Abstract
The flow between two large parallel plates approaching each other symmetrically in a porous medium is studied. The Navier‐Stokes equations have been transformed into an ordinary nonlinear differential equation using a transformation ψ(r, z) = r2F(z). Solution to the problem is obtained by using differential transform method (DTM) by varying different Newtonian fluid parameters and permeability of the porous medium. Result for the stream function is presented. Validity of the solutions is confirmed by evaluating the residual in each case, and the proposed scheme gives excellent and reliable results. The influence of different parameters on the flow has been discussed and presented through graphs.
Highlights
The study through a porous medium is an interesting and hot issue in these days, especially, with the introduction of the modified Darcy’s Law 1, in contrast to the classical Darcy’s Law 2 and the Brinkman model 3
Naduvinamani et al in 12, 13 studied static and dynamic behavior of squeeze-film lubrication of narrow porous journal bearings with coupled stress fluid and a squeeze film lubrication of a short porous journal bearing with couple stress fluids, respectively
The study reported in this paper considers the axisymmetric squeezing flow of a viscous fluid between two large parallel plates in a porous medium separated by a small distance 2H and the plates approaching each other with a low constant velocity V, and the flow can be assumed to be quasisteady
Summary
The study through a porous medium is an interesting and hot issue in these days, especially, with the introduction of the modified Darcy’s Law 1 , in contrast to the classical Darcy’s Law 2 and the Brinkman model 3. Squeezing flows are common in moulding, food industry, and chemical engineering, and they have, been studied for a long time as researchers and scientists have sought to optimize processing operations to produce improved components. These flows are Mathematical Problems in Engineering interesting from rheological perspective 10. Its main application therein is to solve both linear and nonlinear initial value problems in electrical circuit analysis This method constructs the solution in the form of a polynomial. The DTM is an alternative procedure for getting Taylor series solution of the differential equations This method reduces the size of computational domain and is applicable to a variety of problems. We use DTM to find the approximate solutions of the modeled problem
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