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A two-dimensional finite element program has been developed to analyze the transient heat flow paths in low-heat-rejection engine combustion chambers. This analysis tool is used to study the transient heat transfer performance of a ceramic-coated piston with steel-alloy rings reciprocating within a ceramic-coated iiner at a speed of 1900 revolutions per minute. Throughout the cycle, the instantaneous boundaries of the combustion chamber are defined based on the position of the piston against the liner. Then, appropriate boundary conditions are applied to the component surfaces at every instant. Instantaneous piston and liner temperature distributions, heat transfer rates from the working fluid to these two components, as well as heat transfer rates between the two components are calculated by the program. The results are compared against the performance of a baseline cast-iron piston-liner assembly.