Unified approach on numerical implementation of heatfunction boundary conditions for accurate prediction of heatlines involving steady convection in enclosures

Abstract

The tool “Heatlines” is useful to understand heat flow and thermal management in enclosures experiencing convection. The heatline concept was first introduced by Bejan in the early 80’s. This article starts with the fundamental principles of heatlines or heat flow trajectories followed by a generalized governing equation for heatfunction (Π) applicable for fluid, nanofluid, or fluid-saturated porous medium experiencing steady natural or mixed convection within enclosures. An unified approach on derivation of heatfunction boundary conditions is presented based on Dirichlet conditions at junction of walls while Neumann conditions at walls for Π. The solution of Π also requires the selection of location of Π = 0 and this article outlines a generalized overview on the invariance of heatline trajectories irrespective of the location of Π = 0 for enclosures with or without adiabatic walls. Open loop or end to end heatlines demonstrate the heat flow path for conductive heat transport whereas open loop heatlines cross various regimes of dominant conduction or convection zones connecting the hot walls to the cold walls for convective heat transport. Closed loop heatline vortices (qualitatively similar to the flow vortices) depict the convective heat flow via the trajectories of the fluid flow vortices. A few feasible heatlines for conduction and convection dominant heat transport in enclosures (steady state) have been presented to illustrate the physics of “heatlines.” This article also addresses a few earlier works depicting discrepancies in heatline trajectories [discrepancies: heat flow to and from the same walls (isothermally hot/cold or adiabatic) or heat flow from the hot/cold to the adiabatic wall(s)] and proposes qualitative pictures for feasible heatlines for a few earlier case studies. Understanding the feasible implementation of heatlines is required as the inaccurate representation of heatlines may mislead future researchers in interpreting the energy flow.

Keywords:

• Boundary conditions
• heatfunction
• heatlines
• mixed convection
• natural convection