Velocity profile and temperature distribution of a viscous incompressible fluid along a semi-infinite vertical plate with large suction is investigated in this work. The governing equations are solved numerically using perturbation technique. The flow phenomenon has been characterized with the help of flow parameters such as Suction parameter , Prandtl number and Eckart number .The effects of these parameters on the velocity field and temperature distribution have been studied and the results are presented graphically and discussed quantitatively. This type of problem is significantly relevant geophysical and astrophysical studies.
Table of Contents
1. Chapter One
1.1 Introduction
2. Chapter Two
2.1 Mathematical Model of Flow
2.2 Mathematical Formulation
2.3 Method of Transformation for Mat lab Technique
3. Chapter Three
3.1 Result and Discussions
Research Objective and Focus Areas
The primary objective of this research is to numerically determine the velocity profiles and temperature distribution of a viscous incompressible fluid as it flows along a semi-infinite vertical plate subjected to large suction, utilizing a perturbation technique to solve the governing equations.
- Analysis of flow phenomena influenced by the suction parameter, Prandtl number, and Eckart number.
- Application of perturbation techniques to solve coupled non-linear differential equations.
- Examination of the effects of key physical parameters on velocity fields.
- Investigation of temperature distribution variations across the thermal boundary layer.
- Mathematical modeling of steady and transient flow characteristics on moving solid surfaces.
Excerpt from the Book
2.1 Mathematical Model of Flow
By introducing Cartesian Co-ordinate system, X -axis is chosen along the plate in the direction of the flow and Y -axis –is normal to it. Initially it is considered that the plate as well as the fluid is remained at same temperature T(T∞). Also it is considered that the fluid and the plate is at rest after that the plate is to be moving with a constant velocity Uo is its own plate instantaneously at timet >0, the species temperature of the plate is raised to T(Tw > T∞).Where Tw is species temperature at the wall of plate and T∞ be the temperature species far away from the plate. The physical model of the study is shown in Figure 2.1.1.
Within the framework of the above stated assumptions with references to the generalized equations described before the equation relevant to the transient two dimensional problem are governed by the following system of coupled non-linear differential equations.
Summary of Chapters
Chapter One: Provides an introduction to boundary layer flows on moving surfaces and establishes the research motivation by reviewing existing literature on heat transfer and suction effects.
Chapter Two: Details the mathematical modeling, including the formulation of governing continuity, momentum, and energy equations, as well as the transformation methods applied for numerical computation.
Chapter Three: Presents the results and discussions, illustrating the impact of suction, Prandtl, and Eckart parameters on fluid velocity and temperature profiles through graphical representations.
Keywords
Heat transfer, mass transfer, accelerated plate, suction, perturbation technique, boundary layer, viscous fluid, incompressible, velocity profile, temperature distribution, Prandtl number, Eckart number, numerical solution, fluid dynamics.
Frequently Asked Questions
What is the core focus of this research paper?
The paper focuses on the numerical investigation of the velocity and temperature distribution of a viscous, incompressible fluid flowing along a semi-infinite vertical plate characterized by large suction.
Which key physical parameters are analyzed in the study?
The flow phenomenon is characterized by three primary parameters: the suction parameter (fw), the Prandtl number (Pr), and the Eckart number (Ec).
What is the primary research goal?
The main goal is to determine the heat transfer rates and velocity characteristics of the fluid within a thermal boundary layer under the influence of large suction.
Which scientific methodology is employed to solve the equations?
The research utilizes a perturbation technique to solve the governing coupled non-linear differential equations, supplemented by a transformation method for implementation in MATLAB.
What does the main body of the work address?
The main body establishes the mathematical model of the flow, provides the step-by-step mathematical formulation including stream functions, and discusses the resulting velocity and temperature distributions.
Which keywords best describe this study?
Key terms include heat transfer, suction, perturbation technique, boundary layer, viscous fluid, and various non-dimensional numbers like Prandtl and Eckart.
How does the increase in suction parameter affect the velocity profile?
Based on the provided graphical results, the velocity profile is observed to decrease as the suction parameter increases.
What happens to the temperature distribution when the Prandtl number is increased?
The study indicates that the temperature profile decreases with an increase in the Prandtl number.
Does the Eckart number have a significant effect on the profiles?
The results show that both the velocity and temperature profiles exhibit a decrease as the Eckart number is increased, confirming the influence of viscous dissipation.
- Citation du texte
- Jewel Rana (Auteur), 2015, Numerical solution of a viscous incompressible fluid along a semi-infinite vertical plate with large suction, Munich, GRIN Verlag, https://www.grin.com/document/294724
