Optimum flow rates in solar water heating systems with a counterflow exchanger

Abstract

Although optimum collector flow rates in solar water heating systems have been broadly established, the existence of such an optimum has not been demonstrated for systems having a heat exchanger between the collector fluid and the tank water to be heated. Starting from the premise that the overall exchanger conductance ( UA) x can be conceptually held fixed while the flow rates are varied in search of an optimum, we show analytically that optimum flow rates do indeed exist on both sides of the exchanger. We deduce that the optimum value R opt of the exchanger heat capacity ratio R—i.e., the optimum collector-side flow, relative to the tank-side flow—is a function only of the conductance ratio ϱ = (UA) x F′U LA c , as follows: R opt = (1 + ϱ) ϱ . Moreover, an exchanger/collector combination operating with R = R opt is shown to behave, for all practical purposes, like a direct water-heating collector with its area reduced by the factor ϱ (1 + ϱ) . From this we deduce that there exists an optimum tank-side flow rate m ̇ t, opt , in the same sense that there exists an optimum collector flow rate m ̇ t, opt for systems without exchangers, and deduce the relation m ̇ t, opt = ( ϱ (1 + ϱ) ) q m ̇ opt , where q ≈ 0.4. Finally, we use this principle of equivalent behaviour to derive an expression for the most economical value of ( UA) x .