We present a nonlinear unsteady Darcy’s equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy’s law. In the absence of surface tension we derive a generalized Polubarinova–Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow st...

Recent developments in microfluidic and nanofluidic technologies have renewed interest in the influence of surface roughness on the slip behavior of viscous fluids (see the survey by PRIEZJEV and TROIAN [20] and the references cited therein). As a matter of fact, this issue have been subjected to discussion for over two centuries by many distinguished scientists who developed the foundations of...

An LRS Bianchi type-V cosmological models representing a viscous fluid distribution with a time dependent cosmological term Λ is investigated. To get a determinate solution, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density. It turns out that the cosmological term Λ(t) is a decreasing function of time, which is consistent with recent observations ...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

Inviscid two-dimensional (2D) fluid phenomena like hurricanes, jet streams, Jupiter’s Red Spot, and protoplanetary disks are quite common in Nature. Unfortunately, 2D fluid phenomena are difficult to study in the laboratory because the finite size of laboratory apparati commonly introduces unwanted viscous and friction effects. Magnetized electron columns, however, behave like twodimensional fl...

The equations governing the flow of an electrically conducting, incompressible viscous fluid over an infinite flat plate in the presence of a magnetic field are investigated using the homotopy perturbation method (HPM) with Padé approximants (PA) and 4 order Runge–Kutta method (4RKM). Approximate analytical and numerical solutions for the velocity field and heat transfer are obtained and compar...

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The unsteady Couette flow through a porous medium of a viscous, incompressible fluid bounded by two parallel porous plates is studied with heat transfer. A uniform suction and injection are applied perpendicular to the plates while the fluid motion is subjected to an exponential decaying pressure gradient. The two plates are kept at different but constant temperatures while the viscous dissipat...

Direct numerical simulation of self-propelled swimming of three dimensional bionic fish and fish school in a viscous flow in a tank are investigated. The swimming rule and the profile of 3D fish from previous experimental measurements of living fish are used in the study. A parallel software package for the 3D moving boundary problem is obtained, which combines the adaptive multi-grid finite vo...

In this paper, the interpolated bounce-back scheme and the immersed boundary method are compared in order to handle solid boundary conditions in the lattice Boltzmann method. These two approaches are numerically investigated in two test cases: a rigid fixed cylinder invested by an incoming viscous fluid and an oscillating cylinder in a calm viscous fluid. Findings in terms of velocity profiles ...