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To resolve two major problems of conventional CFD-based shape optimization technology: (1) dependence of the outcome on the selection of design parameters, and (2) high computational costs, two types of innovative inverse analysis technologies based on a mathematical theory called the Adjoint Method were developed in previous studies for maximizing an arbitrary hydrodynamic performance aspect as the cost function: surface geometry deformation sensitivity analysis to identify the locations to be modified, and topology optimization to generate an optimal shape. Furthermore, these technologies were extended to transient flows by the application of the transient Adjoint Method theory. However, there are many cases around flow path shapes in vehicles where performance with respect to heat or concentration, such as the total amount of heat transfer or the flow rate of a specific gas component, is very important.