To improve the cooling performance of a nuclear fuel element, it is important to appraise the effect of dimensionless parameters and the geometry on heat‐transfer characteristic of sodium flowing over a nuclear fuel element. To fulfill this objective, the effects of geometry, Reynolds number (ReH), conductivity ratio ( N cc ), and dimensionless total heat generation parameter ( Qt) on a two‐dimensional steady flow of liquid coolant flowing over a nuclear fuel element are studied. For this purpose, the stream function‐vorticity formulation method is applied. Full Navier Stokes equations and energy equation for the fluid domain are solved concurrently with conduction equation of fuel element applying finite difference scheme. The pseudotransient form of the vorticity transport and energy equations is solved using the alternating direction implicit method. A line‐by‐line technique is used for other discretized equations. Isotherms are also plotted and studied in detail. From the obtained results it can be concluded that for fixed values of aspect ratio and Re H there exists a critical value of Qt and N cc beyond and below which peak temperature in the fuel element surpasses its tolerable limit. The results can also be applied to minimize the peak temperature in the nuclear fuel element (hot spots).
A coupled conduction–convection heat transfer analysis is carried out for a two‐dimensional rectangular, vertical parallel plate channel producing volumetric energy (uniform and nonuniform), subjected to laminar forced‐convection incompressible fluid flow under steady‐state conditions. The equations governing the thermal and flow field are solved by using finite difference method, and the resulting algebraic equations are solved by using the tridiagonal matrix algorithm method. Four coolants with their Prandtl numbers (Pr), namely, liquid sodium (Pr = 0.005), sodium‐potassium (Pr = 0.00753), lead (Pr = 0.02252), and helium (Pr = 0.666) are used for the present conjugate analysis. Effects of different thermal and fluid flow parameters such as Reynolds number (ReH) ranging from 500 to 1500, conduction–convection parameter (Ncc), and total heat generation (Qt) on average exit temperature (θae) of coolants are studied. From the obtained results, it is found that the θae of coolant strongly depends on Pr, ReH, Ncc, and Qt when the aspect ratio (Ar) is kept constant. It is also found that with a nonuniform rate of heat generation, the coolant θae is high compared to uniform heat generation rate, whereas with increasing Ncc, the θae decreases, and with increasing Qt, the θae increases irrespective of coolants.
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