Question

A 2-m x 1.5-m section of wall of an industrial furnace burning natural gas is not insulated, and the temperature at the outer surface of this section is measured to be 80 °c. the temperature of the furnace room is 30 °c, and the combined convection and radiation heat transfer coefficient at the outer surface of the furnace is 10 w/m2/k. it is proposed to insulate this section of the furnace wall on the outside with glass wool insulation (with thermal conductivity of 0.038 w/m/k) in order to reduce the heat loss by 90 percent. assuming the outer surface temperature of the metal section still remains at about 80 °c and that the combined heat transfer coefficient at the outer surface of the furnace remains at 10 w/m2/k, determine the thickness of the insulation that needs to be used to reduce the heat loss by 90 percent.

Answer 1

To determine the insulation thickness needed to reduce heat loss by 90%, the initial heat transfer rate is computed using the given surface temperature, room temperature, and heat transfer coefficient. Then the thickness is determined by applying Fourier's law, incorporating the thermal conductivity of the glass wool insulation and external conditions.

To calculate the thickness of the insulation required to reduce the heat loss by 90%, we need to first understand the initial heat loss without insulation. Using the heat transfer equation Q = hA(Twall - Troom), where Q is the heat transfer, h is the heat transfer coefficient, A is the surface area, and (Twall - Troom) is the temperature difference, we calculate the initial heat loss rate.

Then, based on the thermal conductivity of the glass wool insulation, we use Fourier's law Qins = Q/10 = kA(Twall - Troom)/L, where L is the thickness of insulation. Solving for L gives us the needed insulation thickness. As external conditions stay the same, the same h is used in the calculations.

In conclusion, by using the above equations and given thermal conductivity for glass wool, one can determine the required insulation thickness to achieve a 90% reduction in heat transfer.