Exact Solution of Second Grade Fluid in a Rotating Frame through Porous Media Using Hodograph Transformation Method

Abstract

In this paper exact solution for a homogenous incompressible, second grade fluid in a rotating frame through porous media has been provided using hodograph-Legendre transformation method. Results are summarised in the form of theorems. Two examples have been taken and streamline patterns are shown for the solutions.

Analytical Solution of Equations Governing Aligned Plane Rotating Magnetohydrodynamic Fluid Through Porous Media by Martin’s Method

“…is the condition satisfied by β as obtained from Equation (1), ( 4) and (15). Using (15) in the above system of equations ( 8) to ( 14) we get the following system of partial differential equations…”

“…This was usually done by famous Darcys law, as a result of this, the viscous term in the equations of fluid motion will be replaced by the resistance term − η k V , where η is the viscosity of the fluid, k is the permeability of the medium and V is the seepage velocity of the fluid. Many researchers [11][12][13][14][15][16][17][18][19] have studied fluid flows through porous medium in different flow problems. The basic equations and Navier-Stokes equations governing the flow of magnetohydrodynamic (MHD) fluid are non-linear partial differential equations and have no general solution.…”

Flow of MHD micropolar fluid through porous medium: a hodograhic approach for exact solution

“…Micropolar fluids [54] are the class of fluids which show certain microscopic effects due to the local structure and microrotation of the fluid elements. In these fluids the rotation of the rigid particles which are contained in a small volume element is described by micro-rotation vector [26].…”

“…In the development of the theory of the micropolar fluid credit goes to Eringen [21,22,20] who introduced and worked out the micropolar fluid model. The study of the flow and behavior of micropolar fluids have become prominent field of research with notable number of research papers devoted to micropolar fluid flow investigations [24,25,40,70,18,2,54]. In addition, study of the flow of micropolar fluid in the presence of magnetic field under various conditions and different physical parameters have been carried out by many researchers [3,30,62,8,9,10,13,12,7,41,31,29,32].…”

Exact Solutions of non-Newtonian Fluid of Rotating MHD Flows Through Porous Media with Hall Effect by Complex Variable Technique

“…The theory of rotating fluid was also considered by Dieke [7], in the study of solar physics involved in the sunspot development, the solar cycle and the structure of rotating magnetic stars. Various studies on rotating MHD/ non-MHD fluid or fluid in a rotating frame of reference have been carried out by many researchers [8,25,21,12,4,18,19,20,10,17,24,14,16,5]. Many works are there in the literature where in MHD fluid analysis has been carried out with Hall effect.…”