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Single Room Cooling With On/Off Thermostat  File Size 9.26K | Date Added August, 21, 2000 You can you use and modify any of these worksheets with the Vissim 7 trial

Simplified Room Model Description Basic Information A typical house (1500 sf) requires 3 tons of cooling 1 ton of cooling = 12000 BTU/hr Density of air = .076 lb/f^3 400 f^3/min = 1 ton of cooling or 1 ton of cooling, 60*.076*400 = 1824 Lb/Hr is required Specific heat of air = .24 BTU/(lb - deg F) All units in Lb/hr, deg F Q = heat flow in units of BTU/hr = delta-T*S*w Typically (for cooling), Tin = 55 deg F Tair = 85 deg F or higher Troom = Tout = 68 to 75 deg F The model computes the temperature in a room into which cooled air is flowing. People in the room are used as heat input disturbances. Assumptions No heat storage in the room walls Room air is completely mixed. Parameters: Qp = rate of heat flow from people Qout = rate of heat flow carried out by air leaving room Qin = rate of heat flow carried in by air entering room Qe = rate of heat flow through room walls Troom = Room temperature Tin = temperature of air entering room Tout = temperature of air leaving room Tair = temperature of air surrounding room C = thermal capacitance of air in room R = thermal resistance of walls w = air flow out of room S = specific heat of air Equilibrium equation for rate of heat flow: Qp + Qout - Qin + Qe = 0 , where: Qp = C *Troom Qout = w*S*Troom Qin = w*S*Tin Qe = (Troom - Tair) / R Substitution yeilds: C*d(Troom)/dt + w*S*Troom - w*S*Tin + (Troom - Tair)/R = 0

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