Heat flux display and heat transmission coefficient calculation with the finite element method

The heat conduction equation for random points is used with the finite element method (FEM) to generate two-dimensional maps of temperature fields in heat conducting bodies. The heat fluxes at random locations are expressed in terms of their magnitude and direction. Consideration of only the grid edges along the outer, heat transferring surfaces of the body is demonstrated to yield the heat resistance or heat transmission coefficient. The elements used are parabolic eight point quadrilateral members of the Serendipity family. The method is useful for house insulation, heat exchanger design, and cryogenic equipment.