Similarity solution

About: Similarity solution is a research topic. Over the lifetime, 2074 publications have been published within this topic receiving 59790 citations.

Flow Induced in Fluid‐Particle Suspension by an Infinite Rotating Disk

Abstract: An exact similarity solution is given for the flow of a fluid‐particle suspension over an infinitely large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The boundary‐layer thicknesses of the particle cloud and the fluid are found to be approximately equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques.

Unsteady flow between two disks with heat transfer in the presence of a magnetic field

Abstract: The motion of an electrically conducting fluid film squeezed between two parallel disks with heat transfer in the presence of a magnetic field applied perpendicular to the disks is studied. Attention is given to the case where a similarity solution can be obtained. Approximate analytic solutions are given and a numerical solution to the resulting nonlinear ordinary differential equations for a wide range of values of the three independent parameters which influence the motion is presented. Special attention is given to the effects of squeezing and magnetic forces on heat transfer. The results establish that while squeezing has considerable effects on heat transfer, the effects of magnetic forces are negligible.

New one-dimensional model equations of magnetohydrodynamic turbulence

Abstract: New one-dimensional model equations of magnetohydrodynamic turbulence depending on the position x and the time t are proposed considering the x component of the velocity u(x,t) and the y and z components of the magnetic field by(x,t) and bz(x,t). It is found that the model equations conserve the total energy and the quantity similar to the cross helicity, and that they have a similarity solution, u(x,t)∼x/t and by(x,t), bz(x,t)∼C/t in the inviscid limit. A shock type solution is obtained where both the velocity and the magnetic fields have a jump in a narrow viscous or diffusive region. Numerical simulations are also carried out and the results show that the k−2 energy spectrum develops both for the velocity and the magnetic fields.

Local transformations between some nonlinear diffusion equations

Abstract: Abstract We derive local transformations mapping radially symmetric nonlinear diffusion equations with power law or exponential diffusivities into themselves or into other equations of a similar form. Both discrete and continuous transformations are considered. For the cases in which a continuous transformation exists, many additional forms of group-invariant solution may be constructed; some of these solutions may be written in closed form. Related invariance properties of some multidimensional diffusion equations are also exploited.