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    <subfield code="a">Renewable energy is important for replace the using of electrical energy generated by petroleum. Energy consumption from petroleum must be reduced because of the limited petroleum resources and contribute of pollution to the earth. Solar power has become a source of renewable energy and solar energy applications should be enhanced. Solar water heating system was a practical application to replace the using of electrical water heater. More research is needed to increase capability and reduce production costs of solar water heating system and make the solar water heating system more efficient and practical. The objective of this project is to do investigation on solar water heating  system in terms of mathematical theory to produce a mathematical model of solar water heating system. The analysis done by using a mathematical model developed to obtain data on temperature in the changes of flat plate collector area, storage tank insulation volume, piping size and mass flow rate of water. Efficiency of flat plate collector and storage tank insulation is calculated for any changes in size and volume. Solar fraction is calculated for any changes in the size of a flat plate collector and storage tank insulation in the consideration of changes in temperature and mass flow rate of water.  Analysis showed the water temperature will increase with increasing area of flat plate collector, decreased with the increasing volume of insulated storage tank, and decreased with increasing size of the pipe. an These studies can provide data for the optimum design with high capacity and the mathematical models will facilitate the future study.</subfield>
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