The viscous flow induced by a shrinking sheet is studied. Existence and (non)uniqueness are proved. Exact solutions, both numerical and in closed form, are found.

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Viscous flow due to a shrinking sheet

The momentum and heat transfer in a laminar liquid film on a horizontal stretching sheet is analyzed by the Homotopy analysis method (HAM). Analytic series solutions are given and compared with numerical results given by other authors. The good agreement between them shows the effectiveness of HAM to the problem of liquid film on an unsteady stretching surface.

Analytic solutions for a liquid film on an unsteady stretching surface

This work is concerned with the magnetohydrodynamic (MHD) viscous flow due to a shrinking sheet. The cases of two dimensional and axisymmetric shrinking have been discussed. Exact series solution is obtained using the homotopy analysis method (HAM). The convergence of the obtained series solution is discussed explicitly. The obtained HAM solution is valid for all values of the suction parameter and Hartman number.

The application of homotopy analysis method for MHD viscous flow due to a shrinking sheet

In this paper the problem of momentum and heat transfer in a thin liquid film of power-law fluid on an unsteady stretching surface has been studied. Numerical solutions are obtained for some representative values of the unsteadiness parameter S and the power-law index n for a wide range of the generalized Prandtl number, 0.001 ≤ Pr ≤ 1000. Typical temperature and velocity profiles, the dimensionless film thickness, free-surface temperature, and the surface heat fluxes are presented at selected controlling parameters. The results show that increasing the value of n tends to increase the boundary-layer thickness and broadens the temperature distributions. The free-surface temperature of a shear thinning fluid is larger than that of a Newtonian fluid, but the opposite trend is true for a shear thickening fluid. For small generalized Prandtl numbers, the surface heat flux increases with a decrease in n, but the impacts of n on the heat transfer diminish for Pr greater than a moderate value (approximately 1 ≤ Pr ≤ 10, depending on the magnitude of S).

Heat transfer in a power-law fluid film over a unsteady stretching sheet

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

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Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates.

The axisymmetric motion of a fluid caused by an unsteady stretching surface that has relevance in extrusion process and bioengineering has been investigated. It has been shown that if the unsteady stretching velocity is prescribed by rb/(1 − αt), then the problem admits a similarity solution which gives much insight to the character of solutions. The asymptotic and numerical solutions are obtained and they could be used in the testing of computer codes or analytical models of more realistic engineering systems. The results are governed by a nondimensional unsteady parameter S and it has been observed that no similarity solutions exist for S > 4

The Axisymmetric Motion of a Liquid Film on an Unsteady Stretching Surface

http://iopscience.iop.org/article/10.1016/0169-5983(96)00002-0/pdf

Arbitrary squeezing of a viscous fluid between elliptic plates

An analysis of a laminar squeeze flow of an incompressible Newtonian fluid between parallel plane annuli is presented The local and convective inertia of the flow are considered in the investigation The solution is obtained as a power series in a single nondimensional parameter (squeeze Reynolds number) S, for small values of S Expressions for the pressure and load capacity are given and are compared with those based on the assumption of inertialess flow As applications, the constant velocity squeezing state and the case when the walls perform reciprocating harmonic oscillations with finite amplitude are considered The changes in load capacity with the changes in the parameters that govern the motion have been investigated

An Investigation of a Squeeze Film Between Two Plane Annuli

The squeeze flow of an electrically conducting fluid between two parallel disks with injection at the lower porous disk in the presence of a magnetic field applied perpendicular to the disk is investigated. Analytic solutions are obtained through the use of a regular perturbation scheme. The results show that the effect of injection is to increase the load carrying capacity in the hydromagnetic squeeze film and this increase is more than that observed without injection.

Rukmani Sridharan

Papers

The Axisymmetric Motion of a Liquid Film on an Unsteady Stretching Surface

Arbitrary squeezing of a viscous fluid between elliptic plates

An Investigation of a Squeeze Film Between Two Plane Annuli

Effect of Injection on the Squeeze Flow in the Presence of a Magnetic Field