Rajai S. Alassar

Forced Convection Past an Oblate Spheroid at Low to Moderate Reynolds Numbers

Forced convection past a heated oblate spheroid is studied in an attempt to investigate the effect of the axis ratio on the heat transfer rate. The time-dependent full Navier-Stokes and energy equations are solved using a series truncation method. The axis ratios considered range from 1/2 to 1 (a perfect sphere)

Heat convection from a sphere placed in an oscillating free stream

Abstract The problem of heat convection from a sphere placed in an oscillating viscous free stream is considered for the two cases of forced and mixed convection regimes. The sphere surface is assumed isothermal and the free-stream oscillations are always in the vertical direction resulting in axisymmetric flow and thermal fields for both regimes. The study is based on the solution of the unsteady Navier–Stokes and energy equations for a Boussinesq fluid of constant Prandtl number (Pr=0.71) . The main parameters considered are the Reynolds number, Grashof number, and Strouhal number. Comparison of results with published data shows a good agreement for the special case of steady forced and mixed convection. The details of the resulting thermal fields are presented in the form of isotherm patterns and the local Nusselt number distribution.

Oscillating viscous flow over a sphere

Abstract This paper deals with the problem of oscillating viscous flow over a sphere. The flow is assumed axisymmetric and governed by the Navier-Stokes equations for incompressible fluids. The method of solution is based on the series truncation method where the stream function and vorticity are expressed in terms of a finite series of Legendre and first associated Legendre functions. The effects of the Reynolds and Strouhal numbers on the flow characteristics are studied and compared with available data from previous work and also from potential flow solutions. Results are presented for periodic variation of the drag coefficient, surface vorticity and pressure distributions for Reynolds numbers ranging from 5 to 200. The time variation of the velocity field during one complete oscillation is presented in the form of streamline and equivorticity patterns. The periodic variation of the angle of separation as well as the length of the separation bubble are also presented. Calculations are performed for the time-averaged stream function and vorticity through which the double boundary layer structure is confirmed for the range of Reynolds and Strouhal numbers considered.

Remarks on some associated Laguerre integral results

Motivated essentially by their possible need in a fairly large number of physical and chemical contexts, Mavromatis and Alassar [1] derived several associated Laguerre integral results by eliminating an unnecessary constraint used in an earlier paper on the subject by Mavromatis [2]. The main object of the present sequel to these recent works is to investigate and apply much more general families of integral formulas, involving products of two or more Laguerre polynomials, which have been considered in the mathematical literature rather extensively.

A generalized formula for the integral of three associated Legendre polynomials

Abstract In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3 F 2 hypergeometric function and the 3 − j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.

Steady flow past an oblate spheroid at small Reynolds numbers

The problem of uniform steady viscous flow over an oblate spheroid is solved in the low-Reynolds-number range 0.1 ≤ Re ≤ 1.0. The full Navier-Stokes equations are written in the stream function-vorticity form and solved numerically by means of the series-truncation method. Spheroids having axis ratio ranging from 0.245 to 0.905 are considered. The obtained drag coefficients are compared with previous analytical formulae which were based on the solution of the linearized Stokes equations. As expected, the deviation between the present results and the analytical formulae is small for low-Re flows, however, it increases with the increase of Re. The present results provide a measure for establishing the range of validity of the analytical solutions.

Oscillating flow over oblate spheroids

SummaryThis paper deals with the problem of oscillating viscous flow over an oblate spheriod. The flow is assumed incompressible and axisymmetric and the motion is governed by the Navier-Stokes equations. The method of solution is based on the series truncation method where the stream function and vorticity are expressed in terms of a finite series of Legendre functions. The effects of the Reynolds and Strouhal numbers on the flow characteristics are studied and compared with previous available solutions. Results are presented for the periodic variation of the drag coefficient, surface vorticity and pressure distributions for Reynolds numbers ranging from 5 to 100 and Strouhal numbers ranging from π/4 to π while keeping the spheroid axis ratio unchanged. The time variation of the velocity field during one complete oscillation is presented in the form of streamline and equi-vorticity patterns. The periodic variation of the angle of separation as well as the length of the separation bubble are also presented. The double boundary layer structure previously observed in the case of a sphere is also detected.

Hagen–Poiseuille Flow in Semi-Elliptic Microchannels

In this paper, an exact solution of Hagen–Poiseuille flow in microchannels with semi-elliptic cross sections is obtained. The velocity, shear stress distribution, and the friction factor are calculated and compared to known approximate solutions in the literature. The solution is also verified by comparing the limiting case when the axis ratio approaches unity to the exact solution obtained for semicircular channels.

Two new associated Laguerre integral results

New associated Laguerre integral results are obtained by eliminating an unnecessary restriction in [1]. The expression used to obtain these new results is compared to that given in [2] and shown to be different and of greater generality. Finally, some physical moments are discussed that require such integrals.

Analytical solution of oscillating inviscid flow over oblate spheroids with spheres and flat disks as special cases

The hydrodynamic forces acting on an oblate spheroid placed in an oscillating free stream are obtained for the special case of inviscid flow. The flow is assumed incompressible and axisymmetric and the free stream oscillations are harmonic. The flow direction is always along the spheroids axis of symmetry. Analytical expressions are obtained for the potential and stream functions as well as the surface pressure distribution and the hydrodynamic force coefficient. The analysis is based on the solution of the unsteady equations of motion and continuity in oblate spheroidal coordinate system. The parameters involved are the major to minor axes ratio and the Strouhal number. The solutions for the two limiting cases of oscillating flows over disks and spheres can be easily obtained from the presented analytical solution.