Cap angle
Chapter 7 CONCLUSIONS AND FUTURE SCOPE
Chapter 7
The heat transfer phenomenon of unconfined contaminated spherical bubbles in power- law liquids is numerically investigated using Ansys Fluent. Thickness of thermal boundary layer decreases with decreasing cap angle and/or power-law indices and/or increasing Reynolds numbers and/or Prandtl numbers. At Re = 200 for α ≥ 60o, the distortion in isotherm contours becomes more intense with increasing Prandtl number and/or decreasing power-law indices. The surface Nu of contaminated bubbles follow the path of surface Nu of clean and fully contaminated bubble, respectively, along the mobile and immobile portions of the contaminated bubble surface with a sudden decrease in the value of the Nusselt number at the leading edge of the stagnant cap. This sudden decrease in surface Nu at the leading edge of the stagnant cap increases with the decreasing power-law index. The average Nusselt number of contaminated bubbles increases with the increasing Peclet number and/or with the decreasing cap angle and/or with the decreasing power-law index.
The momentum characteristics of the partially contaminated bubbles confined in tubes of different size are numerically investigated using Ansys Fluent over wide ranges of pertinent parameters. The size of the recirculation wake at the rear of the partially contaminated bubbles decreases with the decreasing wall factor (i.e., increasing wall retardation) and/or with the increasing power-law index and/or with the decreasing cap angle. The wall retardation effect on the surface pressure coefficient in highly shear-thinning fluids is large enough to suppress the sudden rise in the pressure coefficient at the leading edge of the spherical stagnant cap. However, the retardation effects could not suppress the sudden rise in the shear stress at the leading edge of the stagnant cap of the contaminated bubbles even in highly shear-thinning fluids. In the present case of the motion of confined bubbles there is no existence of the crossover Reynolds number in Cd versus Re curves with respect to the power-law index unlike in the case of the motion of
unconfined bubble. For all values of the Reynolds number, the drag ratio decreases with the increasing cap angle and/or with the increasing power-law index.
The wall retardation effect on heat transfer phenomena of contaminated single bubble in power-law fluids are studied using Ansys Fluent. At Re = 200 for α ≥ 60o, the distortion of isotherm contour appeared because of recirculation wake formation becomes more intense with increasing Prandtl number and/or decreasing power-law indices. The average Nusselt number increases with increasing Reynolds number and/or Prandtl number and/or cap angle. The average Nusselt number increases with increasing wall retardation at moderate Reynolds and Prandtl numbers. Mixed trends observed with respect to power-law indices for different Reynolds numbers, Prandtl numbers and cap angles.
The rise of swarms of contaminated bubbles in power-law fluids has been studied using the in-house solver numerically over wide ranges of pertinent dimensionless parameters. For α ≤ 30°, the recirculation wake is not observed for any combination of Reynolds number and the bubble holdup. The size of the recirculation wake is increased with increasing Reynolds number and/or decreasing bubble holdup and/or decreasing power-law indices and/or with the increasing cap angle. Regardless of values of the Reynolds number and stagnant cap angle, as the value of the holdup increases, the maximum value of the surface pressure coefficient at the leading edge of the stagnant cap decreases. On the other hand, for fixed value of bubble holdup, as the value of the Reynolds number increases, the rise in vorticity value at the leading edge of the stagnant cap increases. The drag coefficient of contaminated bubble swarms decreases with the decreasing bubble holdup and/or with the increasing power-law indices and/or with the decreasing cap angle and/or with the increasing Reynolds number. On the other hand, regardless of values of the bubble holdup, mixed trends observed on the effect of cap angle on the ratio
between pressure and friction drag coefficients for large values of the Reynolds numbers. The mass transfer phenomena of contaminated bubble swarms in power-law are studied using in- house solver. Concentration boundary layer becomes thinner with increasing Reynolds number and/or Schmidt number and/or decreasing power-law indices and/or cap angle. The reduction in surface Sh at leading edge of stagnant cap increases with increasing power-law index. The average Sherwood number increases with increasing Reynolds number and/or Schmidt number and/or bubble holdup and/or decreasing cap angle and/or power-law indices.
7.2. Scope for Future Work
Momentum and mass transfer phenomena of contaminated spherical droplets in power-law fluids for confined and unconfined cases.
Momentum and mass transfer phenomena of contaminated spherical bubbles and droplets in other non-Newtonian fluids.
Momentum and mass transfer phenomena of ensembles of partially contaminated droplets in non-Newtonian fluids.
Momentum and mass transfer phenomena of contaminated spherical bubbles and droplets by considering Marangoni effects.