Question

The air temperature on a clear night is observed to remain at about 4oC. Yet water in puddles outside is reported to be frozen. Taking the convection heat transfer coefficient to be 18 W/m2K, determine the value of the maximum effective sky temperature that night. Assume the water surface to have an emissivity of 1. Consider carefully all assumptions made in your analysis.

Answer 1

Freezing temperature of water Ts = 0°C + 273 = 273 K

Air temperature Ta = 4°C + 273 = 277 K

Let maximum effective sky temperature = T K

Emissivity of water surface e = 1

convection heat transfer coefficient h = 18 W/m2K

Heat transfer by convection from air to water surface = heat transfer by radiation from water surface to sky

h (Ta - Ts) = e * * (Ts⁴ - T⁴)

18 W/m2K * (277 - 273)K = 1*5.67*10^-8 W/m2K4 * (273⁴ - T⁴)K4

72 = 5.67*10^-8 (273⁴ - T⁴)

(273⁴ - T⁴) = 1269841269.84

T⁴ = 273⁴ - 1269841269.84

T⁴ = 4284730571.158

T = 255.84 K