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A convolution method for inverse heat conduction problems

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The problem of determining the temperature at one end of a rod by means of interior temperature measurements has considerable practical importance and has been well studied, however, few exact solutions have been found. Most of the applicable results therefore, have been obtained from the (numerical) analysis of discretized systems. In this paper we present an analytic method for obtaining solutions to this problem which does not require differentiation (only integration) of the interior temperature readings and is valid for general finite energy boundary data and for general radiation boundary conditions at the known end of the rod.

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Gilliam, D.S., Mair, B.A. & Martin, C.F. A convolution method for inverse heat conduction problems. Math. Systems Theory 21, 49–60 (1988).

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