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This paper studies a prototype of inverse initial boundary value problemswhose governing equation is the heat equation in three dimensions. An unknowndiscontinuity embedded in a three-dimensional heat conductive body isconsidered. A {\it single} set of the temperature and heat flux on the lateralboundary for a fixed observation time is given as an observation datum. It isshown that this datum yields the minimum length of broken paths that start at agiven point outside the body, go to a point on the boundary of the unknowndiscontinuity and return to a point on the boundary of the body under someconditions on the input heat flux, the unknown discontinuity and the body. Thisis new information obtained by using enclosure method.

An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method