A Study on Mixed Convection Flow in Different Channels

A Study on Mixed Convection Flow in Different Channels

Chapter One

Aims And Objectives of The Study

The main aims and objectives of the work are:

Investigation of the effect of suction/injection on mixed convection flow between verticalporous plates filled with porous material
Investigation of the relative significance of the governing parameters on the interfacevelocity, the velocity and the temperature on mixed convection flow in a channel partially filled with porous fluid and partially filled with clear
Study of the effect of Darcy number and the stress jump condition at the interface offluid/porous layer for the steady fully developed mixed convection flow in a vertical annulus partially filled with porous material.

CHAPTER TWO

LITERATURE REVIEW

INTRODUCTION

This chapter examines somerelated literature of previous research on the phenomena of fluid flow. Fluid flow has become of extensive research in recent years; the level of research in this field is due to increasing concerns in science and technology about buoyancy-induced motions in many engineering applications such as rocket nozzles, electronics cooling systems, energy storage units, chemical reactors, etc.

For engineers to avoid over heating or damage to components, a thorough investigation and knowledge of heat transfer is inevitable. This chapter therefore, explores some related literature of previous works.

Mixed Convection

The study of mixed convection flow in vertical channels is motivated by its importance in wide range of engineering applications such as electronics cooling system, electrochemical processes, solar collectors etc. Ostrich (1954) solved the problem of fully developed mixed convection between vertical parallel plates with and without heat sources. Rokerya and Iqbal (1971) analyzed mixed convection in a vertical annular duct with uniform heat flux either on the internal surface or on the external surface, where the velocity and temperature profiles were obtained by the Runge-Kutta fourth-order method. An analytical study of fully developed mixed convection in vertical channel was conducted by (Aung and Worku ,1986) in which the boundary condition of uniform wall temperature was considered. Lavine (1988) presented an analytical solution for laminar mixed convection in a channel with a uniform wall heat flux. Cheng et al.(1990) considered either uniform temperature or uniform heat flux at each boundary surface. Barletta (1998) has studied the fully developed mixed convection flow in a vertical channel with viscous dissipation.Hamadah (1991) presented an analysis of laminar fully developed mixed convection in a vertical channel with symmetric and asymmetric heating of the walls. Muralidhar (1990) studied mixed convection flow in a saturated porous annulus, while (Ramanaiah and Malarvizhi , 1990) presented a unified treatment of free and mixed convection on a permeable vertical cylinder in a saturated porous medium. An analytical solution for mixed convection in vertical channel with heat and mass transfer was discussed by (Boulama and Galanis ,2004). Murthy et al.(2004) studied the combined radiation and mixed convection from a vertical wall with suction and injection in a non-Darcy porous medium. Umavathi and Malashetty (2005) investigated magnetohydrodynamic mixed convection in a vertical channel. Grosan and Pop (2007) have investigated thermal radiation effect on fully developed mixed convection flow in vertical channel. Pop et al.(2009) have investigated the effect of heat generated by an exothermal reaction on the fully developed mixed convection flow in a vertical channel. Khaefinejad and Aghanajafi (2009) studied laminar flow with simultaneous effects of mixed convection and thermal radiation in a vertical channel. Rossi de Schio et al. (2011) analytically investigated the steady mixed convection flow in a vertical fluid saturated annulus using the Darcy-Brinkman equation model by introducing a dimensionless reference temperature which is related to the usual parameter.

Porous Media

Fluid flow in channels partially filled with porous medium and partially filled with clear fluid has increased in the last few decades because of its various applications which include ceramic processing, crude oil extraction, energy storage units, thermal insulation, solidification of casting, geothermal energy utilization, petroleum reservoirs, storage of grain, buried electrical cables etc.The fundamental nature and the growing volume of work in this area is amply documented in the books by Nield and Bejan (2006), Ingham and Pop (2005), Vafai (2005), Pop and Ingham (2001), Bejan et al. (2004), de Lemos (2006) and Vadesz (2008).

The problem of fluid flow at the porous medium/clear fluid interface was first studied by (Beavers and Joseph,1967) in which the Darcy law was utilized to model the flow in the porous medium. The non-Darcian effects are accounted for by using the Brinkman-Forchheimer- extended Darcy equation for the flow in the porous medium by (Vafai and Thiyagaraja ,1987). The exact solution for the fully developed steady flow in the interface region was presented by (Vafai and Kim,1990). Ochoa-Tapia and Whitaker (1995a) studied exclusively the boundary conditions at the porous medium /clear fluid in the interface region.

CHAPTER THREE

MATHEMATICAL ANALYSIS

INTRODUCTION

In this chapter the derivation of the momentum and energy equations on the fluid flow formation were considered. And using the appropriate non-dimensional parameters, the non-dimensional equations were obtained from dimensional equations.

