Numerical Investigation of the Natural Convection Flows for Low-Prandtl Fluids in Vertical Parallel-Plates Channels

Laminar natural convection of metallic fluids $(Pr⪡1)$ between vertical parallel plate channels with isoflux heating is investigated numerically in this work. The full elliptic Navier-Stokes and energy equations have been solved with the combination of the stream function and vorticity method and the finite-volume technique. An enlarged computational domain is employed to take into account the flow and thermal diffusion effects. Results are presented in terms of velocity and temperature profiles. The investigation also focuses on the flow and thermal development inside the channel; the outcomes show that fully developed flow is attained up to $Ra=103$⁠, whereas the thermal fully developed condition is attained up to $Ra=104$⁠. Further, correlation equations for the dimensionless induced flow rate, maximum dimensionless wall temperatures, and average Nusselt numbers as functions of the descriptive geometrical and thermal parameters covering the collection of channel Grashof numbers $1.32×103⩽Gr∕A⩽5.0×106$ and aspect ratios $5⩽A⩽15$⁠. Comparison with experimental measurements has been presented to assess the validity of the numerical computational procedure.