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Consider the transient heat transfer of a solid object suddenly exposed to an unbounded flow at different temperature. Based on the Lumped-heat capacity model (LHCM), the response time of heat transfer to the solid can be used to determine the convective heat transfer coefficient. Assume that the solid initial temperature, the ambient fluid temperature, and a temperature at the center of solid at a given time (after the exposure) are measurable. (1) Ignoring the radiation, derive an equation to correlate the convective heat transfer coefficient to the measured temperatures, the given time (when the temperature of solid is measured) and the solid material properties. (2) Based on the result of (1), how to check if LHCM can be applied to this case? (3) How does the thermal radiation affect the determination of the convective heat transfer coefficient, if the radiation effect needs to be included?