Thermal Convection With Large Viscosity Variation in an Enclosure With Localized Heating

Abstract

The present study is undertaken in order to gain an understanding of certain aspects of convective transport in a magma chamber. We have chosen to represent the chamber by an enclosure with localized heating from below. Results of both laboratory experiments and computer modeling are reported. The experimental apparatus consists of a transparent enclosure with a square planform. An electrically heated strip, with a width equal to 1/4 of the length of a side of the enclosure, is centered on the lower inside surface of the enclosure. For the experiments reported here, the top of the fluid layer is maintained at a constant temperature and the depth of the layer is equal to the width of the heated strip. The large viscosity variation characteristic of magma convection is simulated by using corn syrup as the working fluid. Measured velocity and temperature distributions as well as overall heat transfer rates are presented. The experiment is numerically simulated through use of a finite element computer program. Numerically predicted steamlines, isotherms, and velocity distributions are presented for the transverse vertical midplane of the enclosure. Good agreement is demonstrated between predictions and measurements.

Effects of temperature-dependent viscosity on Bénard convection in a porous medium using a non-Darcy model

“…He also concluded that when the viscosity varied within one order of magnitude, the concept of effective Rayleigh number would work while it was conceded that possible localized flow in a part of the flow region might invalidate this argument if the property variation were more severe. It is interesting to note that, in an example of a fluid clear of solid material, for natural convection of corn syrup with a temperature-dependent viscosity, even extreme viscosity variations, did not have a significant effect on the overall heat transfer coefficient provided the properties were evaluated at the mean temperature and a correction factor was used [32]. This conclusion is in line with what was reported for natural convection of air in a square enclosure [33].…”

“…However, when using this mean temperature, the Nusselt number showed notable differences from the constant property case. This behavior could be expected, to some extent, in the light of [32], where the authors recommended, for the clear fluid case, adding a viscosity fraction to the constant property Nu-Ra correlations to make them useful in variable property cases.…”

Heatline and Energy-Flux-Vector Visualization of Natural Convection in a Porous Cavity Occupied by a Fluid with Temperature-Dependent Viscosity

“…Chu and Hickox [8] reported that even extreme viscosity variations, in case of localized heating, will not have significant effects on the overall heat transfer coefficient provided the properties be evaluated at the arithmetic mean temperature and a viscosity ratio be applied. This conclusion is in line with what reported for free convection of air in a square enclosure by [9].…”

Study of buoyancy driven heat transport in silicone oils and in liquid nitrogen in view of cooling applications

“…A comparison was made against constant property and it was observed that the overall heat transfer is unaffected by the variation of the fluid properties, although the flow and temperature fields in the cavity seem to be different. Chu and Hickox [11] studied localized heating in a horizontal enclosure of square platform. In their work, which was complemented by experiments, a constant-temperature heated strip of fixed width was placed on the bottom wall of the enclosure.…”