Heat Transfer from Confined Contaminated Bubbles to Power‐Law Liquids at Low to Moderate Reynolds and Prandtl Numbers

Abstract

In this work combined effects of the wall confinement and the power-law fluid viscosity on the heat transfer phenomena of contaminated bubbles are reported through numerical investigations. In order to delineate the effect of insoluble surfactants the spherical stagnant cap model is adopted. The solver is thoroughly validated by comparing the present results with their literature counterparts. Further, extensive new results are reported on the isotherm contours and average Nusselt numbers of confined contaminated bubbles in the range of conditions: Reynolds number, Re: 0.1 to 200; Prandtl number, Pr: 1 to 1000; power-law index, n: 0.2 to 1.6 and stagnant cap angle, : 0 to 180°. Briefly, results are indicative of the following observations. The temperature contours are increasingly sucked towards the rear end of the bubble with the increase in Reynolds number and/or with the increase in Prandtl number and/or with the decrease in power-law index and/or with the decrease in stagnant cap angle. At Re ≤ 1 and Pr ≤ 10, the average Nusselt number is almost independent of power-law indices and the stagnant cap angle. For Pe > 10, regardless of values of the confinement ratio and Reynolds number, for ≥ 60 the average Nusselt number decreases with an increasing stagnant cap angle whereas for < 60 the effect of contamination is found to be insignificant. The increase in the average Nusselt number with an increasing confinement ratio would occur only at moderate to large values of Reynolds and Prandtl numbers regardless of the values of the power-law index provided that ≥ 60°. C⃝ 2016 Wiley Periodicals, Inc. Heat Trans Asian Res, 46 (7): 681-702, 2017; Published online in Wiley Online Library (wileyonlinelibrary.com/journal/htj).