Estimation of characteristic length of a horizontal cylindrical annulus for heat transfer through conduction using Rayleigh number

Abstract

Heat transfer from or to a horizontal cylinder has got substantial significance in many engineering applications, such as in heating and cooling devices, steam pipelines, heat exchangers etc. Coaxial cylinder technique may be used for the analysis of heat transferred by conduction through a concentric cylindrical annulus where the two surfaces are maintained at a constant temperature. The annular space is filled with the fluid sample whose thermal conductivity needs to be measured. If a heat flux is imposed on the sample from the inner to the outer cylinder, it propagates through the fluid in a radial direction under steady state condition. Insulating the terminal ends ensures heat flow primarily in radial direction and prevents heat loss at the ends. The focus is on the use of dimensionless numbers used in multi-domain coupled conduction-convection flow problems so as to find out the optimum gap thickness in between the two concentric cylinders at which convection will just onset and upto which conduction is the only heat transfer mode. The values of these numbers can be used as guidelines in finding the optimum value from which an experimental set up for determination of thermal conductivity of various fluids based on co-axial cylinder technique can be designed, it can be later extended to analyse thermal conductivity of nanofluids as well.