Influence of Prandtl number on heat transfer of a flat vertical plate

Liquid metals, such as sodium (Na), lead (Pb), and lead-bismuth (Pb-Bi) eutectic (e), are considered as potential coolants for the fast spectrum nuclear reactors of the next generation. So the main objective of this paper is to study the heat transfer and fluid flow characteristics of liquid metal coolants flowing over a nuclear fuel element having uniform volumetric energy generation. Stream function vorticity formulation method was used to solve the full Navier Stokes equations governing the flow. The energy equation was solved using central finite difference method. For the two-dimensional steady state heat conduction and stream-function equation, the discretisation was done in the form suitable to solve using 'line-by-line Gauss-Seidel' solution technique whereas the discretisation of vorticity transport and energy equations was done using Alternating Direction Implicit (ADI) scheme. After discretisation the systems of algebraic equations were solved using 'Thomas algorithm'. The complete work was done by writing a well-validated indigenous computer code using C-language. The parameters considered for the study were: aspect ratio of fuel element, Ar, conduction-convection parameter Ncc, total energy generation parameter Qt, and flow Reynolds number ReH. The results obtained can be used to minimise the maximum temperature in the fuel element (hot spots) and prevent its melting.