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114 This model retains stability despite its explicit formulation due to the assumed solid-fluid equilibrium. The cause of instability in the simplified explicit formulation was variation in fluid and solid temperatures and the terms that governed heat transfer between them. This mechanism is entirely absent in the infinite-NTU formulation as the fluid and solid are always in thermal equilibrium. Note that this infinite-NTU model could also be formulated implicitly. It is not developed here because an implicit formulation only adds computational complexity to an already efficient and stable method. Figure 6.16 shows that the infinite-NTU solution converges on a temperature profile that is sharper than the analytical solution for the test conditions. This behavior is explained by the fact that thermocline slope is related to NTUfluid (discussed in section 6.3.2). The analytical solution for the test case considers a finite fluid-solid heat transfer coefficient, thus the infinite-NTU solution overestimates the sharpness of the thermocline. As the precision of the infinite-NTU solution decreases the predicted thermocline becomes less and less sharp. Thus, as the resolution of the infinite-NTU solution decreases it first passes through the analytical solution, and then fully diverges. When used with systems having appropriately large values of NTUfluid the error incurred by using this approach will be minimal. Figure 6.16: Comparison of the analytical solution to the Schumann equations with the infinite-NTU numerical solutionPDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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