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Natural and Mixed Convection

Similarity Solution for Unsteady Free Convection From a Vertical Plate at Constant Temperature to Power Law Fluids

[+] Author and Article Information
J. Abolfazli Esfahani

Mechanical Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Azadi square, Mashhad, IranAbolfazl@um.ac.ir

B. Bagherian

Mechanical Engineering Department, Ferdowsi University of Mashhad, P.O. Box 91775-1111, Azadi square, Mashhad, IranBehtashb60@gmail.com

J. Heat Transfer 134(10), 102501 (Aug 07, 2012) (7 pages) doi:10.1115/1.4005750 History: Received December 17, 2010; Revised November 15, 2011; Published August 06, 2012; Online August 07, 2012

The transformation group theoretic approach is applied to perform an analysis of unsteady free convection flow over a vertical flat plate immersed in a power law fluid. The thermal boundary layer induced within a vertical semi-infinite layer of Boussinseq fluid. The system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate boundary conditions via two-parameter group theory. The obtained ordinary differential equations are solved numerically for velocity and temperature using the fourth order Runge-Kutta and shooting method. The effect of Prandtl number and viscosity index (n) on the thermal boundary-layer, velocity boundary-layer, local Nusselt number, and local skin-friction were studied.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Comparison of distribution of normalized velocity for three different size steps at Pr = 100 and viscosity index n = 1.5

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Figure 2

Comparison of distribution of dimensionless temperature for three different size steps at Pr = 100 and viscosity index n = 1.5

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Figure 3

Comparison of unsteady distribution of normalized velocity between present result and Sharma [26] for Newtonian fluid (n = 1) at Prandtl number 1

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Figure 4

Comparison of unsteady distribution of dimensionless temperature between present result and Sharma [26] for Newtonian fluid (n = 1) at Prandtl number 1

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Figure 5

Comparison of steady distribution of normalized velocity between present result and Chen [20] for Newtonian fluid (n = 1) at Prandtl number 0.7

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Figure 6

Comparison of steady distribution of dimensionless temperature between present result and Chen [20] for Newtonian fluid (n = 1) at Prandtl number 0.7

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Figure 7

Normalized velocity distribution versus similarity variable for varios viscosity index n at Pr = 1

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Figure 8

Dimentionless temperature distribution versus similarity variable for varios viscosity index n at Pr = 1

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Figure 9

Normalized velocity distribution versus similarity variable for varios viscosity index n at Pr = 10

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Figure 10

Dimentionless temprature distribution versus similarity variable for varios viscosity index n at Pr = 10

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Figure 11

Normalized velocity distribution versus similarity variable for varios viscosity index n at Pr = 100

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Figure 12

Dimentionless temperature distribution versus similarity variable for varios viscosity index n at Pr = 100

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Figure 13

Development of nondimensional velocity with various values of nondimensional time at x¯=8 for viscosity index n = 0.5 and Prandtl number 100

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Figure 14

Development of nondimensional temperature with various values of nondimensional time at x¯=8 for viscosity index n = 0.5 and Prandtl number 100

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Figure 15

Normalized skin friction for various viscosity index n and various Prandtl number

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Figure 16

Normalized Nusselt number for various viscosity index n and various Prandtl number

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