CHAPTER - I INTRODUCTION

Transcription

1 CHAPTER - I INTRODUCTION 1.1 OBJECTIVE AND SCOPE The aim of the thesis is to study fully developed mixed convection of magnetohydrodynamic and viscous fluid in a vertical double passage channel in the presence of first order chemical reaction. The convective heat transfer in a vertical channel could be enhanced by using special inserts which can be specially designed to increase the included angle between the velocity vector and the temperature gradient vector rather than to promote turbulence. A plane baffle may be used as an insert to enhance the rate of heat transfer in the channel. A thin and perfectly conductive baffle is used so as to avoid a considerable increase in the transverse thermal resistance into the channel. Presence of the baffle may lead to a higher value of Nusselt number according to the baffle position and the value of Gr Re. In this study, the effects of baffle size, position were studied for internal cooling heat transfer augmentation. The plane baffle is to induce cross flow for higher heat transfer coefficients and hence improved heat transfer performance, this objective is not quite achieved in conventional shell-and-tube heat exchanger. The flow separation in ducts with segmented baffles has many engineering applications, e.g. shell-and-tube heat exchangers with segmented baffles, air-cooled solar collectors, and internally cooled turbine blades. Augmentation techniques usually employ baffles attached to the heated surface so as to provide an additional heat transfer surface 1

2 area and to promote turbulence. The flow over baffles has different fluid flow and heat transfer characteristics. The presence of these baffles causes the flow to separate, reattach and create reverse flow. The purpose of the present study focuses attention on the fully developed mixed convection flow in a vertical double passage channel in the presence of first order chemical reaction, at different baffle positions are all considered so as to extensively investigate their distinct influence on the velocity, temperature, concentration, species concentration, velocity gradient and volumetric flow and rate of heat transfer. The process of heat and mass transfer is encountered in aeronautics, fluid fuel nuclear reactor, chemical process industries and many engineering applications in which the fluid is the working medium. The applications are often found in situations viz., fiber and granules insulation, geothermal systems in the heating and cooling chamber, energy processes and astrophysical flows. Further, the thermal convection plays an important role in the control of mountain iron flow in the steady industrial liquid metal cooling in metallurgical process. When mass transfer takes the place in a fluid when at rest, the mass is transformed purely by molecular diffusion a result identified from concentration gradient. There occurs several industrial and atmospheric applications where the transport processes occurring in nature due to temperature and chemical differences. Magnetohydrodynamics (MHD) has attracted the attention of a large number of scholars due to its diverse applications. In astrophysics and geophysics, it is applied to study the stellar and solar structures, interstellar matter, radio propagation through the ionosphere etc. In engineering it finds its application in MHD pumps, MHD bearings etc. 2

3 hydromagnetic flow and heat transfer problems have become more important, industrially. In many metallurgical processes involving the cooling of many continuous strips of filaments by drawing them through an electrically conducting fluid subject to a magnetic field, the rate of cooling can be controlled and final product of desired characteristics can be achieved. Another important application of hydromagnetics to metallurgy lies in the purification of molten metal s from non-metallic inclusions by the application of a magnetic field. When the channel is divided into several passages by means of plane baffles, as usually occurs in heat exchangers or electronic equipment, it is quite possible to enhance the heat transfer performance between the walls and fluid by the adjustments of each baffle position and strength of the separate flow streams. In such configurations, perfectly conductive and thin baffles may be used to avoid significant increase of the transverse thermal resistance. Chin-Hsiang et al. (1989) studied the thermal characteristics of hydrodynamically and thermally fully developed flow in an asymmetrically heated horizontal channel, which is divided in to two passages (by means of a baffle) for two separate flow streams. Salah El-Din (1994) studied analytically, the laminar, fully developed combined convection in a vertical double passage channel with different wall temperature and concluded that the heat transfer in the channel is affected significantly by the baffle position. Maheshwari et al. (2011) studied the performance study of solar air heater having absorber plate with half perforated baffles. Keeping in view the practical applications of inserting baffles in a vertical channel, the object of the present work is to study the following problems. 3

