Research Papers

Use of Analytical Expressions of Convection in Conjugated Heat Transfer Problems

[+] Author and Article Information
R. Karvinen

 Tampere University of Technology, P.O. Box 589, 33101 Tampere, Finlandreijo.karvinen@tut.fi

J. Heat Transfer 134(3), 031007 (Jan 11, 2012) (9 pages) doi:10.1115/1.4005129 History: Received July 09, 2010; Revised August 26, 2011; Accepted September 08, 2011; Published January 11, 2012; Online January 11, 2012

The heat transfer coefficient of convection from the wall to the flow depends on flow type, on surface temperature distribution in a stream-wise direction, and in transient cases also on time. In so-called conjugated problems, the surface temperature distribution of the wall and flow are coupled together. Thus, the simultaneous solution of convection between the flow and wall, and conduction in the wall are required because heat transfer coefficients are not known. For external and internal flows, very accurate approximate analytical expressions have been derived for heat transfer in different kinds of boundary conditions which change in flow direction. Due to the linearity of the energy equation, the superposition principle can be adopted to couple with these expressions the surface temperature and heat flux distributions in conjugated problems. In the paper, this type of approach is adopted and applied to a number of industrial applications ranging from flat plates of electroluminecence displays to the optimization of heat transfer in fins, fin arrays and mobile phones.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

Transient plate temperature for step change in heat generation

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Figure 2

Typical conjugated problem

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Figure 3

Surface temperature of flat plate (Luikov problem)

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Figure 4

Temperature difference across plate cooled by forced convection with heat generation at one surface

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Figure 5

Geometry of plate fins

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Figure 6

Performance of straight fins

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Figure 7

Schematic of dry-wet fin

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Figure 8

Dry-wet boundary with different methods o experiment, —— conjugated solution, - - - - solution with constant heat transfer coefficient

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Figure 9

Schematic of transient channel flow

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Figure 10

Calculated and measured glass temperature. x = 2.1 m

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Figure 11

Response of tube wall temperature for step change in inlet fluid temperature and comparison with measured data. X*=k(τ-x/um)/ρscpsdtx*1/3

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Figure 12

Schematic of fin package

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Figure 13

Centerline temperature θb=Tb-T∞ at bottom of base plate in Fig. 1

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Figure 14

Different levels of heat transfer analysis in mobile phones

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Figure 15

Board design with shortest total wiring length

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Figure 16

Board design with smallest thermal criterion



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