This paper presents a method of analysis of heat conduction problems in solids based on matrix algebra.
Use is made of the analogy that exists between the thermal problem and the flow of electricity in an electrical transmission line. It is shown that the use of matrix algebra greatly facilitates the calculation of transient and periodic heat flow in composite solids.
WTRODUCTIOB
The close analogy that exists between the flow of heat in one dimension and the propagation of electricity in an electric cable has been known for a long time (1, 2, 3) .2 During recent years, several electrical engineers and physicists (4, 5, 6, 7) have systematized the mathematical analysis of propagation problems along transmission lines and cables by the introduction of the concept of the four-terminal network or quadripole and by the introduction of matrix algebra for the systematic analysis of such networks.
It is the purpose of this discussion to call these modern techniques to the attention of engineers who are concerned with heat-conduction problems. The basic principles involved are presented and tive problems. their use is illustrated by applying them to representa-Consider the THE FUNDAMENTAL. EQUATIOHS simple case of a homogeneous rectangular slab of material of uniform thickness shown in Fig. 1. Assume that the heat losses at the edges of the slab are such that they may be neglected and that the temperature of the slab is a function only of the co-ordinate x and the time t. Introduce the following notation : e(x,t) = i(x,t) = R= temperature of all points of slab situated at a distance x from edge of slab as shown in Fig. 1. heat flux or quantity of heat that passes through a plane perpendicular to the x-axis at a distance x from edge of slab per unit area in unit time. thermal or heat resistance per unit length of material of slab in direction of heat flow per unit area. (l/R is thermal conductivity.)