4 1. Effect of first order chemical reaction in a double passage channel. 2. Effect of first order chemical reaction on free convection in a vertical double passage channel for conducting fluid. 3. Magnetohydrodynamic free convection in a vertical double passage channel with the effect of first order chemical reaction. 4. Effect of first order chemical reaction on magnetoconvection in a vertical double passage channel. 5. Heat and mass transfer in a vertical double passage channel filled with electrically conducting fluid. 1.2 LITERATURE REVIEW Recently many investigations have been focused on the baffle-walled channel heat exchangers. Most studies discussed the optimal baffle geometry that enhance heat transfer performance for a given pumping power or flow rate. In the experimental efforts, Founti and Whitelaw (1981) used LDA to deduce the velocity field in an ax asymmetric heat exchanger with baffles on the shell-side surface. The similar distributions of the mean flow velocity and turbulent intensity were found after two sets of baffles from the channel entrance. Later Berner et al. (1984a) and Berner et al. (1984b) obtained experimental results of mean velocity and turbulence distributions in flow around segmented baffles. The first experimental work investigating the use of permeable baffles, instead of using solid plates, was presented by Hwang (1997). In that work, the author found out that heat transfer between the channel walls and the fins was enhanced, showing then that 4

5 for turbulent flow the use of porous baffles benefited heat transfer, i.e., the use of porous baffles in substitution to solid (impermeable) material represented a net gain. Motivated by this article, Yang and Hwang (2003) carried out a numerical investigation of the problem, reaching similar conclusions. To corroborate Hwang s (1997) conclusion, Ko and Anand (2003) carried out an experimental program for turbulent flow with porous baffles made of various materials. However, results (Yang and Hwang, 2003; Ko and Anand, 2003) were not very promising. In their analysis, the porous baffles presented in most cases a flow behavior as good as the one with solid baffles. Celebi and Akyildiz (2002) have simulated the problem of fluid motion in partially filled rectangular tanks using the volume of fluid formation to track the free surface. They solved the complete Navier Stokes equation in primitive variables by the use of the finite difference approximations. A mechanical model of liquid sloshing was developed by Xu and Dai (2003) to investigate the longitudinal dynamic characteristics of partially filled liquid cargo tank vehicles during typical straight-line driving. The dynamic liquid motion is modeled by using a mechanical system that describes the behavior of the liquid motion as a linear spring mass model augmented with an impact subsystem for longitudinal oscillations. Computer simulation of tank vehicles under rough road conditions is performed by incorporating the forces and moments caused by liquid motion into the pitch plane vehicle model. Usually, the sloshing effect is suppressed in a passive manner by introducing additional sub-structures called baffle or sloshing damper into the containers by Gedikli and Erguven (1999) and Modi Akinturk (2002). Also, Welt and Modi (1992), Lee and Cho (2002) and Cho and Lee (2003) demonstrated that the shape 5

6 and design concept of the sloshing damper varies depending on the sloshing motion type, the kind of external excitation and the container shape. Fluid mechanics is that discipline within the broad field of applied mechanics concerned with the behavior of liquids and gases at rest or in motion. This field of mechanics obviously encompasses a vast array of problems that may vary from the study of blood flow in the capillaries (which are only a few microns in diameter) to the flow of crude oil across Alaska through an 800-mile-long, 4-ft-diameter pipe. Fluid mechanics principles are needed to explain why airplanes are made streamlined with smooth surfaces for the most efficient flight, whereas golf balls are made with rough surfaces (dimpled) to increase their efficiency. Many practical problems in fluid mechanics require analysis of the behavior of the contents of a finite region in space (a control) volume. For example, we may be asked to calculate the anchoring force required to hold a jet engine in place during a test. The bases of this analysis method are some fundamental principles of physics, namely conservation of mass, Newton s second law of motion, and the laws of thermodynamics. Thus, as one might expect, the resultant techniques are powerful and applicable to a wide variety of fluid mechanical circumstances that require engineering judgment. Conservation of Mass and Continuity Equation A system is defined as a collection of unchanging contents so the conservation of mass principle for a system is simply stated as Time rate of change Time rate of change of Net rate of flow of the mass of the = the mass of the contents + of mass through coincident system of coincident control volume the control surface 6

