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

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.