A Home Heating Model For Calculus Students

A Home Heating Model for Calculus Students
Authors: Sansgiry, Prashant S. and Edwards, Constance C.
College Mathematics Journal, Vol. 27, no. 5, pp. 394-397, 1996.

This article uses differential equations and Newton's Law of Cooling to develop a model of a home heating system. The authors consider a one-story house with an insulated attic where the furnace raises the inside temperature at a constant rate, H(t). The model describes the temperature in the living area and in the attic of the house. In the simplest case, the outside temperature is kept constant and the furnace is always on. The authors then add some complexity to the model by allowing the outside temperature to fluctuate, and by requiring that the furnace shut off when the air in the living area reaches a fixed threshold (68 degrees). According to the model, the living area will reach a steady state of 68 degrees, but the attic temperature will fluctuate with the outside temperature. (Summary by Sarah Kinicki, Pomona College '12)