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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Kays, W. M., and Crawford, M. E., 1993, Convective Heat and Mass Transfer, 3rd ed., McGraw-Hill, New York.
Whitaker, S., 1972, “Forced Convection Heat Transfer Correlations for Flow in Pipes, Past Flat Plates, Single Cylinders, Single Spheres, and for Flow in Packed Beds and Tube Bundles,” AIChE J., 18, pp. 361–371. [CrossRef]
Liu, D., and Li, Y., 2009, “A Novel Temperature Based Flat-Plate Heat Flux Sensor for High Accuracy Measurement,” IEEE/ASME International Conference on Advanced Intelligent Mechatronics, pp. 1242–1247.
Gilmore, D. G., Lyra, J. C., and Stultz, J. W., 2002, “Heaters,” Spacecraft Thermal Control Handbook, Vol. 1, D. G. Gilmore, ed., The Aerospace Press, El Segundo, CA, pp. 223–245.
Wiedner, B. G., and Camci, C., 1996, “Determination of Convective Heat Flux on Steady-State Heat Transfer Surfaces With Arbitrarily Specified Boundaries,” ASME J. Heat Transfer, 118, pp. 850–856. [CrossRef]
Mick, W. J., and Mayle, R. E., 1988, “Stagnation Film Cooling and Heat Transfer Including Its Effect Within the Hole Pattern,” ASME J. Turbomach., 110, pp. 66–72. [CrossRef]
Mathworks, 2011, Partial Differential Equation Toolbox User's Guide R2011b, Natick, MA.
Haynes, W. M., 2012, CRC Handbook of Chemistry and Physics, CRC, Boca Raton, FL.
Mathworks, 2011, Optimization Toolbox User's Guide R2011b, Natick, MA.
Levenberg, K., 1944, “A Method for the Solution of Certain Non-Linear Problems in Least Squares,” Q. Appl. Math., 2, pp 164–168.
Marquardt, D., 1963, “An Algorithm for Least-Squares Estimation of Nonlinear Parameters,” J. Soc. Ind. Appl. Math., 11, pp. 431–441. [CrossRef]


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Fig. 1

Heat flux plate schematic

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Fig. 2

Notional variable thickness heat flux plates with boundary conditions identified

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Fig. 3

Schematic of electrical flow into 2D element

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Fig. 4

Hypothetical desired q distribution, W/m2

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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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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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