# Fundamental solutions for micropolar fluids

@article{Shu2008FundamentalSF, title={Fundamental solutions for micropolar fluids}, author={Jian-Jun Shu and Jenn Shiun. Lee}, journal={Journal of Engineering Mathematics}, year={2008}, volume={61}, pages={69-79} }

New fundamental solutions for micropolar fluids are derived in explicit form for two- and three-dimensional steady unbounded Stokes and Oseen flows due to a point force and a point couple, including the two-dimensional micropolar Stokeslet, the two- and three-dimensional micropolar Stokes couplet, the three-dimensional micropolar Oseenlet, and the three-dimensional micropolar Oseen couplet. These fundamental solutions do not exist in Newtonian flow due to the absence of microrotation velocity…

## 22 Citations

A general formula for the drag on a sphere placed in a creeping unsteady micropolar fluid flow

- Engineering, Physics
- 2012

In the present work, we investigate the creeping unsteady motion of an infinite micropolar fluid flow past a fixed sphere. The technique of Laplace transform is used. The drag formula is obtained in…

Isothermal Flows of Micropolar Liquids: Formulation of Problems and Analytical Solutions

- Physics, EngineeringColloid Journal
- 2018

Models for flows of a non-Newtonian liquid have been considered within the framework of the micropolar theory. Different forms of constitutive equations and boundary conditions have been compared.…

On the fundamental solutions for micropolar fluid-fluid mixtures under steady state vibrations

- Mathematics, EngineeringAppl. Math. Comput.
- 2012

HEAT FLOW THROUGH A THIN COOLED PIPE FILLED WITH A MICROPOLAR FLUID

- Engineering, Physics
- 2015

In this paper, a non-isothermal flow of a micropolar fluid in a thin pipe with circular cross-section is considered. The fluid in the pipe is cooled by the exterior medium and the heat exchange on…

Unsteady mixed convection boundary layer flow past a sphere in a micropolar fluid

- Physics, Engineering
- 2012

The unsteady mixed convection flow over a sphere in a micropolar fluid is studied. The unsteadiness is due to an impulsive motion of the free stream. The governing boundary layer equations are first…

Axi-symmetric translational motion of an arbitrary solid prolate body in a micropolar fluid

- Physics
- 2010

The translational motion of an arbitrary body of revolution in a micropolar fluid is investigated by a combined analytical–numerical method. The governing equations are obtained under the assumption…

Representation theorems and fundamental solutions for micropolar solid–fluid mixtures under steady state vibrations

- Mathematics
- 2010

On free convection and heat transfer in a micropolar fluid flow past a moving semi-infinite plate.

- Physics
- 2012

In this dissertation we investigate free convective heat and mass transfer in micropolar fluid flow past a moving semi-infinite vertical porous plate in the presence of a magnetic field. The aim of…

Boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretching vertical surface with prescribed skin friction

- Physics
- 2011

The steady laminar mixed convection boundary layer flow and heat transfer of a micropolar fluid near the stagnation point on a stretched vertical surface with prescribed skin friction were…

Spectral Dierence Solution of Two-dimensional Unsteady Compressible Micropolar Equations on Moving and Deformable Grids

- Physics
- 2012

The Micropolar uid theory augments the laws of classical continuum mechanics by incorporating the rotational e ects of uid molecules on the continuum. The theory of Micropolar uids has shown promise…

## References

SHOWING 1-10 OF 21 REFERENCES

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

- Mathematics, Engineering
- 1983

Generalized fundamental solutions for unsteady viscous flows.

- Engineering, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

The hydrodynamic forces acting on a sphere and on a circular cylinder translating in an unsteady rotating flow field at low Reynolds numbers are calculated using the generalized fundamental solutions.

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

- Physics
- 1976

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…

The self-propulsion of microscopic organisms through liquids

- PhysicsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
- 1953

Since the Reynolds number of motion of microscopic organisms through liquids, defined as LρV/μ, where L is the length of the organism, V the velocity with which it moves, ρ the density of the liquid…

Micropolar Fluids: Theory and Applications

- Physics
- 1998

Preface Part I. Description of the Model Ordinary and Polar Fluids Part II. Mathematical Analysis Mathematical Preliminaries Stationary Problems Nonstationary Problems Part III. Application Selected…

H.A. Lorentz: Sketches of his work on slow viscous flow and some other areas in fluid mechanics and the background against which it arose

- Physics
- 1996

With this special issue of the Journal of Engineering Mathematics we commemorate and celebrate the appearance, one hundred years ago (Fig. 1), of a paper [1] by the Dutch physicist H.A. Lorentz in…

On the Effect of the Internal Friction of Fluids on the Motion of Pendulums

- Physics, Education
- 2009

T he great importance of the results obtained by means of the pendulum has induced philosophers to devote so much attention to the subject, and to perform the experiments with such a scrupulous…

A general theorem on the motion of a fluid with friction and a few results derived from it

- Mathematics, Physics
- 1996

The equations of motion for an incompressible fluid with friction can be written as follows