Modeling and Numerical Analysis of Heat and Mass Transfer Phenomenon in Fluid Flow

Abstract

The phenomenon of heat and mass transfer occurs in almost every field of science and engineering as well as in nature. In the methods of power production, fluid flow and heat

transfer processes are involved. Components used in the chemical and metallurgical in- dustries include furnaces, heat exchangers, condensers, and reactors, all of which employ

thermo fluid processes. Heat transfer is frequently a limiting factor in the design of elec- trical machinery and electric circuits. Heat and mass transfer are significant causes of

pollution in the natural environment, as are storms, floods, and fires. When the weather changes, the human body uses heat and mass transfer to maintain its temperature. Owing to these applications, investigation of heat and mass transfer in the steady-state flow of different industrial fluids through one/two-dimensional geometries has been carried out in the present research work. The current research work aims to analyze the physical

problem and then develop a mathematical model that governs the fluid flow under differ- ent conditions using conservation laws for mass, momentum, energy, and concentration.

For solving the modeled PDE’s, a higher-order numerical technique i.e., the finite element method is applied. Further, the effect of the various embedded parameters on the flow, heat, and mass transfer traits are analyzed graphically. This thesis is comprised of seven chapters. Chapter 1 is introductory. This chapter provides the background of the proposed study, its development, applications, and other physical aspects involved in studying heat and mass transfer problems. In addition, some basic definitions along with the motivation behind the work are discussed briefly. The work done by the various researchers in the field of heat and mass transfer by considering different geometries is also given in this chapter. Chapter 2 is devoted to analyze the water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms (moves under the effects of gravity) over a non-linear inclined stretching sheet in the presence of a non-uniform magnetic field. This regime is encountered in the bio-nano-material electroconductive polymeric processing systems currently being considered for third-generation organic solar coatings, anti-fouling marine coatings, etc. Oberbeck-Boussinesq approximation along with ohmic dissipation (Joule heating) is considered in the problem. The governing equations of the flow are non-linear partial differential equations that are converted into ordinary differential equations via similarity transformations. These equations are then solved by the finite element method.

The effect of various important parameters on non-dimensional velocity, temperature dis- vii

tribution, nanoparticle concentration, the density of motile micro-organisms is analyzed

graphically in detail. It is observed from the obtained results that the flow velocity de- creases with rising in the angle of inclination δ while temperature, nanoparticle concen- tration, and density of motile micro-organisms increase. The local skin friction coefficient,

Nusselt number, Sherwood number, motile micro-organism’s density number are calcu- lated. It is noticed that increasing the Brownian motion and thermophoresis parameter

leads to an increase in fluid temperature, which results in a reduction in Nusselt number. On the contrary, the Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. Chapter 3 deals with the bioconvective flow of nanofluids using non-Fourier’s heat flux

theory for heat transfer and non-Fick’s mass flux theory for mass transfer. The bene- fits of including micro-organisms in the suspension incorporate micro-scale mixing and

foreseen enhanced stability of nanofluid. For heat transfer and mass transfer processes, non-Fourier’s heat flux and non-Fick’s mass flux theories are employed. These theories are actively under investigation to resolve some drawbacks of the famous Fourier’s Law and Fick’s Law. The modified parameters in conventional laws are thermal and solutal relaxation times, respectively. The governing equations are remodeled using appropriate

similarity transformations into a system of coupled ordinary differential equations. Fi- nite Element Methodology is used to obtain the solution of non-linear coupled differential

equations. The results of sundry factors are analyzed graphically on velocity, heat trans- fer, mass transfer, and density of micro-organisms. The computational results obtained in

this letter reveal that fluid temperature and concentration of nanoparticles have an inverse relationship with thermal relaxation and solutal relaxation time. In Chapter 4 we have studied the heat and mass transfer effects in three-dimensional mixed convection flow of Eyring Powell fluid over an exponentially stretching surface with convective boundary conditions. We have employed the Cattaneo-Christov heat flux model

for heat transfer that considers the interesting aspect of thermal relaxation time. First- order chemical reaction effects are also taken into account. Similarity transformations

are invoked to reduce the leading boundary layer partial differential equations into the ordinary differential equations. The nonlinear, coupled ordinary differential with boundary conditions has been analyzed numerically by using the finite element method. In chapter 5 and 6, we investigate the flow through porous cavities. The flow through cavities has its own importance because in cavities, no external source such as electric power is required for induction of convectional heat transfer. Due to the absence of power sources, convectional heat transfer in cavities is free from magnetic noise, fee, and sound. In most of the industrial and engineering applications such as air conditioning devices, food processing

industries, float glass production, disposal of nuclear waste, ceramic processing, geothermal systems cavities filled with porous media are used because dissipation area of porous is greater than conventional fins thereby enhancing heat convection. Also, The irregular motion of the fluid flow around the individual pores mixes the fluid more effectively. In Chapter 5, we have examined the phenomenon of natural convection in a square porous cavity containing Casson fluid. The non-Newtonian model of Casson fluid is utilized to obtain the governing equations of a flow problem. The thermal control inside the cavity is managed by partially heating the bottom wall and symmetric cooling of the side walls while the top wall is adiabatic. The penalty finite element method is used to solve the non-linear coupled equations of the flow problem. The effect of different lengths of heated zone ε, Rayleigh number Ra and Darcy number Da has been examined on flow velocity and temperature distribution inside the cavity. The impact of effective viscosity of the fluid by varying Casson fluid parameter γ on the flow of fluid and heat transport has also been investigated. The results are demonstrated by plotting streamlines, isotherms, and average Nusselt number over wide ranges of governing parameters. The obtained results show that with an increase in Casson fluid parameter γ and Darcy number Da, heat transfer and flow circulation increase. It is also observed that the conduction dominant heat transfer takes place for low Darcy number over a wide range of the Rayleigh number (102 ≤ Ra ≤ 106 ).

In recent years, due to development of technology scientists are able to combine the nanoflu- ids of different characteristic in a single host fluid which have further improved thermo- physical properties. These fluids are named as hybrid nanofluid. Chapter 6 is devoted to

studying the heat transfer characteristics of hybrid nanofluid in a partially heated porous cavity. A partial section of the bottom wall of the cavity is being heated while the rest portion of the bottom wall and top wall are considered are adiabatic. Further, the side walls are kept at a lower temperature than the heated portion. The Penalty Finite element method is used to solve the dimensionless non-linear coupled partial differential equations of the flow problem. A comparison of results with the previous study has been made under particular cases, which shows good consistency. The results are demonstrated in terms of

streamlines, isotherms, and average Nusselt number over wide ranges of governing param- eters, namely Darcy number (Da), Rayleigh number (Ra), different lengths of the heated

zone (ε), and volume fraction of nanoparticles (φ). The obtained results show that with an increase in the percentage of hybrid nanofluid φ and Darcy number Da, heat transfer and flow circulation increase. It is also observed that the rate of heat transfer in the porous medium increases with an increase in the volume fraction of nanoparticles. In Chapter 7 we have discussed the conclusions of all the chapters. Also, the work pre-

sented in this thesis provides the theoretical and numerical framework for investigating the steady incompressible flow of fluids through one and two-dimensional systems. Therefore, the possible future work is also described in the last chapter.