Convective Heat Transfer Boundary Layer Flow Driven Along a Curved Surface in the Presence of Exothermic Cataytic Chemical Reaction

Abstract

The main focus in present study is to deal with convective heat transfer in the pres ence of exothermic catalytic chemical reaction along a curved surface. Some of the important physical features such as viscous dissipation, temperature dependent vis cosity and thermal conductivity, magnetohydrodynamics and transient behavior are incorporated to understand their theoretical significance. The phenomena of both heat and mass transfer are included for various engineering processes. Further, the mathematical models for the above said phenomena are developed in keeping view the coordinate system. The exact solutions for the models considered in this thesis are available only in simplified situations. There are some numerical challenges as well, for instance, the presence of the tangential component of acceleration due to gravity, gx, appearing in the momentum equation which is describing curved form of the considered geometry. The simulations of these models may lead to a profound understanding of the physical process. Chapter 1 briefly introduced the main assumption of the thesis and also comprehend the related literature review. In Chapter 2, the different modes of heat transfer, the developed form of the conservative equations and the dimensionless parameters in volved in the dimensionless models are introduced. The fundamental equations for the conservative laws of mass, momentums, energy and mass concentration are de veloped accordingly for the ready reference in the thesis work. A mathematical model for free convective flow along the curved surface by encoun tering exothermic catalytic chemical reaction is a center of discussion in Chapter 3. The mathematical equations involved are the non-linear coupled partial differential xix xx equations. The tangential component of acceleration due to gravity gx is included in the momentum equation that shaped the surface in the form of a curve. The reported results are introduced along a curved surface for the first time. The phenomenon of exothermic catalytic chemical reaction for two dimensional, steady state natural con vection flows along a curved surface under the effect of various emerging parameters are examined numerically. The primitive variable formulation for Finite Difference Method (FDM) is utilized for the computation of coupled governing transport equa tions. Chapter 4 deals with effect of temperature dependent viscosity and thermal conduc tivity for the steady incompressible fluid flow along a curved surface. To illustrate the characteristics of mass transfer and heat transfer natural convection flow by con sidering the exothermic catalytic chemical reaction, modeling is formulated in terms of nonlinear partial differential equations. The term of temperature dependent vis cosity is introduced in momentum equation and the thermal conductivity term in the energy equation. The designed model is then approximated by the implementation of FDM. The physical behavior of the parameters involved in the said model and other quantities such as heat transfer rate θw, skin friction τw, and mass transfer rate Φw has been discussed. The mathematical model given in Chapter 3 has modified by indulging viscous dis sipation effects in energy equation and results has been discussed in Chapter 5. The proposed dimensioned flow model is made dimensionless by introducing appropriate dimensionless variables. The obtained non-dimensional model of partial differential equations is then transformed by primitive variable variable formulation. The results of the transformed equations are computed by use of Finite Difference Method. For the analysis of the above said phenomenon, the plots have been sketched to examine the effect of Prandtl number Pr, Eckert number Ec, dimensionlesschemical reaction rate constant λ, Schmidt number Sc and the exothermic parameter β on velocity U, mass concentration Φ, temperature distribution Θ, rate of heat transfer Θw, skin friction τw, and mass transfer Φw respectively. xxi Chapter 6 is devoted to inspect numerical behavior of combined effects of magnetic field and exothermic catalytic chemical reaction for fluid along the curved surface. The set of boundary layer equations has been formulated. The influence of rele vant dimensionless materials parameters on velocity profile, mass concentration and temperature distribution as well as on rate of heat transfer, skin friction, and mass transfer are plotted in graphs and also presented in tables. The transient behavior of mixed convective flow including the effects of exothermic catalytic chemical reaction along a curved surface is included in Chapter 7. For this purpose, mathematical model is developed for the transient mixed convection flow problem in form of coupled nonlinear partial differential equations. The numerical for mulation of the coupled non-dimensional mixed convection problem is demonstrated for both steady and transient cases along the curved surface. The Implicit Finite Difference Method for the unsteady problem has been used. The novelty used in this technique is that first we secure results for steady part to calculate the unknown physical quantities such as profile of velocity U, profile of temperature, θ and profile of concentration φ, and then used them in unsteady part to understand the physical behavior of transient heat transfer τheat, skin friction τskin and mass transfer τmass for diverse values of the dimensionless parameters, that is, body shape parameter n, modified mixed-convection parameter λC, mixed-convection parameter λT , Prandtl number Pr, exothermic parameter β, chemical reaction parameter λ 2 , temperature relative parameter γ, energy activation parameter E, index parameter n and Schmidt number Sc. Lastly, Chapter 8 highlighted the important findings of all the physical models devel oped in the previous chapters 3 - 7 and also the main conclusions have been draw.