Final answer:
To calculate the surface temperature of a heated flat plate in turbulent airflow, apply the convective heat transfer equation using the given uniform heat flux and air properties, along with empirical correlations to determine the convective heat transfer coefficient.
Step-by-step explanation:
The question involves calculating the plate surface temperature, Ts(L), for air flowing over a heated flat plate in a thermodynamics and heat transfer context. The flow is assumed to be fully turbulent, and the air has an initial temperature of 25°C, moving at 5 m/s with a uniform heat flux provided to the plate.
To solve for Ts(L), we need to apply principles of heat transfer, specifically the convective heat transfer equation. Given the uniform heat flux q is 1250 W/m², the equation can be rearranged to solve for the temperature difference (ΔT) between the plate surface and the air, where ΔT = q / (hA), and h is the convective heat transfer coefficient that can be determined from empirical correlations for turbulent flow over a flat plate. The area A is the surface area through which heat is being transferred.
To find h, one might use the Dittus-Boelter equation for turbulent flow over a flat plate, which relates h to the fluid velocity, fluid properties, and plate dimensions. Once h is calculated, it can be used to determine ΔT, and then the surface temperature of the plate Ts(L) can be found by adding this temperature difference to the initial air temperature of 25°C.