Analytical solution of transient heat transfer with variable source for applications in nuclear reactors

The volumetric heat source in a nuclear fuel element, may vary with time and/or with space for an uncontrolled operating condition. The time required to attain the melting point of the cladding material was determined considering two trial variations of the source term, one with time only and the other with time and space as well. A general analytical solution for this transient heat transfer problem with variable source that can take care of any functional variations of source is presented. The dependence of the time required for melting of the cladding material with other parameters, e.g., Biot number, source strength, etc. are also investigated.