In this section we review literature on the problem of free convection of Casson fluid flow from a horizontal circular cylinder with partial slip, porous medium and viscous dissipation.
a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation
We start by discussing flow around cylinders and the effect of partial slip in fluid flow.
Further to the discussions of radiation effects, Casson fluid flow, porous medium and viscous dissipation in previous chapters, we present a brief review of these fluid flow phenomena in this context.
The study of Casson fluid around cylinders is important in the understanding of fluid flow around veins and arteries in humans, in the circulation of oil in automotive engines and design of automatic cooking machines, in which cooking oil and soup are used. With this in mind it is necessary to conduct a study of Casson fluid flow with partial slip, porous medium, magnetic field and viscous dissipation effects. The flow of Casson fluid is applied in many situations in industry such as petroleum production, multiphase mixtures, pharmaceutical formulations, coal in water, paints, lubricants, jams, sewage, soup, blood, contaminated lubricants, molten metal and synovial fluid. These fluids show different characteristics from the Newtonian fluids which cannot be fully represented by the Navier-Stokes equations. To represent these non-Newtonian fluids some modifications to the Navier-Stokes equations are necessary (Ramachandra et al., 2013a; Mukhophadhyay and Vajravelu, 2013).
with viscous dissipation
The study of fluid flow over different geometries is important as it refers to many prac- tical situations, some of which have been mentioned earlier in this section. The study of fluid flow past a cylindrical geometry was studied by among others Anwar et al. (2008) who investigated mixed convection boundary layer flow of a viscoelastic fluid over a horizontal cylinder; Deka et al. (2014) investigated transient free convection flow past an accelerated vertical cylinder in a rotating cylinder; Ribeiro et al. (2014) studied viscoelastic flow past a confined cylinder with three dimensional effects and stability and Patel and Chhabra (2013) studied steady flow of Bingham plastic fluids past an elliptical cylinder. In this chapter we consider a cylinder embedded in Casson fluid with transpiration at its walls. We also consider partial slip at the surface of the cylinder.
In 1823, Navier deduced that there is a partial slipping at a solid boundary, and that this slip force is directly proportional to the slip velocity (Prabhakara and Deshpande, 2004).
Partial slip is a condition of a surface with little or no friction, it is characteristic of a lubricated surface. In many practical situations it is often important to consider partial slip conditions depending on the problem concerned. It is therefore important to study the fluid flow in Casson fluid with partial slip conditions. Studies which included partial slip include the work of Ramachandra et al. (2013a) which considered velocity and thermal slip factors.
In this chapter, the flow of fluid is affected by the presence of radiation and magnetic field. Further to the studies referred to in Chapter 3, we highlight the studies that focused on effects of radiation and magnetic field in a non-Newtonian fluid. Shateyi and Marewo (2013) investigated numerical analysis of MHD stagnation point flow of Casson fluid; they considered thermal radiation in their work. Chamkha et al. (2003) studied thermal radiation effects on MHD forced convection flow adjacent to a non-isothermal wedge in the presence of heat source or sink. Pramanik (2013) studied Casson fluid flow and heat transfer past an exponentially porous stretching surface in the presence of thermal radiation. Narayana et al. (2013) studied free magnetohydrodynamic fluid flow and convection from a vertical spinning cone with cross diffusion effects. Nadeem et al. (2014) studied numerical study of MHD boundary layer flow of a Maxwell fluid past a stretching sheet in the presence of nano-particles. Chen (2004) investigated combined heat and mass transfer in MHD free convection from a vertical surface with Ohmic heating and viscous dissipation.
a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation
The flow of fluid in porous medium was discussed in Chapter 4 and in this section we investigate the effect of non-Newtonian fluid flow in porous medium. Studies in porous media and viscous dissipation have been carried out by among others, Makanda et al. (2013) who studied natural convection of viscoelastic fluid from a cone embedded in a porous medium with viscous dissipation. Awad et al. (2011) investigated convection from an inverted cone in a porous medium with cross diffusion effects. Hayat et al. (2010) studied heat and mass transfer for Soret and Dufour effects on mixed convection boundary layer flow over a stretching vertical surface in a porous medium filled with viscoelastic fluid. Cheng (2010) studied Soret and Dufour effects on free convection boundary layer over a vertical cylinder in a saturated porous medium. Chamkha and Rashad (2012) investigated natural convection from a vertical permeable cone in nanofluid saturated porous media for uniform heat and nanoparticles volume fraction fluxes.
From the literature cited above, it appears that no analysis has yet been published con- cerning effects of radiation on MHD free convection of Casson fluid from a horizontal circular cylinder with partial slip in non-Darcy porous medium with viscous dissipation, under the given boundary conditions. The velocity and thermal slip conditions and transpiration effect are considered at the surface of the cylinder. The free stream conditions are considered to be at a lower temperature than the surface of the cylinder. The work considered in this chapter was based on the work put forward by Ramachandra et al. (2013a) in the study of momentum and heat transfer in Casson fluid. We extend the model to consider the radiation, magnetohydrodynamics and viscous dissipation effects.
In summary, this section has shown that investigating fluid flow over circular geometry, free convection, partial slip, radiation and magnetic effects is necessary to study. The system of partial differential equations will be solved by the bivariate quasi-linearisation method (BQLM). These aspects will be considered in the mathematical formulation of the problem of free convection of fluid flow from a horizontal circular cylinder. Studies in Casson fluid include among others Mukhopadhyay et al. (2013) and Nadeem et al. (2012).
with viscous dissipation