Two-dimensional inverse problem in estimating heat fluxes of an enclosure with unknown internal heat sources

The methodology in estimating the unknown temporal and spatial variation of inside heat fluxes of a heat-generated enclosure is derived by using the conjugate gradient method in a two-dimensional inverse problem. The advantage of the conjugate gradient method is that there is no need to assume a specific functional form for the unknown quantities beforehand, since the solution automatically determines the functional form over the domains specified. Such a technique can be applied to determine the internal wall heat fluxes acting on the inner and upper surfaces in the cylinder of an internal combustion engine, simultaneously, from the knowledge of transient temperature measurements taken inside the cylinder block and head, respectively, which is discussed in detail. The other application is the determination of inside heat fluxes of a nuclear fuel rod. Once wall heat fluxes inside the cylinder are determined, the exhaust heat produced by the cylinder head and block can be calculated. Furthermore, the cooling system for the cylinder can be established from the knowledge of heat transfer rate to it to avoid crack damage.