Heatlines: Modeling, visualization, mixing and thermal management

Abstract

The bulk motion of fluid and diffusive transport within fluid are two processes during natural or forced convection. The complexity of the convective heat flow is realized since last few decades and the analysis of the heat flow as well as thermal characteristics gradually becomes cumbersome. Although earlier researchers studied convective heat flow via velocity profiles, streamlines and isotherms, these tools were not enough for the efficient visualization of the unique features of convection heat flow. An efficient tool, termed as ‘heatline’ (mathematically represented as heatfunction) was first proposed by Kimura and Bejan in 1983 for the heat flow visualization during convective heat flow. The aim of this article is to review existing works on ‘heatline’ involving various physical systems. The mathematical implications of heatfunctions based on derivations of governing equations and boundary conditions for heatfunctions are presented in detail. The non-homogeneous boundary conditions for heatfunctions arise due to hot or cold or adiabatic walls as well as the junction between the walls and these conditions vary with the location of the reference or datum of the heatfunction. The physics on the heat flow via ‘heatlines’ are found to be invariant with the locations of the reference value of the heatfunction. The heat flow visualization is analyzed for various test cases from simple one dimensional boundary layer problem to convection in two dimensional complex cavities. The detailed explanations of earlier works on ‘heatlines’ during one dimensional flow involving forced or natural convection with various applications are discussed. Further, applications of ‘heatlines’ during convective heat flow within enclosed cavities involving uniform or non uniform heating of walls, discrete heating or cooling, conjugate convection and mixed convection are discussed and ‘heatlines’ are found to be successful to demonstrate various complex heat flow paths and multiple heat flow circulation cells. Overall, the analysis of convective heat flow from simple to complicated geometries via ‘heatline’ is crucial for the visualization of the thermal transport, mixing and efficient thermal management.