Insulated Furnace

by Tom Angelina

Submitted : Spring 2010

A furnace operates at 2000 degrees Fahrenheit and is isolated from the surroundings (at 75 degrees Fahrenheit) by a metal wall of thickness L = 1/8 inch. The total surface area of the furnace is 60 square feet. The furnace is to be covered with a layer of insulation of thickness W. There is a cost associated with the heat lost to the surroundings. However, there is a cost associated with adding insulation as well. As a result, there is an optimum insulation thickness that will minimize the total cost to the company. The goal is to find this optimum thickness W that will minimize the total annual cost, the resulting annual insulation cost, and the heat loss rate.

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