A transient, multi-dimensional, heat conduction problem can be solved using analytical (exact and approximate) and numerical methods [1, 2]. They are the first stage of solution procedures for solving the inverse heat conduction problems (IHCPs) . Among them, the numerical approximate form of the Green’s function equation based on a heat-flux formulation can be relevant in investigation of the IHC problems because it gives a convenient expression for the temperature in terms of the unknown heat flux components. Also, it states that the temperature or heat flux computation employs only one basic “building block” solution, which is the solution of a direct problem subject to a partial heating by a boundary condition of Neumann type. This solution was derived by exact analysis using Green’s functions in Ref. .
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