BASIC CONCEPTS OF HEAT DISSIPATION EQUATIONS AND INVERSE PROBLEM THEORY

Heat dissipation is a fundamental physical process describing the transfer and distribution of thermal energy within solid bodies, fluids, and engineering systems. Mathematical models of heat dissipation are primarily based on the heat conduction equation, derived from the principles of energy conservation and Fourier's law of heat conduction. These equations enable the prediction of temperature distributions and thermal behavior in various scientific and industrial applications. Inverse problem theory plays a crucial role in heat transfer analysis when unknown parameters, boundary conditions, or internal heat sources must be determined from measured temperature data. Unlike direct problems, where system parameters are known and temperature fields are calculated, inverse heat transfer problems seek to reconstruct hidden information from observed thermal responses. Such problems are often ill-posed, requiring specialized mathematical techniques, regularization methods, and optimization algorithms to obtain stable and accurate solutions.