The unsteady free convection and mass transfer boundary layer flow past an accelerated infinite vertical porous plate by taking into account the viscous dissipation is considered when the plate accelerates in its own plane. The dimensionless momentum, energy and concentration equation in the presence of uniform transverse magnetic field has been solved analytically by perturbation technique. The usual similar transformations are applied to the steady momentum, energy and concentration equations and we obtained a set of ordinary differential equations. Then the solutions of the problem of the ordinary differential equations are obtained by using perturbation technique. The expression for velocity field, temperature field, concentration field, skin friction, Nusselt number (Nu) and Sherwood number (Sh) has been found. The results are discussed in detailed with the help of graphs to observe the effect of different parameters.
Table of Contents
I. INTRODUCTION
I. The governing equation
II. Solution of the problem
III. Results and discussion
IV. Conclusion
V. References
VI. Appendix
Research Objectives and Themes
This research aims to provide an analytical solution to the unsteady free convection and mass transfer boundary layer flow over an accelerated infinite vertical porous plate, incorporating the effects of viscous dissipation. The study investigates how various flow parameters influence velocity, temperature, and concentration distributions, with significant relevance to geophysical and astrophysical phenomena.
- Analytical modeling of unsteady MHD free convection and mass transfer.
- Application of perturbation techniques for solving complex non-linear equations.
- Investigation of viscous dissipation, thermal radiation, and chemical diffusion effects.
- Parametric analysis of velocity, temperature, and concentration profiles through graphical representation.
- Determination of physical quantities such as skin friction, Nusselt number, and Sherwood number.
Excerpt from the Book
I. INTRODUCTION
Consider a two dimensional unsteady flow of a laminar, incompressible, viscous, electrically conducting and heat generation fluid past a semi-infinite vertical moving plate embedded in a uniform porous medium and subjected to a uniform transverse magnetic field in the presence of a pressure gradient has been considered with free convection, thermal diffusion and thermal radiation effects taking in to an account. According to the coordinate system the x* -axis is taken along the porous plate in the upward direction and y-* axis normal to it. The fluid is assumed to be gray, absorbing–emitting but not scattering medium. Now to solve the momentum, energy and concentration equations usual similarity transformations are introduced. We get a set of ordinary differential equation to obtain the solutions of the problem. The ordinary differential equations are solved by using perturbation technique. The expressions for velocity field, temperature distribution, concentration field, skin friction, Nusselt number (Nu) and Sherwood number (Sh) have been obtained. The results are discussed in detailed with the help of graphs to analyze the effect of different flow parameters.
Summary of Chapters
I. INTRODUCTION: Provides the research background and context regarding free convection and mass transfer over a vertical porous plate, while citing relevant prior literature.
I. The governing equation: Establishes the mathematical framework, including the continuity, momentum, energy, and concentration equations under specific boundary layer assumptions.
II. Solution of the problem: Details the application of the perturbation technique to solve the system of non-dimensionalized governing equations.
III. Results and discussion: Presents the numerical results through various graphical figures to illustrate the impact of different physical parameters on the flow field.
IV. Conclusion: Summarizes the key findings of the research, confirming how various parameters like Grashof number and magnetic field affect the flow characteristics.
V. References: Lists the academic literature and previous studies consulted for this research.
VI. Appendix: Contains the explicit mathematical expressions and coefficients derived for the velocity, temperature, and concentration distribution solutions.
Keywords
Free convection, mass transfer, unsteady flow, perturbation technique, viscous dissipation, MHD, porous medium, thermal radiation, Nusselt number, Sherwood number, skin friction, boundary layer, velocity profiles, temperature distribution, concentration field.
Frequently Asked Questions
What is the primary subject of this research paper?
The paper focuses on the analytical solution of unsteady free convection and mass transfer boundary layer flow over an accelerated infinite vertical porous plate, taking viscous dissipation into account.
What are the central thematic fields?
The research intersects fluid dynamics, magnetohydrodynamics (MHD), heat and mass transfer, and porous media mechanics.
What is the main objective of the study?
The objective is to derive expressions for the velocity field, temperature distribution, and concentration field by solving governing partial differential equations using a perturbation technique.
Which scientific methods are utilized?
The authors utilize similarity transformations to convert partial differential equations into ordinary differential equations, which are then solved using a perturbation technique.
What does the main part of the work cover?
The main part covers the formulation of governing equations, the derivation of solutions, and a detailed discussion of how various physical parameters influence the flow behavior.
Which keywords characterize this work?
Key terms include free convection, mass transfer, unsteady flow, perturbation technique, viscous dissipation, and magnetohydrodynamics.
How does the magnetic field affect the flow velocity according to the study?
The results indicate that the velocity distribution across the boundary layer decreases as the values of the magnetic field parameter (M) increase.
What is the significance of the radiation parameter?
The radiation parameter (R) is shown to influence both temperature and concentration profiles, as well as the Nusselt number and skin friction coefficient.
What role does the Soret number play?
The study concludes that the concentration profiles increase with an increasing Soret number (S0), and the Sherwood number also increases as the Soret number increases.
- Quote paper
- Rubel Ahmed (Author), B.M. Jewel Rana (Author), S.F. Ahmed (Author), 2015, Analytical solution of the MHD free convective unsteady flow over a vertical plate with heat source, Munich, GRIN Verlag, https://www.grin.com/document/295132
