (Apr 09, 2009) (8 pages) doi:10.1115/1.3090811 History: Received May 24, 2008; Revised October 15, 2008; Published April 09, 2009

## Abstract

The convection heat transfer induced by a stretching flat plate has been studied. Similarity conditions are obtained for the boundary layer equations for a flat plate subjected to a power law temperature and velocity variations. It is found that a similarity solution exists only for a linearly stretching plate and only when the plate is isothermal. The analysis shows that three parameters control the flow and heat transfer characteristics of the problem. These parameters are the velocity slip parameter $K1$, the temperature slip parameter $K2$, and the Prandtl number. The effect of these parameters on the flow and heat transfer of the problem has been studied and presented. It is found that the slip velocity parameter affect both the flow and heat transfer characteristics of the problem. It is found that the skin friction coefficient decreases with increasing $K1$ and most of the changes in the skin friction takes place in the range $0. A correlation between the skin friction coefficient and $K1$ and $Rex$ has been found and presented. It is found that $cf=23Rex−0.5(K1+0.64)−0.884$ for $0 with an error of ±0.8%. Other correlations between Nu and $K1$ and $K2$ has been found and presented in Eq. 28.

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## Figures

Figure 13

Variation in the thermal boundary layer thickness with the variation of jump parameter K2 for different Prandtl numbers and K1=1

Figure 14

Variation in skin friction parameter with the variation of slip parameter K1 for all values of Pr and K2

Figure 15

Variation in Nusselt number with the variation of slip parameter K1 for different values of Pr and K2=1

Figure 16

Variation in Nusselt number with the variation of jump parameter K2 for different values of Pr and K1=1

Figure 1

Schematic for the problem under consideration

Figure 2

Variation in the dimensionless transverse velocity distribution with the similarity parameter η at different slip parameter K1

Figure 3

Variation in the dimensionless axial velocity distribution with the similarity parameter η at different slip parameter K1

Figure 4

Variation in the dimensionless shear parameter distribution with the similarity parameter η at different slip parameter K1

Figure 5

Variation in the dimensionless temperature distribution with the similarity parameter η at different slip parameter K1

Figure 6

Variation in the dimensionless temperature gradient distribution with the similarity parameter η at different slip parameter K1

Figure 7

Variation in the dimensionless temperature distribution with the similarity parameter η at different jump parameters K2, K1=1, Pr=1

Figure 8

Variation in the dimensionless temperature gradient distribution with the similarity parameter η at different jump parameters K2, K1=1, Pr=1

Figure 9

Variation in the dimensionless temperature distribution with the similarity parameter η at different Prandtl numbers for K1=1, K2=0.5

Figure 10

Variation in the dimensionless temperature gradient with the similarity parameter η at different Prandtl numbers for K1=1, and K2=0.5

Figure 11

Variation in the displacement thickness with the variation in the slip parameter K1 for all values of K2 and Pr

Figure 12

Variation in the thermal boundary layer thickness with the variation of slip parameter K1 for different Prandtl numbers and K2=1

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