Rayleigh-Benard convection in Herschel-Bulkley fluid

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.