Hot water heating coils are key components in air conditioning systems undergo heat transfer. The most widely used exchangers (coils) take the form of fin and tube configuration in association with the application of air conditioning systems. In this research, thermodynamic modeling and mathematical optimization of hot water heating coils at steady conditions, approaching minimum energy consumption are achieved. The modeling procedure for heating coils is done based on the log mean temperature difference (LMTD) method. The objective function for optimization is pressure drop of air crossing coil per heating load of the system. This unction comprises all thermal and geometrical parameters of the coils such as coil surface area, number of rows, fin spacing and air side pressure drop of the coil. The objective function is minimized using Lagrange multipliers method. The optimization results are composed of minimum pressure drop, optimum surface area, optimum number of rows and fin spacing. The effects of varying the heating load, fin efficiency and the surface area of the coils on optimum behavior of them are investigated as well.

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