7 Newton s Second Law Newton s second law of motion for a system is Time rate of change of the = Sum of external forces linear momentum of the system acting on the system First Law of Thermodynamics The first law of thermodynamics for the system is Time rate of increase Net time rate of energy Net time rate of energy of the total stored = addition by heat transfer + addition by work transfer energy of the system into the system into the system The Mechanism By Which Heat Transfer The heat transfers are usually referred as modes of heat transfer. There are three of these: conduction, convection and radiation. Conduction: This occurs at molecular level when a temperature gradient exists in a medium, which can be solid or fluid. Heat transfers along the temperature gradient by conduction. Convection: Happens in fluids in one of two mechanisms: random molecular motion which is termed diffusion or the bulk motion of a fluid carries energy from place. Convection can be either forced through for example pushing the flow along the surface or natural as that which happens due to buoyancy forces. Radiation: Occurs where heat energy is transfers by electromagnetic phenomenon, of which the sun is particularly important source. It happens between surfaces at 7

8 different temperatures even if there is no medium between them as long as they face each other. In many practical problems, these three mechanisms combine to generate the total energy flow, but it is convenient to consider them separately at this introductory stage. We need to describe each process symbolically in an equation of reasonably simple form, which will provide the basis for subsequent calculations. We must also identify the properties of materials, and other system characteristics, that influence the transfer of heat. Free Convection Natural or Buoyant or Free convection is a very important mechanism that is operative in a variety of environments from cooling electronic circuit boards in computers to causing large scale circulation in the atmosphere as well as in lakes and oceans that influences the weather. A free convection flow field is a self-sustained flow driven by the presence of a temperature gradient. (As opposed to a forced convection flow where external means are used to provide the flow). As a result of the temperature difference, the density field is not uniform also. Buoyancy will induce a flow current due to the gravitational field and the variation in the density field. In general, a free convection heat transfer is usually much smaller compared to a forced convection heat transfer. It is therefore important only when there is no external flow exists. The study showed that the heat transfer was improved when heaters is close to the right corner. Yasin et al. (2006) studied the laminar natural convection in porous media 8

9 right-angle triangular enclosures. They solved Darcy and energy equations adopting alternative direction implicit finite difference techniques. Forced convection flows in channels with abrupt expansion or contraction are widely encountered in engineering applications, such as cooling passages of turbine blades, diffusers, combustors and heat exchangers. These separated flows are intrinsically irreversible because of viscous dissipation, reattachment and recirculation. The flow over backward facing step (BFS) was studied by several investigators both theoretically and experimentally to find the physics of such separated flows. Most of research works on BFS has been extensively carried out from fluid mechanics and heat transfer perspectives. The results showed that the conduction heat transfer zone is dominant for low Rayleigh numbers. Yasin et al. (2007) conducted a numerical study to investigate the 2D laminar natural convection in a porous triangular enclosure with a square body. Fuad et al. (2007) studied the laminar natural convection inside right triangular enclosures. Khudheyer et al. (2010) has studied the heat transfer characteristics in an enclosure with vertical baffles Heat transfer is the area that deals with the mechanism responsible for transferring energy from one place to another when a temperature exists. Natural convection is one of the most economical and practical methods of cooling and heating. Natural convection is caused by temperature or concentration induced density gradient within the fluid. Natural convection flow occurs as a result of influence of gravity forces on fluids in which density gradients have been thermally established. Bilgen (2005) conducted a study for conjugate heat transfer in a thin fin mounted enclosure at different conductivity ratio, 9

