S. R. Majumdar

Drag on an axially symmetric body in the Stokes’ flow of micropolar fluid

The Stokes’ flow problem is considered for micropolar fluids in which the obstacle has an axis of symmetry, and the flow at distant points is uniform and parallel to this axis. A general expression for the drag is derived by using the arguments involving an axisymmetric point force and application is illustrated for the flow past a sphere.

Unsteady flow of an elastico-viscous fluid in tubes of uniform cross-section

Abstract In this paper, the uniqueness of solution for internal bounded unsteady flows of a shortmemory fluid is first established. Closed-form solutions are then obtained for the equations characterizing flows of such fluids in circular and rectangular tubes of uniform cross-section under an arbitrary pressure gradient. Special cases including the oscillatory flow between two parallel plates are discussed.

Fundamental Oseen solution for the 2-dimensional flow of a micropolar fluid

Abstract The steady, incompressible flow of a micropolar fluid in 2 dimensions is considered. The Oseen linearization of the convective operator is introduced, and the associated problem for the fundamental solution is formulated. Solution of the fundamental problem is obtained in explicit form under a certain restriction on the physical parameters of the problem. Utilization of the fundamental solution in the investigation of general flow problems is discussed.

Longitudinal and torsional oscillation of a rod in a polar fluid

Abstract This paper examines the problem of an infinite rod undergoing both torsional and longitudinal oscillations in an unbounded incompressible fluid medium. With the aid of transform methods a class of exact solutions are obtained. Some numerical work is done to reveal the effect of micropolar parameters on the microrotation and velocity fields which are depicted graphically.

Flow due to the longitudinal and torsional oscillation of a cylinder

SummaryAn exact solution is obtained for the motion of a fluid contained in an infinité circular cylinder which is undergoing both torsional and longitudinal oscillations. An analytical expression is obtained for the viscous drag on the cylinder and the velocity is depicted graphically. Where possible, comparisons are made with corresponding results for the external problem.

Causal fundamental solutions for the slow flow of a micropolar fluid

Causal Fundamental solutions for the slow two dimensional flow of a micropolar fluid are constructed. Explicit solution requires the factorisation of a fourth order partial differential operator into two quadratic operators which is achieved under a certain condition on the parameters of the problem. The use of the fundamental solutions in unsteady flow problems is indicated

A uniqueness theorem for compressible micropolar flows

SummaryUsing an energy integral method it is proved that the motion of a non-heat conducting compressible micropolar fluid in a bounded regionV=V(t) is uniquely determined by the initial distributions of velocity, microrotation, density and temperature, together with certain boundary conditions.

Capillary‐gravity waves generated in a viscous fluid

The linearized initial‐value problem of capillary‐gravity waves generated by a moving oscillatory surface pressure distribution in a viscous incompressible fluid of infinite depth is solved. It is found that viscosity apart from introducing a damping factor into the amplitude of each wave plays an important role in the critical case. While the solution in the inviscid fluid becomes singular for certain values of the parameters of the problem, the solution in viscous fluid remains valid for all values of the parameters, though the amplitudes are relatively large in the critical case.

Isotropic Wave Dispersion

An isotropic multidimensional medium is propagating dispersive radiation from a suddenly triggered immersed point source. The latter’s subsequent action is postulated as being transient. A contour integration technique accounts for a part time zero condition plus other supplementary hypotheses (e.g. that of stability), leading via the stationary phase technique to an asymptotic solution valid for large time. One set of results holds at comparably far range. In the ensuing dispersion, concentrically expanding trains of Kelvin approximated waves get emitted. These wave trains are generally bounded by spherical advancing frontal and/or rear edges near which Airy-type approximations can be made. Several such edges may coincide or almost coincide. Another set of results, involving Hankel or Bessel functions, holds at any given finite range; it indicates slow wave packets and implies, consistent with a transient source, the ultimate attainment of a steady state of silence, possibly within a ‘slowest’ spherical edge. Applications are illustrated for elastic plate deflexions and Klein-Gordon governed motions.

Flat plate drag in a micropolar fluid

SummaryThe drag experienced in a micropolar fluid is investigated by considering uniform streaming past a flat plate. Some recent results on the fundamental solution of the Oseenlinearization of the micropolar flow equations are used to reduce the problem to that of solving a scalar integral equation. The integral equation is analyzed by the application of both asymptotic and variational methods. Results indicate that the drag experienced in a micropolar fluid always exceeds that found in the absence of any micropolarity; however one of the parameters which characterizes a micropolar fluid can be used to minimize the drag.