When the operating condition of a gas-turbine engine changes from one steady state to another, the cooling must ensure that the solid’s temperatures to never exceed the maximum allowable throughout the transient process. Exceeding the maximum allowable temperature is possible even though cooling is increased to compensate for the increase in heating because there is a time lag in how the solid responds to sudden changes in its convective heating and cooling environments. In this paper, a closed-form integral solution (referred to as the 1-D model) is generated to study the unsteady heat transfer in a flat plate subjected to sudden changes in convective heating and cooling. Comparison with the exact solution shows the 1-D model to be accurate within 0.1%. The 1-D model can be used to estimate the over temperature and its duration in a flat plate subjected to sudden changes in heating and cooling rates. For a given change in heating rate, the 1-D model can also be used to estimate the minimum cooling needed to ensure the new steady-state temperature will not exceed the maximum allowable. In addition, this model can estimate the precooled wall temperature needed before imposing a sudden increase in heat load to ensure no over temperature. This 1-D model was generalized for application to problems in multidimensions. The generalized model was used to estimate the duration of over temperature in a two-dimensional problem involving a step change in the heat-transfer coefficient on cooled side of a flat plate and provided results that match the exact solution within 5%.

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