Abstract
The hydraulic analogue has no equal as a research tool in the visual study of the transient heat transfer problems. The experimental time can be designed long enough to carry out the manual adjustments of the analogue components, thus avoiding the costly automatic devices which would otherwise be built into the apparatus. The truncation error of the finite difference network and the construction error of the hydraulic analogue were investigated. The stability of the finite difference equations used in the designs were discussed, and some design parameters as guidance were suggested. An ingenious device of variable resistor for the simulation of the variation of thermal conductivity was used. The telescopic-tubes device for the variation of boundary temperature was satisfactory. Oils were found to be ideal for use, as they are free from the growth of organism and are not corrosive to the metal surfaces. Besides, suitable choice of oil can give almost any required length of experimental time. Using the shock heating problems of insulated rod and infinite plate for the comparison of hydraulic analogue accuracy, the central and end storage arrangements for the designs were also investigated. Shock heating problems of the infinite hollow cylinders of outer/inner diameter ratios of 5:1, 11:3, 15:7, 9:5, 19:11, and 27:19; and of the hollow spheres of outer/inner diameter ratios of 3:1, 2:1, and 3:2, were solved using the hydraulic analogue. In the application of the hydraulic analogue to the freezing and cooling problem of a finite cylindrical casting in a water cooled cast-iron mould, many components were designed to take into account of the latent heat, the variations of thermal conductivity, specific heat, density and boundary heat transfer coefficient, with temperature. The problem involved heat flow in two dimensions, and the mould interface temperature varied with the casting interface temperature. Salient points concluded from the results are: (1) The mould interface temperature was found more likely to vary with the casting interface temperature, and it would be a better approximation to use a reasonable relationship between the two temperatures for the boundary conditions of the casting rather than the usual assumption of constant temperature at the boundary. (2) It was found that there is a long period of partial contact between the casting and the mould during solidification, and the neglect of the conduction heat transfer would cause serious discrepancies. (3) It was found that the cooling curves within the steel casting investigated are quite accurate for use in the approximate analysis of thermal stress or solidification mechanisms of any similar casting problems.