An inverse analysis is employed to estimate the unknown temperature distribution over the heater surface of a square cavity with natural convection from the knowledge of desired temperature and heat flux distributions over a given design surface. The direct problem of natural convection in a square cavity is solved by the finite volume method. The conjugate gradient method is used for minimization of an objective function, which is expressed by the sum of square residuals between estimated and desired temperatures over the design surface. The performance and accuracy of the present method for solving inverse convection heat transfer problems is evaluated by comparing the results with a benchmark problem and a numerical experiment.

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