Role of suction/injection on mixed convection flow in a vertical porous channel filled with porous material

Role of suction/injection on Mixed Convection flow in a vertical porous channel filled with porous material is studied as in figure 3.1. The distance between the walls is . Choose a Cartesian coordinate system with �� − axis vertically upwards along the direction of th, thermal expansion coefficient . The plates are heated asymmetrically with one plate maintained at a temperature ₁ while the other plate at a temperature ₂ where ₂. Due to this temperature difference between the plates, flow occurs in the channel. In addition, the origin of the axes is such that the channel walls are at positions and . It is assumed that fluid ibeing injected in to the channel with certain constant velocity () on one plate (, and it is sucked off from the other plate () at the same rate.

CHAPTER FOUR

DISCUSSION OF THE RESULTS

INTRODUCTION

This chapter discusses the results obtained in chapter four which are presented graphically.

Discussing the results of problem 3.1

In order to see the effect of the suction/injection(), Prandtl number( and Darcy number() on the velocity ()) and temperature()), graphs are plotted for various values of the governing parameters.

CHAPTER FIVE

SUMMARY AND CONCLUSIONS

SUMMARY

The first problem reports the analytical study of the impact of suction/injection on mixed convection flow between vertical porous plates filled with porous material. The second problemis the fully developed mixed convection flow between vertical parallel plates partially filled with porous material in which the interface velocity, the velocity and the temperature are obtained analytically. The third problem studies the effect of Darcy number and the stress jump condition at the interface of fluid/porous layer for the steady fully developed non-Darcian mixed convection flow in an annulus partially filled with porous material. In the first problem, the plates are heated such that one plate is maintained at a temperature T₁ while the other plate is maintained at a temperature T_2. And in the second and third problems, the wall of the clear fluid is heated while that of the porous medium is cooled.The dimensionless form of the governing equations are solved analytically using the method of undetermined coefficients and the analytical solutions obtained were presented graphically and discussed.

CONCLUSIONS

In order to analyze the impact of the suction/injection parameter) on mixed convection flow between vertical porous plates filled with porous material, a mathematical model has been developed. The governing equations have been solved analytically and the numerical results obtained are presented graphically. Results show the reference temperature(�₀) decreases the temperature as it increases. And it is observed that by increasing injection (�� > 0)through the hot plate, temperature increases while by increasing suction through the cold plate it decreases temperature. It is observed also that the fluid velocity is strongly affected by the suction/injection parameter(��) and the reference temperature(�₀) . Also, Darcy number increases the fluid velocity and it can be used to suppress the onset of flow reversal.For 0, the solution is recovered to the solution by Weidman and Medina(2008).

A fully developed mixed convection flow between vertical parallel plates partially filled with clear fluid and partially filled with porous material is considered. The effects of are investigated. It is found that by increasing the porous layer thickness the probability of reverse flow is less.The velocity is significantly affected throughout the porous region for higher Darcy number. For all values of Darcy number, the interface velocity is influenced by the adjustable coefficient in the stress jump condition. It can be concluded that fluid flow can be suppressed by imposing porous matrix in the channel.

RECOMMENDATIONS

This research work investigated mixed convection flow in different geometries in which the fluid considered is non-Darcian where the walls of the channels are maintained at different temperature. To have a wider understanding and application of this phenomenon of mixed convection, the effect of the governing parameters can be investigated on the boundary conditions. Darcian fluids can also be considered in the presence of magneto-hydrodynamic with uniform temperature on the walls of the plates.

REFERENCES

Al-Nimr, M.A., and Darabsch, T.T (1995) Analytical solutions for transient laminar fully Developed free convection in open ended vertical concentric porous annul.ASMEHeatTransfer,vol. 117, pp. 762-764
Aung, W. and Woyku, G. (1986) Theory of fully developed combined convection including Flow reversal.ASME Journal of Heat Transfer vol.108, pp.485-488
Barletta, A.(1998) Laminar mixed convection with viscous dissipation in a vertical channel. International Journal of Heat Mass Transfer, vol.41 pp.3501-3513.
Bejan, A., Dincer, I., Lorente, S, Miguel, A.F, Reis, A.H.(2004) Porous and Complex Flow Structures in Modern Technologies. Springer, New York.
Beavers, G.S, Joseph, D.D, (1967) Boundary Conditions at a Natural Permeable Wall
FluidMechanics j. Fluid Mechanics vol. 30 pp. 197-207
Bua, H.H, Torrence,K.E, (1981) Onset of Convection in a permeable medium between vertical coaxial cylinders. Phys. Fluids vol. 25 pp. 1755-1766
Buhler, K., (2003) Special solutions of the Boussinesq-equations for free convection between vertical walls. Heat Mass Transfer vol.39 pp.631-638

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