A thin, flat & square plate measuring 2 m x 2 m is freely hanging in ambient air at 25°C. It is exposed to the solar radiation falling on one side of the plate at the rate of 500 W/m² . The plate temperature will remain constant at 30°C, if the convective heat transfer co-efficient is __________ W/m² °C.

ANS:B - 100

To determine the convective heat transfer coefficient (ℎh) required for the plate temperature to remain constant at 30°C when exposed to solar radiation, we can use Newton's law of cooling, which relates the rate of heat transfer (Q) to the temperature difference (ΔT) and the convective heat transfer coefficient (ℎh). The equation is: Q=hAΔT Where:

• Q is the rate of heat transfer (in watts, W),
• ℎh is the convective heat transfer coefficient (in watts per square meter per degree Celsius, W/m²°C),
• A is the surface area of the plate (in square meters, m²),
• ΔT is the temperature difference between the plate and the surrounding air (in degrees Celsius, °C).

Given:

• Surface area of the plate, A = 2 m×2 m=4 m22m×2m=4m2
• Solar radiation falling on one side of the plate, Q = 500 W/m²
• Plate temperature, T = 30°C
• Ambient air temperature, Tambient​ = 25°C

The temperature difference, ΔT, is calculated as ΔT=T−Tambient​=30°C−25°C=5°C. Now, we can rearrange the equation to solve for ℎh: h=AΔTQ​ h=4m2×5°C500W/m2​ h=20m2°C500W/m2​ h=25W/m2°C Therefore, the convective heat transfer coefficient required for the plate temperature to remain constant at 30°C when exposed to solar radiation is 25 W/m²°C.