This paper derives a new recurrence relation for inverse Laplace transformation, which is not listed in Appendix V, “Table of Laplace transforms” in the Carslaw and Jeager textbook. An exact solution can be given using the recurrence relation in order to analyze the temperature distribution in composite slabs with one very thin layer of poor heat conductivity, such as a oxide layer on a carbon steel, in a very short time, after which heat transfer suddenly takes place. The temperature distributions for the scale with a thickness of 0.001, 0.01, and 0.1 mm are calculated in a short time from 1.0 μs to 10 ms. In the case of a fix recurrence number, n = 6, the numerical result calculated for the scale thickness of 0.001 mm is found to be just available in the time range less than 100 μs. In addition, a slope of the temperature curve in the scale becomes almost linear after the time when its temperature change reaches the interface between layers.

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