Equações de Temperatura em Salas

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Problem 2.24PP
An air conditioner supplies cold air at the same temperature to each room on the fourth floor of 
the high-rise building shown in Fig.(a). The floor plan is shown in Fig.(b). The cold airflow 
produces an equal amount of heat flow q out of each room. Write a set of differential equations 
governing the temperature in each room, where 
To = temperature outside the building,
Ro = resistance to heat flow through the outer walls,
Ri = resistance to heat flow through the inner walls.
Assume that (1) all rooms are perfect squares. (2) there is no heat flow through the floors or 
ceilings, and (3) the temperature in each room is uniform throughout the room. Take advantage 
of symmetry to reduce the number of differential equations to three.
Figure Building air-conditioning; (a) high-rise building; (b) floor plan of the fourth floor 
ui syiiiineiiy (OTeuube me iiuinuei ui uiiieteiiiiai equauuiis lu iiiiee.
Figure Building air-conditioning; (a) high-rise building; (b) floor plan of the fourth floor
Step-by-step solution
step 1 of 2
“C" Thermal cs^acity o f Air 
*'1” Corners are equivalent 
“2” Arc equivalent
Step 2 of 2
Assuming; ^ >7J > ^ > 7 J 
For * 3" - (1)
Fo, -2 - = --------- (2)
s, R, Ro
F o r - r = + - ( 3 )
RequideEquations are (l)& (2 )& (3 )