Reliable one-dimensional approximate solutions for insulated oblate spheroid containers

Abstract

Since there is no reliable surface-area formula available for the calculation of the heat-transfer characteristics of an insulated oblate spheroid, in this investigation, highly accurate oblate spheroid surface area is obtained by a simple numerical integration method. Based on the accurate oblate spheroid surface area, a reliable one-dimensional approximate solution of an insulated oblate spheroid container can be obtained with a one-dimensional RPSWT model. By comparing with accurate three-dimensional numerical results, it is found that in cases of low external convective coefficient ( h o = 8.3 W m −2 K −1), long–short-axes ratio a / b ≦ 3 , and insulation thickness t / R 2 ≦ 2 , errors are within 3%. In rarer situations with a / b ≦ 5 and t / R 2 ≦ 2 , the errors are within 5.5%. The above results are almost independent with the internal flow convective coefficient ( h i from 30 to 10 5 W m −2 K −1) and dimensionless container size (0.5 R 2 h o/Ks from 1.55 to 155).