10 Rayleigh number and geometrical parameter of the fin. He found that Nusselt number is an increasing function of Rayleigh number and a decreasing function of fin length and relative conductivity ratio. Robillard and Vasseur (1981) studied the maximum density effect and supercooling of two-dimensional transient laminar natural convection heat transfer of water in a rectangular cavity with a convective boundary. Sundaravadivelu and Kandasamy (2000) analyzed natural convection flow of pure water around its temperature of maximum density existing between the temperature 273 K and 285 K, by using a nonlinear temperature dependent equation for density in a square cavity. Tasnim and Collins (2004) investigated numerically the effect of attaching a high conducting thin baffle on the hot-wall of a square cavity. They concluded that adding a baffle on the hotwall can increase the rate of heat transfer by as much as 31.46% compared with a wall without baffle. Asif et al. (2011) studied the heat transfer in a rectangular enclosure with baffles. Bassam and Abu-Hijleh (2002) studied the problem of laminar mixed convection from an isothermal cylinder with low conductivity baffles in cross flow was solved numerically. When using a small number of baffles reduced the Nusselt number more than an even number of baffles, especially at high values of Reynolds number. This is not the case at high values of buoyancy parameter. There is an optimal height, Reynold number dependent, for maximum heat transfer reduction beyond which an increase in baffle height does not result in further decrease in heat transfer. Changwoo Kang and Kyung-Soo Yang (2011) investigated the heat transfer characteristics of baffled channel flow, where thin baffles were mounted on both channel walls periodically in the direction of the main flow. The main objective was to find the physical resin responsible for the 10

11 heat transfer enhancement in finned heat exchangers, and to identify the optimal configurations of the baffles to achieve the most efficient heat removal from the channel walls. The results shed light on understanding and controlling heat transfer mechanism in a finned heat exchanger, being quite beneficial to its design. Nasiruddin and Kumran Sidddiqui (2007) studied the heat transfer enhancement in a heat exchanger tube by installing a baffle was reported. The effect of baffle size and orientation on the heat transfer enhancement was studied in detail. The results show that the Nusselt number enhancement is almost indent of the baffle inclination angle, with the maximum and average Nusselt number 120% and 70% higher than that for the case of no baffle respectively. For a given baffle geometry, the Nusselt number enhancement is increased by more than a factor of two as the Reynolds number decreased from 20,000 to Simulations were conducted by introducing another baffle to enhance heat transfer. The results show that the average Nusselt number for the two baffles case is 20% higher than one baffle case and 82% higher than the no baffle case. The above results suggest that a significant heat transfer enhancement in a heat exchanger tube can be achieved by introducing a baffle inclined towards the downstream side, with the minimum pressure loss. Tsai-Shou Chang and Yann-Huci Shaiau (2005) numerically studied the effects of a horizontal baffle on the heat transfer characteristics of pulsating opposing mixed convection in a parallel vertical open channel. It has been showed that maximum occurs at some specific imposed pulsating frequencies which can be considered to be the natural frequency of the system. 11

12 Fain Chen and Wang (1993) studied the convective instability in two-dimensional enclosures containing a fluid-saturated porous medium with an insulating baffle extending vertically from the bottom boundary is investigated. They found that on the basis of the results obtained by a linear stability analysis covering a wide range of relevant parameters and were believed to be applicable to some engineering designs, such as the insulating systems for building and heat exchangers. Molki and Mostoufizadeh (1989) experimentally investigated the heat transfer and pressure drop in a rectangular duct with repeated-baffle blockages. The baffles were arranged in a staggered fashion with fixed axial spacing. The transfer coefficients are evaluated in the periodic fully developed and entrance regions of the duct. The presence of the baffles enhances these coefficients. The entrance length of the duct is substantially reduced by the baffles. Finally, pressure drop and heat transfer data are employed to evaluate the thermal performance of the duct. Mackley and Ni (2001) reported experimental observations on the dispersion of fluid in horizontal and vertical tubes where periodic baffles and fluid oscillation may be present. Local concentration profile measurements are made both at the center and wall of the tube. They observed that small density differences between the tracer and bulk fluid can significantly modify the expected concentration profile for unbaffled tubes. When baffles and oscillations are present excellent mixing was achieved across the tube and dispersion data were presented for this type flow. Dalogiu and Ayhan (1999) presented the experimental results of natural convection in a rectangular cross-section vertical channel. Along the channel fins connected to both placed were placed, periodically. The channel walls were maintained at uniform heat flux. Results shows that 12

