Advances in Mathematical Physics

Volume 2016 (2016), Article ID 9671513, 12 pages

http://dx.doi.org/10.1155/2016/9671513

## Radiation Effects in Flow through Porous Medium over a Rotating Disk with Variable Fluid Properties

Department of Mathematics & Statistics, Manipal University Jaipur, Jaipur 303007, India

Received 30 June 2016; Revised 3 September 2016; Accepted 15 September 2016

Academic Editor: Ali Cemal Benim

Copyright © 2016 Shalini Jain and Shweta Bohra. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The present study investigates the radiation effects in flow through porous medium over a permeable rotating disk with velocity slip and temperature jump. Fluid properties density , viscosity , and thermal conductivity are taken to be dependent on temperature. Particular case considering these fluid properties’ constant is also discussed. The governing partial differential equations are converted into nonlinear normal differential equation using similarity alterations. Transformed system of equations is solved numerically by using Runge-Kutta method with shooting technique. Effects of various parameters such as porosity parameter , suction parameter , rotational Reynolds number Re, Knudsen number Kn, Prandtl number Pr, radiation parameter , and relative temperature difference parameter on velocity profiles along radial, tangential, and axial direction and temperature distribution are investigated for both variable fluid properties and constant fluid properties. Results obtained are analyzed and depicted through graphs and table.

#### 1. Introduction

The study of rotating disk flows of electrically conducting fluids has practical applications in many areas, such as rotating machinery, lubrication, computer storage devices, oceanography, viscometry, and crystal growth processes. In 1921, Kármán [1] was the first to investigate fluid flow due to a rotating disk. He introduced similarity transformations to transform governing partial differential equations into ordinary differential equations. Further Cochran [2], Benton [3], and Turkyilmazoglu [4] extended the work [1] and investigated flow and heat transfer under different boundary conditions. Chauhan and Gupta [5] investigated steady flow and heat transfer between two stationary naturally permeable disks. Heat transfer from a rotating disk by convection has been investigated theoretically under different physical and thermal conditions by Wagner [6], Millsaps and Pohlhausen [7], Kreith and Taylor [8], H.-T. Lin and L.-K. Lin [9], and Verma and Chauhan [10]. Chauhan and Jain [11] studied flow between rotating disks; they considered highly permeable disk. Turkyilmazoglu [12, 13] investigated flow and heat transfer of nanofluid due to rotating disk and on a radially shrinking rotating disk in the presence of a uniform vertical magnetic field, respectively. The unsteady magnetohydrodynamic (MHD) squeezing flow between two parallel disks (which is filled with nanofluid) is considered by Azimi and Riazi [14]; they have used Galerkin optimal homotopy asymptotic method (GOHAM) to solve the problem. Several researchers [15–17] have also investigated unsteady fluid flow and heat transfer over permeable rotating disk, rotating porous disk, and infinite rotating disk under different boundary conditions.

Radiative effects have several applications in physics and engineering field. Radiative heat transfer phenomena are used in nuclear reactors, power generation system, and high temperature plasma on controlling heating factor in industries and in liquid metal fluids. Several researchers investigated the effects of radiation on convective flows. Mansour [18] and Hossain et al. [19] studied the effect of radiation on free convection of fluid from a vertical plate and porous vertical plate, respectively. Raptis and Perdikis [20] investigated the MHD free convection flow in the presence of thermal radiation. The investigation of the effect of radiation on mixed convection flow of an optically dense viscous incompressible fluid along a heated vertical flat plate with uniform free stream and uniform surface temperature has been done by Hossain and Takhar [21]. A. Devi and R. U. Devi [22] studied thermal radiation effect on MHD flow over a rotating infinite nonporous disk. She also investigated porous rotating disk with Hall effect.

In recent years, the slip flow regime has been widely studied and researchers have been concentrating on the analysis of microscale in microelectromechanical systems (MEMS) associated with the embodiment of velocity slip and temperature jump. Wang [23] examined the flow due to a stretching boundary with partial slip—an exact solution of the Navier-Stokes equations. Osalusi [24] studied the combined hydromagnetic and slip flow of a steady, laminar conducting viscous fluid in the presence of thermal radiation due to an impulsively started rotating porous disk with the variable fluid properties. Khidir [25] investigated the effects of viscous dissipation and ohmic heating on steady MHD convective flow due to porous rotating disk taking into account the variable fluid properties. Sparrow et al. [26] considered the fluid flow due to the rotation of a porous surfaced disk and employed a set of linear slip flow conditions. He observed that a substantial reduction in torque occurred as a result of surface slip. Rashidi and Freidooni Mehr [27] investigated effects of velocity slip and temperature jump on the flow over a porous rotating disk. The combined effects of temperature and velocity jump on the heat transfer, fluid flow, and entropy generation over a single rotating disk have been examined by Arikoglu et al. [28]. Hayat et al. [29] investigated MHD steady flow of viscous nanofluid due to a rotating disk with partial slip.

In most of the research, the fluid properties such as density (*ρ*), viscosity (), and thermal conductivity (*κ*) are assumed to be constant. However, these properties remain unaltered if and only if temperature remains the same or does not change rapidly. Therefore, to predict flow behavior accurately, it is essential to consider variable fluid properties. Zakerullah and Ackroyd [30] analyzed the laminar natural convection boundary layer flow on a horizontal circular disk with variable properties. Herwig [31] and Herwig and Klemp [32] have extended the work [30]. They have investigated effects of variable properties in a tube and concentric annuli, respectively, at constant heat flux. Further, Maleque and Sattar [33, 34] have investigated laminar convective flow, taking into account the variable properties, due to a porous rotating disk. They solved the problems numerically using Runge-Kutta method with shooting technique. This work was extended by Osalusi and Sibanda [35]. They have studied flow in the presence of magnetic field. Rahman [36] made a study on the slip flow with variable properties due to a porous rotating disk.

Rashidi et al. [37] obtained analytical solutions flow and heat transfer over a rotating disk in porous medium. Hussain et al. [38] obtained numerical solution of a disk rotating in a viscous fluid. Rashidi et al. [39, 40] analyzed entropy generation in a MHD flow over a rotating porous disk with variable physical properties. They have also investigated fluid flow over a permeable rotating disk in the presence of Soret and Dufour effect. Alam et al. [41] investigated thermophoretic deposition of micron sized particles on flow due to rotating disk.

The main goal of the present study is to investigate radiation effects in the steady flow over a rotating permeable disk in porous medium with velocity slip and temperature jump. To predict the flow behavior accurately variable thermophysical properties are taken into consideration. To the best of the author’s knowledge, radiation effects of flow over rotating disk with velocity and temperature slip with variable thermal properties have not been studied yet. The novelty of present paper is to investigate flow and heat transfer for variable fluid properties with velocity slip and temperature jump, taken into consideration. Also, combined effects for both variable and constant fluid properties for various physical parameters on flow and heat transfer have been obtained and depicted graphically, which gives more insight about fluid flow (Figure 1).