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Figure 6.15: Comparison of the analytical solution to the Schumann equations with the implicit numerical solution The implicit model requires additional computational overhead, but the guarantee of solution stability makes the implicit model conducive to either coarse or detailed simulation runs. The Infinite-NTU Model The infinite-NTU model adds an additional assumption to the Schumann equations that offers unsurpassed computational efficiency and guaranteed stability. These attributes are achieved by assuming the overall heat transfer coefficient in each node of the finite- difference approximation is effectively infinite. The result is that at the end of every time and distance step the temperature of the solid and the temperature of the fluid are in equilibrium. The finite-difference equations for the infinite-NTU model are derived starting with equations [6.3.26] and [6.3.27] while assumingTf ,(i+1,t+∆t) =Ts,(i,t+∆t) . This simplification yields the following single equation: Tf,(i,t+∆t) =Ts,(i−1,t+∆t) =Tf,(i−1,t)m&fCp,f∆t+Ts,(i,t)msCp,s [6.3.38] m& f C p , f ∆ t + m s C p , s 113PDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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