A numerical study of natural convective heat transfer from upward facing recessed and protruding heated horizontal isothermal circular elements

Abstract

A numerical study of natural convective heat transfer from a horizontal upward facing circular isothermal heated element that is imbedded in a large flat adiabatic surrounding surface has been undertaken. The heated element is either recessed by a small amount into the surrounding flat horizontal adiabatic surface or it protrudes by a small amount out of the surrounding flat horizontal adiabatic surface. The element is at a higher temperature than the surrounding fluid and attention has been restricted to the case where the element is facing upward. The range of conditions considered is such that laminar, transitional, and turbulent flows can occur. The flow has been assumed to be two-dimensional and steady and in dealing with the buoyancy forces the Boussinesq approach has been adopted. The numerical solution has been obtained using the commercial CFD solver ANSYS FLUENT©. The k-epsilon turbulence model with account being taken of buoyancy force effects has been used. The heat transfer rate from the heated element expressed in terms of the Nusselt number is dependent on the Rayleigh number, on whether the heated element is recessed into or protrudes from the surrounding adiabatic surface, on the dimensionless height the element is recessed into or protrudes from the surrounding adiabatic surface, and on the Prandtl number. Results have been obtained for a Prandtl number of 0.74, i.e., effectively the value for air. The effect of the dimensionless height that the element is recessed or protrudes from the surrounding adiabatic surface on the variation of the Nusselt number with Rayleigh number has been studied. The diameter of the circular heated element has been used as the reference length scale and recess and protrusion height-todiameter ratios of between 0 and 0.25 have been considered.