Variational method in the design of an optimum solar water heater storage tank

Abstract

Solar water heaters are now have been accepted as a reliable source of providing hot water heating in many domestic homes and are becoming more popular. Unfortunately, solar water heaters are still considered luxurious hardware in Malaysia. A cheaper and efficient solar water heater system is required to be designed. The only way to produce cheaper and efficient product is through the optimization process to obtain the minimum cost but still maintain the specification required or known as constraints. In this paper, the vertical water storage tank will be analyzed to obtain the optimum cost. Thermosyphon-flow solar water heating system is preferred for obvious economic reasons since they do not require circulation pumps and control units. Average temperature of the hot water in the storage tank is determined through temperature distribution simulation. The overall average temperature obtained is 49.3ºC and is used to solve the optimization problem. The constraints in the optimization process are the tank volume and heat losses from the water in the tank. The Lagrange multiplier method, which is based on the differentiation of the objective function and the constraints is applied. The minimum cost obtained for storage tank volume of 225 litres is RM 1321.66