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Technical Briefs

Analytical Study of the Convection Heat Transfer From an Isothermal Wedge Surface to Fluids

[+] Author and Article Information
M. Bachiri, A. Bouabdallah

Thermodynamics and Energetical Systems Laboratory, Faculty of Physics/USTHB, B.P. 32 El Alia, 16111 Bab Ezzouar, Algiers, Algeriamabach73@yahoo.fr

J. Heat Transfer 134(6), 064502 (May 02, 2012) (5 pages) doi:10.1115/1.4006030 History: Received May 18, 2010; Revised November 30, 2011; Published April 30, 2012; Online May 02, 2012

In this work, we attempt to establish a general analytical approximation of the convection heat transfer from an isothermal wedge surface to fluids for all Prandtl numbers. The flow has been assumed to be laminar and steady state. The governing equations have been written in dimensionless form using a similarity method. A simple ad hoc technique is used to solve analytically the governing equations by proposing a general formula of the velocity profile. This formula verifies the boundary conditions and the equilibrium of the governing equations in the whole spatial region and permits us to obtain analytically the temperature profiles for all Prandtl numbers and for various configurations of the wedge surface. A comparison with the numerical results is given for all spatial regions and in wide Prandtl number values. A new Nusselt number expression is obtained for various configurations of the wedge surface and compared with the numerical results in wide Prandtl number values.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Three principal configurations of the flow over an isothermal wedge surface

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Figure 2

Comparisons between σ(A,α0max) and fηη2(0) at any value of A ∈ [0, 1] and for different configurations of the wedge surface

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Figure 3

Variations of the dimensionless velocity profile for the Blasius problem: dashed line represents Blasius solution; solid line represents analytic approach

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Figure 4

Variations of the dimensionless stream function for the Blasius problem: dashed line represents Blasius solution; solid line represents analytic approach

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Figure 5

Stream function evolutions for different wedge surface geometries

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Figure 6

Velocities distributions for different wedge surface geometries

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Figure 7

Temperatures distributions for large Prandtl number, Pr, values and for three configurations of an isothermal wedge surface: (a) horizontal plate, m = 0; (b) wedge surface, m = 1/3; and (c) vertical plate (stagnation points), m = 1

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Figure 8

Variations of the heat transfer coefficient Nu for different values of Prandtl number, Pr, and for different geometries of an isothermal wedge surface

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