Motion of a spheroidal particle in a micropolar fluid contained in a spherical envelope

2008 ◽  
Vol 86 (9) ◽  
pp. 1039-1056 ◽  
Author(s):  
E I Saad
Keyword(s):  
Micropolar Fluid ◽  
Translational Motion ◽  
Terminal Velocity ◽  
The Body ◽  
Spheroidal Particle ◽  
Oblate Spheroidal ◽  
Spherical Envelope ◽  
Type Boundary ◽  
Type Boundary Condition ◽  
Analytical Expressions

This paper investigates first the Stokes’ axisymmetrical translational motion of a spheroid particle, whose shape differs slightly from that of a sphere, in an unbounded micropolar fluid. A linear slip, Basset-type, boundary condition has been used. The drag acting on the spheroid is evaluated and discussed for the various parameters of the problem. Also, the terminal velocity is evaluated and tabulated for the slip, deformity, and micropolarity parameters. Secondly, the motion of a spheroidal particle at the instant it passes the centre of a spherical envelope filled with a micropolar fluid is investigated using the slip condition at the surface of the particle. The analytical expressions for the stream function and microrotation component are obtained to first order in the small parameter characterizing the deformation. As an application, we consider an oblate spheroidal particle and the drag acting on the body is evaluated. Its variation with respect to the diameter ratio, deformity, micropolarity, and slip parameters is tabulated and displayed graphically. Well-known cases are deduced, the wall effect is then examined and comparisons are attempted between the classical fluid and micropolar fluid.PACS Nos.: 47.45.Gx, 47.15.Gf, 47.50.–d

scholarly journals Cell Models for Non-Newtonian Fluid Past a Semipermeable Sphere

2019 ◽  
Vol 4 (6) ◽  
pp. 1352-1361
Author(s):  
Madasu Krishna Prasad
Keyword(s):  
Boundary Conditions ◽  
Newtonian Fluid ◽  
Micropolar Fluid ◽  
Stokes Equations ◽  
Translational Motion ◽  
Tangential Velocity ◽  
Solid Sphere ◽  
Normal Velocity ◽  
Cell Models ◽  
Spherical Envelope

This paper is focused on investigating the boundary effects of the steady translational motion of a semipermeable sphere located at the center of a spherical envelope filled with an incompressible micropolar fluid. Stokes equations of micropolar fluid are employed inside the spherical envelope and Darcy’s law governs in semipermeable region. On the surface of semipermeable sphere, the boundary conditions used are continuity of normal velocity, vanishing of tangential velocity of micropolar fluid, and continuity of pressure. On the surface of the spherical envelope, the Happel’s, Kuwabara’s, Kvashnin’s, and Cunningham’s boundary conditions, are used along with no spin boundary condition. The expression for the hydrodynamic normalized drag force acting on the semipermeable sphere is obtained. The limiting cases of drag expression exerted on the semipermeable sphere and impermeable solid sphere in cell models filled with Newtonian fluid are obtained. Also, in absence of envelope, the drag expression for the micropolar fluid past a semipermeable sphere is obtained.

Transient Temperature Involving Oscillatory Heat Source With Application in Fretting Contact

2007 ◽  
Vol 129 (3) ◽  
pp. 517-527 ◽  
Author(s):  
Jun Wen ◽  
M. M. Khonsari
Keyword(s):  
Heat Source ◽  
Oscillation Amplitude ◽  
The Body ◽  
Transient Temperature ◽  
Dimensionless Frequency ◽  
Heat Sources ◽  
Infinite Body ◽  
Fitting Method ◽  
Wide Range ◽  
Analytical Expressions

An analytical approach for treating problems involving oscillatory heat source is presented. The transient temperature profile involving circular, rectangular, and parabolic heat sources undergoing oscillatory motion on a semi-infinite body is determined by integrating the instantaneous solution for a point heat source throughout the area where the heat source acts with an assumption that the body takes all the heat. An efficient algorithm for solving the governing equations is developed. The results of a series simulations are presented, covering a wide range of operating parameters including a new dimensionless frequency ω¯=ωl2∕4α and the dimensionless oscillation amplitude A¯=A∕l, whose product can be interpreted as the Peclet number involving oscillatory heat source, Pe=ω¯A¯. Application of the present method to fretting contact is presented. The predicted temperature is in good agreement with published literature. Furthermore, analytical expressions for predicting the maximum surface temperature for different heat sources are provided by a surface-fitting method based on an extensive number of simulations.

Heat Transfer in Composite Spheroids

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajai Alassar
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Prolate Spheroid ◽  
Published Data ◽  
Composite Sphere ◽  
Legendre Series ◽  
The Third ◽  
Type Boundary ◽  
Type Boundary Condition ◽  
The Impact

Abstract Heat transfer from a composite prolate spheroid under the third-type boundary condition is investigated using a Legendre series expansion. The model is verified against published data on cooling boiled eggs and also against the asymptotic solution of a composite sphere. The impact of Biot number on the heat transfer in spheroids with realistic dimensions and properties, such as eggs and olives, is investigated. The results are also presented for varying conductivity ratios and fractional volume of the inner part of the spheroid.

Semi-infinite vortex trails, and their relation to oscillating airfoils

1972 ◽  
Vol 54 (4) ◽  
pp. 679-690 ◽  
Author(s):  
D. Weihs
Keyword(s):  
Iterative Procedure ◽  
Constant Width ◽  
Oscillation Amplitude ◽  
The Body ◽  
Vortex Strength ◽  
Spacing Ratio ◽  
Vortex Streets ◽  
Dimensional Parameters ◽  
Initial Spacing ◽  
Analytical Expressions

Semi-infinite double rows of vortices are used to study the periodic wake of both oscillating and stationary two-dimensional bodies immersed in a uniform incompressible stream. Analytical expressions for the induced Velocities on the body, for trails with constant spacing, which are valid for small values of the oscillation amplitude are presented while, for the general case of vortex shedding, an iterative procedure for the representation of trails of variable spacing is developed and used. Vortex streets due to oscillating bodies are obtained as a function of three non-dimensional parameters: the Strouhal number (initial spacing ratio), a non-dimensional vortex strength and the downstream spacing ratio. Criteria establishing when such trails are expected to widen, become narrow or stay of constant width are presented, as well as expressions for the induced velocities.The trails and their induced velocities enable the calculation of the vortex strength from measurable quantities. Thus they can serve as a method for estimating the hydrodynamic forces on the airfoil due to large amplitude oscillations, such as those observed in the propulsive movements of fish and cetaceans, as well as the small amplitude oscillations due to hydroelastic interactions.

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