CHAPTER 10 - ANALOGUES

Abstract

This chapter provides an overview of direct and indirect analogs. In a direct analog, the analogous variable has the same significance everywhere within the analog system, while in an indirect analog this need not be so and solutions are obtained with the help of a mathematical model. A direct analog to one-dimensional heat flow can be an electrical network of capacitances and resistances in which there is a direct analogy between corresponding points in the thermal and in the electrical system. In an example of an indirect analog, the equation of heat conduction and the boundary conditions are transformed into finite difference equations that are the mathematical model to be solved by an analog. Indirect analogs may range from simple devices for solving particular mathematical problems to general purpose computers. Analogs can further be divided into continuous and discrete types; in the first, continua such as metal sheets are used, and in the second type lumped elements such as resistances and capacitances are used. Among the many possible systems, only mechanical and electrical systems have been used to any extent in heat flow problems. In summary, analog systems become much simpler if the relation between the rates of heat flow and the temperature differences is linear.