A 3D Numerical Simulation of a Cylindrical Towel Heater With Symmetric and Asymmetric Heating

Abstract

In this study a cylindrical towel heater filled with air is simulated numerically in three-dimensions, with the cylinder being heated electrically from the side. The objective is to investigate the efficiency of the heating process as to maintain the towel at a certain temperature, higher than the ambient temperature (ambient temperature outside the heating cylinder), with the heating being symmetric or asymmetric. The process is modeled analytically assuming the towel as a homogeneous and isotropic porous medium, saturated with air, and enclosed by the cylinder. The cylinder wall is heated with a constant, symmetric or asymmetric heat flux, with the bottom surface assumed adiabatic and the top isothermal in equilibrium with the ambient air. The porous-continuum mass, momentum and energy equations for the natural convection inside the cylinder, derived through volume averaging the continuum equations with appropriate closure equations, are written in nondimensional form and solved numerically using the finite-volume method. A parametric study is then performed, after identifying suitable ranges for the parameters involved, to identify the effects of the several controlling parameters, namely the cylinder heating strength (the Rayleigh number), the towel permeability (the Darcy number), form coefficient (the dimensionless form coefficient), and thermal diffusivity (modified Prandtl number). The results, in terms of volume-averaged and surface-averaged temperatures and Nusselt numbers, indicate that the Darcy and Rayleigh numbers have a predominant effect on the natural convection process inside the cylinder, with the inertia coefficient and the modified Prandtl number having lesser influence on the results. For the asymmetric heating configuration, the resulting Nusselt number is higher while the volume-averaged temperature is lower, as compared to the symmetric heating. Hence, a symmetric heating is preferable if a high average towel temperature is the objective of the heater. If a more efficient heating process is sought, on the other hand, than the asymmetric option should be the best alternative.