Growth of the Boundary Layer on a Spherical Gas Bubble

1974 ◽  
Vol 41 (4) ◽  
pp. 873-878 ◽  
Author(s):  
J. L. S. Chen
Keyword(s):  
Boundary Layer ◽  
Rigid Wall ◽  
Solid Sphere ◽  
Bubble Surface ◽  
Gas Bubble ◽  
State Boundary ◽  
Initial Discontinuity ◽  
Irrotational Motion ◽  
Flow Changes ◽  
Layer Flow

The unsteady flow of a pure viscous liquid past a gas bubble starting impulsively from rest is investigated theoretically. The Reynolds number is considered to be large so that boundary-layer ideas are applicable, but the bubble is nevertheless so small that it remains nearly spherical under the action of surface tension. This theory describes the growth of boundary layer due to an initial discontinuity in tangential stress at the bubble surface; the results also show how the flow changes from the irrotational motion to the steady-state boundary-layer flow described by Moore. The drag coefficient of the bubble is evaluated from the energy dissipation in the liquid; it is initially finite—by contrast with the case of flow with a boundary layer at a rigid wall, for which it is initially infinite—and, at a given instant, of smaller order than that for a solid sphere.

scholarly journals Numerical method approach for magnetohydrodynamic radiative ferrofluid flows over a solid sphere surface

2021 ◽  
Vol 25 (Spec. issue 2) ◽  
pp. 379-385
Author(s):  
Yasin Mat ◽  
Muhammad Mohamed ◽  
Zulkhibri Ismail ◽  
Basuki Widodo ◽  
Mohd Salleh
Keyword(s):  
Boundary Layer ◽  
Volume Fraction ◽  
Fluid Velocity ◽  
Solid Sphere ◽  
Skin Friction Coefficient ◽  
Fluid Temperature ◽  
Sphere Surface ◽  
Boundary Layer Equations ◽  
Keller Box Method ◽  
Layer Flow

In this paper, the theoretical study on the laminar boundary-layer flow of ferrofluid with influences of magnetic field and thermal radiation is investigated. The viscosity of ferrofluid flow over a solid sphere surface is examined theoretically for magnetite volume fraction by using boundary-layer equations. The governing equations are derived by applied the non-similarity transformation then solved numerically by utilizing the Keller-box method. It is found that the increments in ferro-particles (Fe3O4) volume fraction declines the fluid velocity but elevates the fluid temperature at a sphere surface. Consequently, the results showed viscosity is enhanced with the increase of the ferroparticles volume fraction and acts as a pivotal role in the distribution of velocity, temperature, reduced skin friction coefficient, and reduced Nusselt number of ferrofluid.

scholarly journals Free convection boundary layer flow on a solid sphere in a nanofluid with viscous dissipation

2019 ◽  
Vol 15 (3) ◽  
pp. 381-388
Author(s):  
Muhammad Khairul Anuar Mohamed ◽  
Nor Aida Zuraimi Md Noar ◽  
Mohd Zuki Salleh ◽  
Anuar Ishak
Keyword(s):  
Boundary Layer ◽  
Brownian Motion ◽  
Free Convection ◽  
Boundary Layer Flow ◽  
Solid Sphere ◽  
Convection Boundary Layer ◽  
Convection Boundary ◽  
Layer Flow ◽  
Free Convection Boundary Layer ◽  
Brownian Motion Parameter

Present study considers the mathematical model of free convection boundary layer flow and heat transfer in a nanofluid over a solid sphere with viscous dissipation effect. The transformed partial differential equations are solved numerically using the Keller-box method. The numerical values for the reduced Nusselt number, reduced Sherwood number and the reduced local skin friction coefficient are obtained, as well as concentration profiles, temperature profiles and velocity profiles are illustrated graphically. Effects of the pertinent parameters, which are the Prandtl number, buoyancy ratio parameter, Brownian motion parameter, thermophoresis parameter, Lewis number and Eckert number are analyzed and discussed. It is found that the increase of Brownian motion parameter promoted the reduce of concentration boundary layer thickness while thermophoresis parameter did oppositely. It is worth mentioning that the results reported here are important for the researchers working in this area which can be used as a reference and comparison purposes in the future.

scholarly journals Heat transport by laminar boundary layer flow with polymers

2012 ◽  
Vol 696 ◽  
pp. 330-344 ◽  
Author(s):  
Roberto Benzi ◽  
Emily S. C. Ching ◽  
Vivien W. S. Chu
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Heat Transport ◽  
Boundary Layer Flow ◽  
Effective Viscosity ◽  
Iterative Scheme ◽  
Streamwise Velocity ◽  
Heated Plate ◽  
State Boundary ◽  
Layer Flow

AbstractMotivated by recent experimental observations, we consider a steady-state boundary layer flow with polymers in forced convection above a heated plate and study how the heat transport might be affected by the polymers. We discuss how a set of equations can be derived for the problem and how these equations can be solved numerically by an iterative scheme. By carrying out such a scheme, we find that the effect of the polymers is equivalent to producing a space-dependent effective viscosity that first increases from the zero-shear value at the plate then decreases rapidly back to the zero-shear value far from the plate. We further show that such an effective viscosity leads to a decrease in the streamwise velocity near the plate, which in turn leads to a reduction in heat transport.

Boundary Layer Flow About and Inside a Liquid Sphere

1997 ◽  
Vol 119 (1) ◽  
pp. 42-49 ◽  
Author(s):  
Maged A. I. El-Shaarawi ◽  
Abdulghani Al-Farayedhi ◽  
Mohamed A. Antar
Keyword(s):  
Boundary Layer ◽  
Solid Sphere ◽  
External Flow ◽  
Droplet Surface ◽  
Laminar Flows ◽  
Surface Velocity ◽  
Immiscible Fluid ◽  
Interface Shear ◽  
Boundary Layer Equations ◽  
Layer Flow

A finite-difference scheme has been developed to solve the boundary-layer equations governing laminar flows around and inside a spherical fluid droplet moving steadily in another immiscible fluid. Using this scheme, results not available in the literature have been obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ*) and large values of the external flow Reynolds number (Re). Detailed results over the range 1.01 ≤ μ* ≤ ∞ (solid sphere) and 100 ≤ Re ≤ 10000 are presented for the velocity profiles outside and inside the droplet, the interface shear stress, the external flow separation angle, the droplet surface velocity and the drag coefficient.

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