Validation of a heat conduction model for finite domain, non-uniformly heated, laminate bodies

Infrared thermographic validation is shown for a closed-form analytical heat conduction model for non-uniformly heated, laminate bodies with an insulated domain boundary. Experiments were conducted by applying power to rectangular electric heaters and cooled by natural convection in air, but also apply to constant-temperature heat sources and forced convection. The model accurately represents two-dimensional laminate heat conduction behaviour giving rise to heat spreading using one-dimensional equations for the temperature distributions and heat transfer rates under steady-state and pseudo-steady-state conditions. Validation of the model with an insulated boundary (complementing previous studies with an infinite boundary) provides useful predictions of heat spreading performance and simplified temperature uniformity calculations (useful in log-mean temperature difference style heat exchanger calculations) for real laminate systems such as found in electronics heat sinks, multi-ply stovetop cookware and interface materials for supercooled salt hydrates. Computational determinations of implicit insulated boundary condition locations in measured data, required to assess model equation validation, were also demonstrated. Excellent goodness of fit was observed (both root-mean-square error and R2 values), in all cases except when the uncertainty of low temperatures measured via infrared thermography hindered the statistical significance of the model fit. The experimental validation in all other cases supports use of the model equations in design calculations and heat exchange simulations.