On the Hydrodynamics and Heat Convection of an Impinging External Flow Upon a Cylinder with Transpiration and Embedded in a Porous Medium

Abstract

This paper extends the existing studies of heat convection by an external flow impinging upon a flat porous insert to that on a circular cylinder inside a porous medium. The surface of the cylinder is subject to constant temperature and can include uniform or non-uniform transpiration. These cylindrical configurations are introduced in the analyses of stagnation-point flows in porous media for the first time. The equations governing steady transport of momentum and thermal energy in porous media are reduced to simpler nonlinear differential equations and subsequently solved numerically. This reveals the dimensionless velocity and temperature fields of the stagnation-point flow, as well as the Nusselt number and shear stress on the surface of the cylinder. The results show that transpiration on the surface of the cylinder and Reynolds number of the external flow dominate the fluid dynamics and heat transfer problems. In particular, non-uniform transpiration is shown to significantly affect the thermal and hydrodynamic responses of the system in the circumferential direction. However, the permeability and porosity of the porous medium are found to have relatively smaller influences.

Mixed convection and thermodynamic irreversibilities in MHD nanofluid stagnation-point flows over a cylinder embedded in porous media

“…The current study builds upon the earlier work of the authors [5] and advances that on four main fronts. These include consideration of a nanofluid flow, addition of gravitational and magnetohydrodynamic effects upon the convection problem and also evaluation of the encountered thermodynamic irreversibilities.…”

“…Because of the non-uniformity of transpiration, the flow configuration around the cylinder can be un-axisymmetric. Although the investigated configuration is rather generic, it finds specific applications in magnetic chemical separation [5]. The following assumptions are made through this work.…”

“…In particular, evaluation of thermodynamic irreversibilities encountered during forced convection of nanofluids in porous media has been identified as an underdeveloped area demanding more research [2]. The general problem of forced convection of nanofluids through porous media has been, so far, visited by few researchers [5]. The existing studies can be generally categorised into two classes of nanofluid flows in porous conduits [6,7] and those over rotating porous discs [8,9].…”

“…A review of literature reveals that the problem of stagnation-point flow formed upon curved surfaces in porous media has been rarely studied. An exception to this is the most recent work of the authors, in which they developed a semi-similar solution for the stagnation flow upon the surface of cylinder embedded in a homogenous porous medium [5]. This investigation was concerned with the hydrodynamics and heat convection only [5].…”

“…An exception to this is the most recent work of the authors, in which they developed a semi-similar solution for the stagnation flow upon the surface of cylinder embedded in a homogenous porous medium [5]. This investigation was concerned with the hydrodynamics and heat convection only [5]. Importantly, it was limited to ordinary fluids and did not consider magnetic and gravitational effects nor it involved analysis of entropy generation.…”