Heat-balance Integral Method for Heat Transfer in Superfluid Helium

The heat-bal ance in te gral method is used to solve the non-lin ear heat dif fu sion equa tion in static tur bu lent superfluid he lium (He II). Al though this is an ap prox i mate method, it has proven that it gives so lu tions with fairly good ac cu racy in non-lin ear fluid dy nam ics and heat trans fer. Us ing this method, it has been pos si ble to de velop pre dic tive so lu tions that re pro duce an a lyt i cal so lu tion and ex per i men tal data. We pres ent the so lu tions of the clamped heat flux case and the clamped tem per a ture case in a semi-in fi nite us ing in de pend ent vari able trans for ma tion to take ac count of tem per a ture de pend ency of the thermophysical prop er ties. Good ac cu racy is ob tained us ing the Kirchhoff trans form whereas the method fails with the Good man trans form for larger tem per a ture range.