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Research Papers: Natural and Mixed Convection

# Mixed Convection From a Convectively Heated Vertical Plate to a Fluid With Internal Heat Generation

[+] Author and Article Information
O. D. Makinde1

Institute for Advance Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P. O. Box 1906, Bellville 7535, South Africamakinded@cput.ac.za

A. Aziz

Life Fellow ASME Department of Mechanical Engineering, School of Engineering and Applied Science, Gonzaga University, Spokane, WA 99268aziz@gonzaga.edu

1

Corresponding author.

J. Heat Transfer 133(12), 122501 (Sep 29, 2011) (6 pages) doi:10.1115/1.4004432 History: Received June 25, 2010; Revised June 13, 2011; Published September 29, 2011; Online September 29, 2011

## Abstract

A numerical approach has been adopted to study steady mixed convection from the right face of a vertical plate of finite thickness. Cold fluid flowing over the right face of the plate contains a heat generation that decays exponentially with a dimensionless distance from the wall. The left face of the plate is in contact with a hot flowing fluid. The heating process on that side is characterized by a convective boundary condition that takes into account the conduction resistance of the plate as well as a possible contact resistance between the hot fluid and the left face of the plate. Using a pseudo similarity approach, the continuity, momentum, and energy equations for mixed convective flow over the right face of the plate are transformed into a set of coupled ordinary differential equations. It is found that for a true similarity solution, the convective heat transfer coefficient associated with the hot fluid must be proportional to x−1/2 , and both the thermal expansion coefficient and the internal heat generation rate for the cold fluid must be proportional to x−1 , where x is the upward distance along the plate. The equations give local similarity solutions. The effects of local Grashof number (defined to represent a mixed convection parameter), Prandtl number, Biot number, and the internal heat generation parameter on the velocity and temperature profiles are illustrated and interpreted in physical terms. The present results agree closely with the existing results for the special cases of the problem. This close agreement lends support to the validity of the present analysis and the accuracy of the numerical computations. The paper also contains a table in which the data for the local skin friction and local Nusselt number are provided for various combination values of the parameters that govern the momentum and energy transport in the mixed boundary layer.

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## Figures

Figure 1

Flow configuration and coordinate system

Figure 2

Velocity profiles for Pr = 0.72, Grx = 0.1, and λx  = 10

Figure 3

Velocity profiles for Grx  = Bix  = 0.1, and λx  = 10

Figure 4

Velocity profiles for Pr= 0.72, Bix  = 0.1, and λx =10

Figure 5

Velocity profiles for Pr= 0.72 and Grx  = Bix  = 0.1

Figure 6

Temperature profiles for Pr = 0.72, Grx = 0.1, and λx =10

Figure 7

Temperature profiles for Grx  = Bix  = 0.1, and λx  = 10

Figure 8

Temperature profiles for Pr = 0.72, Bix  = 0.1, and λx =10

Figure 9

Temperature profiles for Pr= 0.72 and Grx  = Bix  = 0.1

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