Shape factors in multiple‐pipe systems

Abstract

Problems in conductive heat transfer frequenrtly do not lend themselves to simple mathematical treatment. Except for a few geometrical configurations such as parallel plates and concentric cylinders, an exact mathematical solution is often either impossible or difficult, owing to the irregular shape of the body conducting heat and the complicated boundary conditions involved. Through the use of experimentally determined shape factors, many of these problems can be solved easily.A simple, inexpensive means f o r the experimental determination of shape factors has been presented by Andrews(1). The method consists essentially of drawing with a silver paint on a conducting paper the figure whose shape factor is desired. The electrical resistance of this figure is then compared to the electrical resistance of a standard figure whose shape factor can be calculated mathematically. Equation (1) is then used t o calculate the shape factor of the desired figure. The shape = SF unknown std.shape factorRstd.'Runknown(1) where SF = shape factor R = resistance in ohms factor so determined is then used in Equation (2) to calculate the heat transferred by conduction. Figure 1 shows the electrical circuit used to obtain accurate values of the resistances which are used in Equation (1). The shape factors obtained by this method are independent of the thermal conductivity of the material transferring heat or of the terminal temperatures of the heat flow path. As the units of the shape factor ai-e length, i t may be considered to be an effective area for heat transfer divided by a unit effective length of heat transfer path.The use of buried conduits con-