Abstract
The hydraulic analogue has a very great potential as a research tool, it is capable of solving complex heat transfer problems for which formal mathematical solutions are difficult to obtain and where numerical solutions involve lengthy and complex calculations. The great advantage of the hydraulic analogue over other types of analogue is the comparative ease with which complex thermal conditions can be simulated. Part I of the present work describes the application of the hydraulic analogue to three-dimensional heat conduction problems. The construction of a three-dimensional hydraulic analogue is described and this analogue is used to obtain the transient temperature distributions in a cube of conducting material with three-dimensional heat flow. The analogue solution is compared with a numerical solution and a maximum total error (i.e. a constructional error and a 'lumping' error due to the finite difference approximation) of +/- 2% of the temperature range was found in the analogue solution. Before the three-dimensional problem was solved, two preliminary tests were carried out in order to investigate the constructionalaecuracy of the analogue components. These tests consisted of a one- dimensional and a two-dimensional heat conduction problem; these were solved on the three-dimensional analogue and a maximum error of +/- 2% was found in the analogue solutions. The stability and accuracy of the finite difference solutions to the heat conduction equation are discussed. Part I of this work shows therefore, that three-dimensional conduction problems can be solved with acceptable accuracy using an hydraulic analogue. The boundary conditions in the Part I problems were very simple and to show that more complex boundary conditions can be simulated by a hydraulic analogue and also to show that flow systems can be represented,the work in Part II is presented In Part 2 the geometry has cylindrical symmetry and the problems considered are one and two-dimensional only. The analogue of Part 1 is not used. Part 2 describes a new hydraulic analogue for solving the complicated heat transfer problems associated with the transient operation of regenerators. In particular, start-up flow in a tube is considered. Here, the gas stream presents complicated boundary conditions for the inside surface of the tube, varying both with time and position. The boundary conditions are simulated in the hydraulic analogue using a series of positive displacement pumps to enable the change in enthalpy of the gas stream to be represented. The disadvantage of investigating the transient temperature responses in a regenerator using the hydraulic analogue is the very long experimental time required. However, if the thermal capacity of the gas stream is ignored, then the hydraulic analogue is shown to be a very useful method. The accuracy of the finite difference approximations used in the analogue design is investigated. Using certain simplifying assumptions, the heating-up period for an actual gas flow/refractory tube sustem is analysed using an hydraulic analogue. The analogue results are compared with the actual transient temperatures obtained by direct measurement on an existing rig; the maximum discrepancy between the two solutions was +/- 6% of the maximum temperature range.