13 Nusselt number for finned channel were less than those of the smooth channel. Shokouhmand et al. (2011) were studied the effect of porous insert position on enhanced heat transfer in a parallel plate channel partially filled with a fluid saturated porous medium. The flow field and thermal performance of the channel were investigated and compared for two configurations: first the porous insert was attached to the channel walls, and second the same amount of the porous material was positioned in the channel core. They compared their results to the analytical solutions, a reasonable agreement was observed. The effects of various parameters like Darcy number, porous medium thickness, etc. on the conduit thermal performance were investigated in both channel configurations. They found that the position of the porous insert has significant influence on the thermal performance of the channel. Nie et al. (2009) studied the numerical simulations of three dimensional laminar forced convection flow adjacent to backward facing step in rectangular duct were presented to examine effects of baffle on flow and heat transfer distributions. The step height is maintained as constant. A baffle is mounted onto the upper wall and its distance from the backward facing step is varied. The inlet flow is hydrodynamically steady and fully developed with uniform temperature. They found that the maximum Nusselt number on the stepped wall develops near the sidewall, and it moves further downstream as the location of baffle moves in the stream wise direction. The friction coefficient at the stepped wall decreases as the distance of the baffle from the inlet increases. Barletta and Celli (2008) investigated the combined forced and free flow in a vertical with an adiabatic wall and an isothermal wall. The laminar parallel and fully developed regime is considered. A uniform horizontal magnetic field is assumed to be applied to the fluid. 13

14 The dimensionless governing parameters affecting the velocity and temperature profiles were the Hartmann number number within a bounded range of the ratio between the Grashof number and the Reynolds number. Outside this range, no parallel flow solutions of the problem exist. The use of electrically conducting fluids under the influence of magnetic fields in various industries has led to a renewed interest in investigating hydromagnetic flow and heat transfer in different geometries. For example, Sparrow and Cess (1961) considered the effect of a magnetic field on the free convection heat transfer from a surface. The coal-fired magnetohydrodynamic generator channel is subjected in an unusually severe thermal environment. The fluid mechanics and the heat transfer characteristics of the generator channel are significantly influenced by the presence of the magnetic field. The slag layer on the walls of the channel further complicates the problem. An analysis of this important heat transfer problem for realistic generator conditions will necessarily be very complicated. The complexity of the physical process is compounded further by the difficult-to-handle wall boundary conditions. Modelled the physics of the problem as realistically as possible, but in the contest of simplex geometry. The general MHD flow problems are studied considering the imposed magnetic field in a direction perpendicular to the direction of the flow. They have investigated the flow of electrically conducting fluid past between two vertical plates where one of the plates is adiabatic and other plate is of variable temperature, in the presence of a magnetic field placed at different angles θ (where θ varies from 0 to π 2 ) to the motion of the fluid. Zimmerman and Acharya (1987) numerically studied natural convection in an enclosure with perfectly conducting horizontal end walls and finitely conducting baffles. They found out growing and 14

15 spreading of the counter-clockwise vortex in the entire rectangular cavity appears to be a slower process than in the case of square cavity. Khudheyer (2012) studied the turbulent natural convection inside an inclined square enclosure with baffles. Muhaimin et al. (2009) studied the effect of chemical reaction, heat and mass transfer on nonlinear MHD. The development of transport models in porous media had a bearing in the progress of several applications such as geology, chemical reactors, drying and liquid composite molding, combustion and biological applications. In this review, the impact of the theory of transport in porous media on medical and biological sciences is discussed for different applications. Chamka and Sameh (2011) have studied unsteady MHD heat and mass transfer by mixed convection flow in the forward stagnation region of a rotating sphere in the presence of chemical reaction and heat source. Mahdi Shahrokhi et al. (2011) studied the numerical modeling of the effect of the baffle location on the flow field, sediment concentration. 1.3 PLAN OF WORK The literature survey made above has helped me to take up the problems investigated in this thesis. In order to achieve the objectives set above, the work plan of the thesis is as follows: The literature survey pertained to the work presented along with the objectives and scope of the thesis in chapter-i. 15

