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in section 6.3.1. Rf-s is based on a Nusselt number of two, the no-flow limit in equation [6.3.12]. The magnitude of axial conduction and environmental losses compared with fluid-solid convection is evaluated in the following ratios: r = Rf −s axial loss [6.3.44] [6.3.45] Rlosses For the test conditions (section 6.3.1) raxial and rloss were both computed to be less than 0.001 indicating that in the absence of fluid flow, fluid-solid interaction still dominates axial conduction and losses to the surroundings. It is then appropriate to treat the fluid- solid tank as a continuous medium for the simulation of an idle storage tank. The consideration of convective losses, absent in the charge-discharge case, introduces a modeling dilemma. For the charge/discharge models, temperature gradients in the radial direction of the tank are not an issue as the fluid is presumed to be introduced uniformly (in temperature and flow) across the cross-section of the bed and shell losses were ignored. When considering convective losses, the relatively low effective conductivity in the bed will likely introduce temperature gradients in the radial direction (from the core of the tank to the wall). The significance of these temperature gradients is usually considered by examining the Biot number. The Biot number represents the ratio of resistance to conductive heat transfer from the core of the tank to the wall and the resistance to convective heat transfer from the tank’s surface. It is defined for this case as follows: loss,w tank = h r [6.3.46] keff Traditionally temperature gradients are negligible if the Biot number is less than 0.1, for the test case the Biot number for radial temperature gradients is well above this threshold (>1.0). Generally, the radial temperature gradient would be accommodated by expanding the heat transfer model to two dimensions. However, the computational requirements of long-term simulations are a 2-dimensional heat transfer model is not practical. In order to approximate the impact of the radial temperature gradients while retaining conduction Bi = R 131 Raxial conduction r =Rf−s RconvectionPDF Image | Organic Rankine Cycle Solar-Thermal Powerplants
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