Numerical study of a thin film flow of fourth grade fluid

Abstract

Purpose -The purpose of this paper is to study the thin film flow of a fourth grade fluid subject to slip conditions in order to understand its velocity profile. Design/methodology/approach -An exact expression for flow velocity is derived in terms of hyperbolic sine functions. The practical usage of the exact flow velocity is restrictive as it involves very complicated integrals. Therefore, an approximate solution is also derived using a Galerkin finite element method and numerical error analysis is performed. Findings -The behavior of fluid velocity with respect to various flow parameters is discussed. The results are not restrictive to small values of flow parameters unlike those obtained earlier using homotopy analysis method and homotopy perturbation method. Originality/value -An approximate solution based on finite element technique is derived.

Some exact solutions of two-dimensional Navier–Stokes equations by generalizing the local vorticity

“…Since their introduction, different physical models have been exploited in literature to deal with assorted physical situations. [1][2][3][4][5][6][7][8][9][10] In mathematical sense, these equations are a challenging system of nonlinear equations in the presence of viscous flows. No general analytical method exists for attacking this system for an arbitrary viscous flow problem.…”

Numerical simulations of heat transfer to a third grade fluid flowing between two parallel plates

“…There are a number of theoretical results concerning Couette-Poiseuille flow [15,16,17,18,19] The principle concern of this investigation is the numerical exploration of heat transfer phenomenon in fluids of grade three bounded between two parallel plates under no-slip and no temperature jump assumptions. It is worthy to mention that identical problem has been studied for numerical and asymptotic solutions for different flow and geometric configurations; see for instance [20,21,22,23,24]. The heat transfer flow under consideration has been mathematically modeled by Siddiqui et al in [21] wherein they provided a solution using the paradigm of homotopy perturbation method (HPM) of He.…”

“…Subsequently, Roohi et al in [23] used the Liao's homotopy analysis method (HAM) to find an asymptotic solution. Makukula et al [22] devised a quasi-linearization based spectral homotopy analysis approach. It is valuable to note that the asymptotic solutions are valid for small values of pertinent flow parameters.…”

Magnetohydrodynamics flow of nanofluid due to stretching/shrinking surface with slip effect

“…[4][5][6][7][8] Similar related flow problems with different physical configurations have been reported by many researchers in the previous studies. [9][10][11] While investigating the flow behavior of nanofluid in different channels, certain physical properties are necessarily discussed. For example, thermal conductivity is the most significant thermophysical property of nanofluids which must be studied to demonstrate the capability of these new engineered suspensions for heat transfer applications.…”