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Technical Briefs

Achieving a Specific Nonuniform Heat Flux With an Electrical Heat Flux Plate

[+] Author and Article Information
James L. Rutledge

e-mail: james.rutledge@us.af.mil

Marc D. Polanka

e-mail: marc.polanka@afit.edu
Air Force Institute of Technology,
Wright-Patterson Air Force Base,
OH 45433

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received June 22, 2012; final manuscript received March 27, 2013; published online July 11, 2013. Assoc. Editor: Bruce L. Drolen.

J. Heat Transfer 135(8), 084502 (Jul 11, 2013) (7 pages) Paper No: HT-12-1302; doi: 10.1115/1.4024277 History: Received June 22, 2012; Revised March 27, 2013

A voltage applied across a uniform plate results in a uniform ohmic heat dissipation, useful for conducting heat transfer experiments or preventing unacceptably low temperatures on spacecraft components. Most experiments to date involve application of a known uniform heat flux to the surface of a model. Measurement of the resulting temperature distribution facilitates calculation of the heat transfer coefficient, h. The dependence of h on the boundary condition, however, may necessitate a specified nonuniform heat flux. In this paper, a novel methodology is developed for designing a nonuniform thickness heat flux plate to provide a specified spatially variable heat flux. The equations are derived to solve the two dimensional heat flux with a variable cross sectional area. After showing that this inverse heat transfer problem cannot be readily linearized, a methodology utilizing a smooth surface polynomial was applied. Then, for a prescribed, desired heat flux distribution, a 7th order polynomial (including 36 terms) yielded a normalized root mean squared error of 1% over the surface. This distributed heat flux could result in significant power and thus cost savings for a variety of applications.

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References

Figures

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Fig. 3

Schematic of electrical flow into 2D element

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Fig. 2

Notional variable thickness heat flux plates with boundary conditions identified

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Fig. 1

Heat flux plate schematic

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Fig. 4

Hypothetical desired q distribution, W/m2

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Fig. 7

Percent increase in q for N = 7 polynomial thickness distribution with lower bound on thickness constrained to 2 × 10−4 m

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Fig. 5

Calculated thickness distribution (m) and current vectors using curve fit optimization (N = 7). Thickness ranges from 1.87 × 10−4 m to 7.23 × 10−4 m.

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Fig. 6

Percent increase in q per micron thickness increase for N = 7 polynomial thickness distribution

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