Improved Lumped Models for Transient Combined Convective and Radiative Cooling of Multilayer Spherical Media

In this work, we studied the transient combined convection and radiation of multilayer spherical media with volumetric heat generation, extending the previous work on the particular case of a spherical body subjected to radiative cooling. The proposed lumped models were obtained through two-point Hermite approximations for the average temperature and heat flux in each layer. For the average temperature, the plain trapezoidal rule ( approximation) was employed in all layers, except for the innermost layer, where the second-order two-side corrected trapezoidal rule ( approximation) was utilized. For the heat flux, the plain trapezoidal rule ( approximation) was employed for all the layers. The transient heat conduction in a TRISO-coated fuel particle being composed of five layers (namely, fuel kernel, buffer of porous carbon, inner pyrocarbon, silicon carbide, and outer pyrocarbon) was analyzed using the proposed lumped models, the results of which were verified by comparison with the finite difference solution of the original distributed parameter model. Parametric studies were conducted to examine the effects of the dimensionless heat generation rate, the radiation-conduction parameter, and the Biot number on the temporal variations of the average temperatures.