This paper deals with solutions of inverse heat conduction problems to specify surface heat flux from temperature histories in a body. Heat flux at each timestep is determined as the calculated temperature at a measurement point exactly matching the measurement. This is applied not only to planar bodies, but also cylindrical and spherical bodies. Although this method can cause numerical instability for small timesteps, we find that this is not always true. A fully implicit finite difference method gives stable solutions for any timestep length though there exists restriction of node spacing. Stability of this scheme is explained using the eigenvalue of the matrix. The obtained heat flux waveform shows some delay. We find that a scheme using interpolation with quadratic functions to find the mean temperature of control volumes leads to a delay of at least half a timestep. This interpolation causes numerical instability for very large node spacings, but this restriction is sufficiently acceptable. The effects of noise are studied to show the amplifying factor from temperature to heat flux as a function of timestep. Simulations confirm the effectiveness of this factor. It is also shown that filtering prior to this inverse solution is effective.

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