Effects of Contamination and Power‐Law Fluid Viscosity on Heat Transfer Phenomena of Spherical Bubbles

Abstract

Heat transfer phenomena of spherical bubbles in unbounded contaminated power‐law liquids were numerically studied within the framework of a stagnant spherical cap model by solving the governing conservation equations of mass, momentum, and energy using a segregated approach. The governing equations were solved with the semi‐implicit method for pressure‐linked equations. The momentum terms were discretized by quadratic upstream interpolation for convective kinematics. Isotherm contours reveal that the thermal boundary layer becomes thinner with the decreasing power‐law index and/or the stagnant cap angle. The surface Nusselt number distributions indicate a sudden decrease at the leading edge of the stagnant cap and this reduction is found to be a strong function of all pertinent parameters. The average Nusselt numbers of contaminated spherical bubbles rise with the smaller cap angle and/or the lower power‐law index.

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

“…The stagnant cap model has been extensively adopted to interpret experimental results and found that this model is consistent with experimental results not only at low to moderate Reynolds numbers but also at large values of the Reynolds numbers. Furthermore, this model is also tested theoretically by many researchers and proved to be reliable under a wide range of Reynolds numbers . As per this model, contaminants can adsorb at the first front half of the bubble surface and move towards the backside of the bubble because of the surface advection caused by the main flow .…”

“…Therefore, both from theoretical and industrial applications viewpoints, development of results on the motion and heat transfer from the contaminated confined bubbles to surrounding contaminated non‐Newtonian liquids is a prerequisite for the rational design and operation of liquid–gas contacting equipment. In this connection, recently Kishore and coworkers reported numerical results on a series of analogous problems. For instance, Kishore and colleagues delineated the flow and drag behavior of contaminated bubbles in Newtonian and shear‐thinning power‐law fluids in the range of conditions: Re = 10 to 200, n = 0.6 to 1 and α = 0 to 180˚ using their in‐house CFD solver namely semi‐implicit marker and cell algorithm implemented on a staggered grid arrangement in spherical coordinates.…”

“…Their study reported in was extended by Nalajala and Kishore for a much wider range of conditions such as Re = 0.1 to 200; n = 0.2 to 1.6 and α = 0 to 180˚ using ANSYS Fluent. The corresponding heat transfer characteristics of single unconfined contaminated bubbles in power‐law fluids is numerically investigated by Nalajala and Kishore for a range of conditions Re = 0.1 to 200; n = 0.2 to 1.6, Pr = 1 to 1000 and α = 0 to 180˚ using ANSYS Fluent. In a recent work, Nalajala and Kishore presented numerical results on the motion of confined contaminated bubbles in surrounding power‐law liquids over a wider range of Reynolds number, power‐law index, stagnant cap angle and confinement ratio.…”

Coalescence Characteristics of Side‐by‐Side Growing Bubbles in Carboxymethyl Cellulose Solutions

“…In a typical gas‐liquid contactor, coalescence behavior between bubbles is often encountered and will inevitably cause the loss of specific area directly related to the rate of mass transfer between the two phases of the gas‐liquid system, and even back‐mixing. However, due to the inherent complex nature of bubble phenomena, bubble coalescence in non‐Newtonian fluids could lead to a marked influence on the contact efficiency and chemical reaction between the two phases , . An adequate understanding of the bubble coalescence features of two bubbles generated side by side in a non‐Newtonian fluid is essential for the improvement and optimization of bubble column reactors in industrial settings, as well as for gaining overall insights into the coalescence mechanism.…”

Coalescence Deformation of Bubble Pairs Generated from Twin Nozzles in CMC Solutions

“…Bubble behavior in non‐Newtonian fluids has been a topic of significant interest in a variety of industrial applications, such as gas absorption, food processing, wastewater treatment, and biochemical reactions 1–3. In typical equipment that employs bubble flows, such as a bubble column and bioreactor, the coalescence of bubbles generated from submerged nozzles is frequently encountered and will cause a loss of the specific area and two‐phase contact time, which is related to the rate of mass transfer between gas and liquid phases 4, 5. Therefore, a study on the coalescence characteristics of twin‐forming bubbles in non‐Newtonian fluids assists in the improvement and optimization of bubble column reactors in industrial settings.…”