The influence of radiant heat loss on the melting conditions of a material with internal heat release

Abstract

The RELEVANCE of the study lies in obtaining approximate analytical and numerical solutions for the problem of estimating the thermal state of thermal power equipment elements, such as thermal storage units and promising chemical reactors.The PURPOSE is to investigate the behavior of stationary solutions of heat conduction equations system in a space domain with internal heat release; to determine the conditions for the start and completion of melting, as well as the dependence of these conditions on the intensity of radiant heat loss at the outer boundary; to study the influence of individual factors on the phase boundary position.METHODS. Numerical methods are used: for a known type of solution, the coefficients are determined in such a way that the boundary conditions (in the general case, nonlinear) are satisfied. Newton's method is used to find the coefficients.RESULTS. The relationships between heat transfer parameters (convective and radiant heat transfer coefficients) and the phase transition boundary position in a cylindrical sample are obtained. These dependences allow to determine the critical values of the heat release intensity corresponding to the beginning of the sample melting (appearance of the liquid phase) and the complete sample melting (reaching the melting temperature at the outer boundary). These dependencies are compared with approximate formulas to assess the range of applicability of the latter.CONCLUSION. The presented calculations give the conditions for the beginning and end of melting of the heat-generating material. The conditions for complete melting of the sample can be determined accurately. The conditions for the onset of melting are obtained in the form of a nonlinear equation, the only physical (i.e., real and positive) root of which gives the critical value of the heat release intensity. In a linear approximation, a simplified formula can be obtained that relates the critical value of heat release intensity to radiant heat loss.