Estimation of Nighttime Temperatures in Unheated Shelters

Abstract

When net radiation flux on the ground turns the direction from incoming to outgoing about half an hour before the sun down, temperature within unheated shelters accelerates lowering and in a few hours approaches the air temperature outside shelters. It is not uncommon that the air temperature in row coverings and unheated small glasshouse gets below the outside air temperature on calm and clear nights in cold seasons.
Interrelations between inside and outside air temperatures and shelter wall temperatures under the process mentioned above were formulated on the basis of heat balance and with several assumptions.
The temperature of the shelter roof wall (T_w) goes down faster than the inside air temperature (T_i) in the evening, and becomes equal to the outside air temperature (T₀) when T_i is still higher than T₀ or T_w by εR(T₀)/h_i where εR(T₀) is the net heat loss through radiation from the roof wall of which temperature is equal to T₀, and hi is inside heat transfer (latent and sensible) coefficient This is the moment that convection heat transfer on the outer surface vanishes, and that heat loss consists of radiation only.
When T_i is equal to T₀, the wall temperature T_w will be lower than them by εR(T₀)/(h_i+h₀+h_r), where h_o is outside heat transfer coefficient and h_r is radiative heat transfer coefficient for the wall.
T_w of the roof wall can generally be written as equation (4). Examples of the relationship between three temperatures T_i, T₀ and T_w, are illustrated in figure 1.
On the assumption that T0, R and soil heat flux B are steady, the critical condition under which T_i in the shelter goes below T₀ is expressed as follows.
B/R(T₀)<F/γ(1-h_r+ε·h₀/h_i+h₀+h_r)
or
B/RT_i=T₀<F/γ(1-ε·h₀/h_i+h₀)
where R(T₀) is net radiation flux measured over the roof wall of which temperature is T₀, RT_i=T₀ is similar value measured when T_i=T₀, F is mean coefficient in radiation for all surface of the shelter, γ is rate of floor area to wall area, and ε is emissivity of the wall
Figure 3 shows the critical values of inversion calculated for a semicircle row cover under the various values of h_o and h_i.
The terminal difference in air temperatures of inside and outside the shelter will be obtained from following equation,
T_i-T₀=γB-(1-εC)FR(T₀)/h_i·C+h_ad, C=h₀+h_r/h_i+h₀+h_r, where h_ad is ventilating heat transfer coefficient.
The heat capacity within a shelter such as the raw covering and the small plastic or glass greenhouse is about tens times as large as the coefficient of heat loss from the surface of the shelter. Let us suppose that the outside temperature suddenly falls one unit degree from the steady condition, it will take only a few minutes to reach new equilibrium between outside and inside temperatures. Then, the above mentioned equaions obtained under steady conditions are thought to hold under the natural condition that the outside air temperature falls gradually.