An experimental investigation of heat transfer through insulation uniformly applied to a flat end cylinder

Abstract

The determination of the heat transfer through a flat wall of which one surface is isothermal at a temperature of t_a and the other surface is isothermal at a temperature t_b is the simple problem of heat transfer. The equation: Q= (kA(t_a - t_b))/L Permits an easy solution of the problem where Q is the heat transfer, k is the thermal conductivity, A is the area through which the heat is transferred, and L is the distance between the two surfaces. The equation is only applicable where the area A is constant. This equation may be used without appreciable error for insulated enclosures such as furnaces where the insulation thickness is very small in comparison with the dimensions of the enclosure.

Shape factors have been applied to this basic equation so the equation may be used in the determination of heat transfer where the area A is not constant and the effect of corners can not be neglected. The equation then becomes Q= (fkA((t_a - t_b))/L Where f is the shape factor.

In 1947, T. S. Nickerson for a Master’s thesis at V.P.I. determined the values of the shape factor where the above equation is applied to cylindrical enclosures having flat ends and relatively thick walls of uniform thickness. Mr. Nickerson solved this problem analytically by the relaxation method. His solution depended upon the inside and outside surfaces of the insulation about the enclosure being isothermal surfaces. The values were calculated for combinations of ratios of insulation thickness to length of enclosure and length of enclosure to diameter of enclosure.

This investigation is an experimental determination of these values using gypsum plaster cylinders of different combinations of ratios of length to diameter. However, before tests could be conducted on the cylindrical enclosures, the conductivity of gypsum plaster, the insulation about the cylindrical enclosure, had to be found. The method of determination of the conductivity and the values are given in Appendix A.