Numerical solution of radiation view factors within a thermoelectric device

The geometry of a TED (thermoelectric device) is three-dimensional and is dependent upon device functionality and the thermoelectric material used within. To properly design and model a TED, radiation heat transfer should be resolved within the cavity, especially at high operating temperatures. Radiation heat transfer is often ignored or over-simplified due to the computationally intensive process of resolving the radiation view factor Fij within a particular geometry. This study utilizes hybrid CPU-GPU high-performance computing to numerically resolve Fij between the interior hot- and cold-side ceramic plates within a unit cell TED, taking into account the shadow effect contributions of interconnectors and thermoelectric material legs through a point-in-polygon algorithm. To provide values of Fij for a variety of potential design applications, the packing density θ was varied between 0.1 and 0.9, the height to width ratio of the thermoelectric elements was varied between 0.5 and 1.75 and top and bottom interconnector thicknesses were varied between 0.125 and 0.25 mm. Results indicate Fij behaves non-linearly with θ exhibiting exponential decay with an increase in θ. Increasing the leg height to width ratio of the thermoelectric material and interconnector thickness non-linearly and monotonically decreases Fij, respectively.