Rayleigh–Benard convection in Herschel–Bulkley fluid

Abstract

The intent of the present work is to investigate Rayleigh–Benard convection in a viscoplastic fluid prepared from Carbopol (Ultrez 20) gel. Thermorheological characterization of the test fluid has been presented and rheological properties are represented by Herschel–Bulkley model. Further, temperature dependency of rheological parameters is described by Arrhenius model. Rayleigh–Benard convection phenomenon in a square enclosure filled with viscoplastic fluid has been investigated numerically as well as experimentally. The proposed computational model uses the temperature-dependent rheological properties. Results of the proposed model show a fair agreement with our own experimental data. Use of temperature-dependent rheological properties has improved the predictions significantly. With the increase in yield stress, there is a phenomenal change in diminishing convective flow patterns. Critical Rayleigh number representing the onset of convection has been determined for different concentrations of the gel. Nusselt number correlations as a function of Rayleigh number and yield number have been developed for two different values of Prandtl number.