Heating and cooling of a building can be modeled by the ODE T \'= k 1 ( T - T a

Question

Heating and cooling of a building can be modeled by the ODE

T'= k1(T - Ta) + k2(T - Tw) + P

where T = T(t) is the temperature in the building at time t, Ta the outside temperature, Tw the temperature wanted in the building, and P the rate of increase of T due to machines and people in the building, and k1 and k2 are (negative) constants. Solve this ODE, assuming P = const, Tw = const, and Ta varying sinusoidally over 24 hours, say, Ta = A - C cos(2pi/24)t.Discuss the effect of each term of the equation on the solution.

Explanation / Answer

Ans. k1(T - Ta) follows from Newton

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