16 Chapter-II deals with formulation of basic equations, boundary conditions and dimensionless parameters. In chapter-iii we consider free convection heat and mass transfer in a vertical channel in the presence of chemical reaction. The considered channel is divided in to two passages by means of a thin plane baffle. Each stream has its own pressure gradient and hence the velocity, temperature and concentration will be individual in each stream. After placing the baffle, the fluid in one of the passage is concentrated. The first order chemical reaction is used as an example of calculation to obtain the analytical solutions. The coupled nonlinear ordinary differential equations governing the fluid motion is solved using regular perturbation method. The temperature and concentration fields are observed to be governed by complex interaction among dispersion and natural convection mechanisms. Result are drawn for varying physical parameters,such as ratio of Grashof number to Reynolds number, modified Grashof number to Reynolds number, Brikman number and chemical reaction parameter on the flow field at different positions of the baffle. It is found that the ratio of Grashof number to Reynolds number, modified Grashof number to Reynolds number, Brinkman number enhances the flow where as first order chemical reaction parameter suppresses the flow at all the baffle positions in both the streams. Chapter-IV reports investigation on laminar free convection in a vertical double passage channel for electrically conducting fluid in the presence of first order chemical reaction. The channel is divided in to two passages by inserting a thin plane conducting baffle. After placing the baffle one of the passages is concentrated. An analytical solution 16

17 has been developed for the coupled nonlinear ordinary differential equations using regular perturbation method. The results show that the thermal and mass Grashof number and Brinkman number enhances the flow where as Hartmann number and first order chemical reaction parameter suppresses the flow at all the baffle positions in both the streams. Chapter-V deals with the study of dispersion of solute for conducting fluid in a vertical double passage channel with first order chemical reaction. The channel is divided in to two passages by means of a thin perfectly conducting baffle. Approximate analytical solutions are found for the coupled nonlinear ordinary differential equations using regular perturbation method. The solutions are evaluated and shown graphically for thermal Grashof number, mass Grashof number, Brinkman number, Hartmann number and chemical reaction parameter at different baffle positions. It is found that the thermal Grashof number, mass Grashof number, Brinkiman number enhances the flow where as the magnetic parameter, chemical reaction parameter reduces the flow at all the baffle positions. Further the effects of governing parameter on the volumetric flow rate, species concentration, total heat rate, skin friction and Nusselt number is also observed and tabulated. The objective in chapter-vi is to study magnetohydrodynamics electrically conducting fluid in a vertical double passage channel taking in to account the presence of first order chemical reaction. The channel is divided in to two passages by means of a thin, perfectly conducting plane baffle and hence the velocity will be individual in each stream. The governing equations are solved by using regular perturbation technique valid 17

18 for small values of Brinkman number. The results are obtained for velocity, temperature and concentration. The effect of various dimensionless parameters such as thermal Grashof number, mass Grashof number, Brinkman number, first order chemical reaction parameter and Hartmann number on the flow variables are discussed and presented graphically for open and short circuits. Further the effect of governing parameters on the volumetric flow rate, species concentration, total heat rate, skin friction and Nusselt number is also observed and tabulated. In chapter-vii we investigate the influence of first order chemical reaction in a vertical double passage channel in the presence of applied electric field. The wall and ambient medium are maintained at constant but different level of temperature and concentration such that the heat and mass transfer occur from the wall to the medium. The channel is divided in to two passages by means of a thin perfectly conducting baffle. The coupled nonlinear ordinary differential equations are solved analytically by using regular perturbation method. The variation in velocity, temperature and concentration with thermal Grashof number, mass Grashof number, Brinkman number, first order chemical reaction parameter, Hartmann number and electrical field load parameter for a wide range of values of these parameters are analyzed and shown pictorially. Further the effect of governing parameters on the volumetric flow rate, species concentration, total heat rate, skin friction and Nusselt number is also observed and tabulated. 18