In this book, an attempt is made to analyze the heat and mass transfer effects on a laminar two-dimensional steady/unsteady convection flow of a viscous incompressible and radiating Newtonian/non-Newtonian fluid past a stretching wedge/stretching sheet/thin liquid film bounded by a porous/non-porous medium, by taking viscous dissipation, uniform/non-uniform heat source/sink, activation energy, and binary chemical reaction, aligned/non-aligned magnetic strength into account. The approximate solutions are obtained by using Runge-Kutta with the shooting method. A parametric study is carried out to illustrate the behavior of the velocity, temperature, concentration, skin-friction, Nusselt number, and Sherwood number for variations in the various thermophysical and hydrodynamical parameters and are represented in figures and tables.
This book deals with the various aspects of flow, heat and mass transfer of boundary layer flow problems related to magneto hydrodynamic non- Newtonian flows , with special emphasis on dusty flow and heat transfer so that the subject is perceived by the post graduate students, researchers and post-doctoral researchers.. This study is essentially numerical in character. By applying the similarity transformations, the system of non-linear partial differential equations are reduced into a set of non-linear ordinary differential equations. Obtained equations are then solved numerically using Runge-Kutta-Fehlberg-4th order method, along with Shooting technique.
The book consists literature survey on Darcy-Brinkman-Forchheimer flow and heat transfer equations and Bénard-Marangoni and Bénard-Darcy convection problems. Next is approximate solution of the Darcy-Brinkman-Forchheimer (DBF) flow equation using a combination of finite difference and homotopy continuation (HCM) method. DBF flows are considered in a porous channel, tube and annulus. The algorithm developed for the solution of the DBF equation succeeds in obtaining the flow velocity accurately up to 12 decimal digits. It is found that time complexity of the algorithm for the considered computer system, programming language, GCC compiler and memory is O(n3). A detailed analysis is made regarding optimal number of equations required for each set of parameters' values, for a convergent solution. Comparison is made between the results of the problem with that obtained using shooting method (Runge-Kutta-Fehlberg (RKF-45).
Majority of the current numerical simulation methods for time-dependent flows are limited to second order accuracy in time discretization. Moreover, usual simulation methods rely on explicit time discretization methods for which numerical stability of solution is generally guaranteed only with very small time step sizes. Major commercial CFD software programs provide options for implicit time advancing, but the accuracy is limited to second order in time. In this book a stable simulation method is proposed that can be used to achieve arbitrarily high order of accuracy in time advancement in simulation of time-dependent flows and heat transfer. The strategy is to combine the state-of-the-art mathematical tools with proven flow simulation algorithms to develop simulation techniques with higher-order accuracy. A special class of implicit Runge-Kutta methods is used in conjunction with SIMPLE algorithm. The proposed method is called SIMPLE DIRK method. This book will be helpful to university students and researchers who are involved in research and code development for simulation of time-dependent flows and heat transfer.
The study of Radiative heat transfer in a nanofluid with the influence of magnetic field over a stretching surface has been investigated numerically. This model is used for the laminar boundary layer flow of a nanofluid. This study is considered for two cases as steady and unsteady. Similar and non similar solutions are presented here. At first for the steady case the system of governing equation are transformed into nonlinear ordinary coupled differential equations. These equations are solved numerically using the Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme with the help of a computer programming language Compaq Visual Fortran 6.6a. Numerical results are obtained for the velocity, temperature and concentration distributions, as well as Skin-friction coefficient, Nusselt number and Sherwood number at the sheet. The obtained results are presented graphically and also in tabular form. After that, for the unsteady case, the governing equations have been non-dimensionalised by usual transformation. Numerical solutions for the velocity, temperature and concentration distributions are obtained for associated parameters.
In this work, similarity and numerical solutions for some problems of unsteady heat transfer over different surfaces in the boundary layer of fluids through a porous medium are discussed. In these problems, we studied the influences of magnetic field, permeability of porous medium, heat generation / absorption, thermal conductivity, variable temperature. The governing equations are first cast into a dimensionless form by a nonsimilar transformation and the resulting equations are solved numerically by using the Runge-Kutta numerical integration, procedure in conjunction with shooting technique. The obtained results are shown in graphics and tabulated representation followed by a quantitative discussion. The main aim of this book which consists of four chapters, is to study similarity solutions of boundary layer of some fluid. In the following, a brief discussion of the chapters is given.
In India power generation is carried out through coal based power plants. The efficiency of coal power plants depends on coal combustion phenomenon. Hence there is need for understanding of coal combustion. Study of coal combustion through experimentation is tedious and expensive. This leads to use modeling techniques for understanding coal combustion. Therefore present book explains about the development of a model to describe coal combustion. The model presented in this work couples the heat transfer equation with the chemical kinetics equations. The combustion rate has been modeled by considering the first order reaction. The dependence of the convective and radiative heat transfer coefficient on Nusselt number is incorporated in present work. A finite volume method is used for solving heat transfer equation and Runge- Kutta fourth order method for the chemical kinetics equations. The model explained in present book is useful in power generation domain. The present work is helpful for research scholars and professionals who believe power of modeling.
The aim of this book is to investigate linear and nonlinear stability of mono-diffusive (pure thermal) or double-diffusive (thermo-solutal) convection in a porous medium with induced inclined gradients. In this chapter 1 has provided some key definitions, and discuss the underlying theory of stability and instability with respect to linear and nonlinear stability analyses inherent in understanding flows through porous media. Chapter 2 deals with the problem of pure thermal convection induced by inclined thermal gradients with an internal heat source. Chapters 3 and 4, the stability analysis is performed on the double-diffusive Hadley flow induced by both thermal and solutal gradients, when it is subjected to gravity variations. In Chapter 5, the double-diffusive Hadley-Prats flow with a concentration based heat source is investigated through linear and nonlinear stability analyses. In both cases, the resulting eigenvalue problems have been numerically integrated using a combination of Shooting and Runge-Kutta methods. In the last Chapter, a summary of the present work and some future directions are discussed.
This book contains the elementary aspects of flow, heat and mass transfer of boundary layer flow problems related to Oldroyd-B fluid and Casson fluid with suspended nano particles, with special emphasis on slip flow and nonlinear thermal radiation so that the subject is perceived by the post graduate students, researchers and post-doctoral researchers. This text is also introduces numerical computational tools for solving differential equation models that arises in fluid flow, heat and mass transfer of non-Newtonian fluids. Suitable similarity transformations are applied to the governing partial differential equations to obtain coupled nonlinear ordinary differential equations. The reduced equations are solved numerically by using Runge-Kutta-Fehlberg fourth-fifth order method with Shooting technique.