The Critical Heat Transfer Characteristics of an Insulated Sphere Considering Heat Radiation

Abstract

This study is to investigate the critical heat transfer characteristics of an insulated sphere considering heat radiation. It is found that the results considering heat radiation are very big different from those of neglecting heat radiation. The critical heat transfer characteristics deeply depend on the sphere surface emissivity, ε0, and insulation surface emissivity ε, surrounding temperature Tsur and the internal convection heat transfer coefficient hi. In situations of necessary critical heat transfer condition of insulated sphere radius R2 must less than critical radius Rcr = 2Ks/h0 (i.e., R2/Rcr<1), the critical heat transfer will occur for neglecting heat radiation (ε0 = ε = 0). In situation of R2/Rcr<1, the external convection heat transfer coefficient h0 should be at small value, and thus heat radiation must be considered. For considering heat radiation, the critical heat transfer only occur at ε0 = εwith small value (for examples, the critical heat transfer only occur at ε0 = ε≦0.3 R2/Rcr = 0.75 in this study); the greater the value of ε0 = ε is, the smaller the critical insulated thickness tcr and neutral insulted thickness te will be. While ε0<ε, the insulated heat transfer rate qa is greater than that of non‐insulation qa0 (i.e., qa/qa0>1) at thinner insulation, the maximum value of qa/qa0 occurs at the near zero insulated thickness (t/R2→0); qa/qa0 = 0 locates at some insulated thickness te, then qa/qa0 is less than 1 after te; the greater the value of (ε‐ε0) is, the higher the value of (qa/qa0)max at t/R2→0 and greater the te will be; the values of (qa/qa0)max and te of considering heat radiation are dependent on the internal convection heat transfer coefficient hi, other than those of neglecting heat radiation are independent of hi; the higher the hi, the greater the (qa/qa0)max and te will be. While ε0>ε, all qa/qa0 are less than 1, thus there is no critical heat transfer will be occurred even in situation of R2/Rcr<1.