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

Abstract

Solar energy is a renewable resource because it is non-exhaustible and is available in abundance. The average daily total solar radiation amount in Malaysia is about 4500 Wh/m2, K.S Ong (1994). Intermittency and non-availability at night are the main drawbacks to the use of solar energy. However, heat storage devices could be designed to store heat for up to 24 hours if necessary. Solar water heaters are now 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 items in Malaysia. Users will always seek the product with cheaper price but at the same time still fulfill their need. Thus, 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 call as constraints. In this project the hot 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 the temperature distribution simulation. The overall average temperature obtained is 49.30C. The overall average temperature is used to solve the optimization problem. The constraints involve for the optimization are the tank volume and heat losses allowed from the water in the tank. The Lagrange multiplier method, which is based on derivatives of the objective function and the constraints are applied. The optimum independent variables and Lagrange multipliers is solved by computational approach. The minimum cost obtained for hot water storage tank with 225 l capacity is RM 1322.15. The Lagrange multipliers represent the sensitivity coefficient, which define as the rate of change of the objective function with the constraint at the optimum. This optimization method is very useful for the manufacturer in adjusting the design variables to come up with the final design.