MHD FLOW AND HEAT TRANSFER THROUGH A POROUS MEDIUM OVER A STRETCHING / SHRINKING SURFACE WITH SUCTION By Ali Mansoor Alanbri & Rakan Saud Alharbi Mathematics Department, College of Science, Majmaah University, Alzul…, KSA Rajab 14, 1436 Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 1 / 48
In The Name of ALLAH Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 2 / 48
Supervised By Supervised By Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 3 / 48
Supervised By Supervised By Dr. Farooq Ahmad Gujar Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 3 / 48
Acknowledgments Acknowledgments Praise and glory is to Allah, the Cherisher and Sustainer of the worlds, without His will, faith and support, we would not have been able to accomplish this laborious task. We bow to Him in reverence and gratitude. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 4 / 48
Acknowledgments Acknowledgments Praise and glory is to Allah, the Cherisher and Sustainer of the worlds, without His will, faith and support, we would not have been able to accomplish this laborious task. We bow to Him in reverence and gratitude. Peace and blessing to Hazrat Muhammad (Peace Be Upon Him) who is the cause of conceiving the universe. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 4 / 48
Acknowledgments We are highly obliged and very grateful to our respected teacher and supervisor, Dr. Farooq Ahmad Gujar, whom we always found helpful and courteous. We owe a great debt of gratitude to him for his valuable suggestions in the selection of a suitable topic and the research problems. We are very much obliged for his day to day guidance, their keen supervision and friendly a¤ection. They have always been the most cordial and cooperative throughout the research work and during the compilation of this project. We are highly obliged. We are also very grateful to our respected teacher Dr. Sajjad Hussain, whom we always found helpful. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 5 / 48
Acknowledgments We are highly obliged and very grateful to our respected teacher and supervisor, Dr. Farooq Ahmad Gujar, whom we always found helpful and courteous. We owe a great debt of gratitude to him for his valuable suggestions in the selection of a suitable topic and the research problems. We are very much obliged for his day to day guidance, their keen supervision and friendly a¤ection. They have always been the most cordial and cooperative throughout the research work and during the compilation of this project. We are highly obliged. We are also very grateful to our respected teacher Dr. Sajjad Hussain, whom we always found helpful. We are obliged and very grateful to my respected teacher, Prof. Dr. Adel Zaki, Head of the Department of Mathematics, Majmaah University, College of Science, Alzul… whom we always found helpful. We am very much obliged for his day to day guidance. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 5 / 48
Acknowledgments We are also highly obliged and very grateful to respected Dr. Mohammad Saleh Aloboudi, Dean of College of Science, Majmaah University, Alzul…. It has been a privilege and great honor for us to learn with a great man of such prominent characteristics. We love and respect him the most for his high morality and honorable sincerity, his guidance is a ray of light in our research. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 6 / 48
Acknowledgments We are also highly obliged and very grateful to respected Dr. Mohammad Saleh Aloboudi, Dean of College of Science, Majmaah University, Alzul…. It has been a privilege and great honor for us to learn with a great man of such prominent characteristics. We love and respect him the most for his high morality and honorable sincerity, his guidance is a ray of light in our research. We express heartiest thanks to Dr. Thamir Shelih Al-Harbi, Dean of Scienti…c research, Majmaah University, KSA who also helped us in publishing the research work in ISI listed journal. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 6 / 48
Abstract Abstract Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 7 / 48
Abstract Abstract This article examines MHD ‡ow and heat transfer through a porous medium over a shrinking surface with suction. The governing partial di¤erential equations of ‡uid motion are converted in to ordinary di¤erential form by using similarity functions. The resulting equations have been solved numerically to observe the e¤ects of physical parameters of this study namely magnetic parameter M 2 , permeability parameter K , suction parameter λ and Prandtl number Pr . Results are presented in graphical form. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 7 / 48
AMS Subject Classi…cation AMS Subject Classi…cation: Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 8 / 48
AMS Subject Classi…cation AMS Subject Classi…cation: [2000] Primary 05C38, 15A15; Secondary 05A15, 15A18 Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 8 / 48
Key Words Classi…cation Key Words: Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 9 / 48
Key Words Classi…cation Key Words: MHD ‡ow, Heat Transfer, Porous medium, Prandtl number, Suction, Shrinking / Stretching surface. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 9 / 48
Publication in ISI listed Journal Research work has been got published in ISI listed Journal: [2] Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 10 / 48
Publication in ISI listed Journal Research work has been got published in ISI listed Journal: [2] Farooq Ahmad, Sajjad Hussain, Ali Mansoor Alanbari and Rakan Saud Alharbi, MHD Flow And Heat Transfer Through A Porous Medium Over A Stretching/Shrinking Surface With Suction, Sci.Int.(Lahore), 27(2), 931-935, 2015. [2] Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 10 / 48
Publication in ISI listed Journal Research work has been got published in ISI listed Journal: [2] Farooq Ahmad, Sajjad Hussain, Ali Mansoor Alanbari and Rakan Saud Alharbi, MHD Flow And Heat Transfer Through A Porous Medium Over A Stretching/Shrinking Surface With Suction, Sci.Int.(Lahore), 27(2), 931-935, 2015. [2] http://sci-int.com/pdf/749916686931-935-Farooq.%20Ahmad- paper%202-MATH%20-%20KSA-.pdf Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 10 / 48
Publication Paper in ISI listed Journal Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 11 / 48
Detail of the Project The project comprises 5 chapters. Chapter 1. This chapter consists of seven sections. The section 1.1 gives the detail of the project and the section 1.2 covers the nomenclature of the project. The section 1.3 covers general terms and concepts, the section 1.4 covers types of the ‡uids and the section 1.5 covers some important de…nitions. The section 1.6 consists objects of the project, and the last section 1.7 shows research publications from the project / research work. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 12 / 48
Detail of the Project The project comprises 5 chapters. Chapter 1. This chapter consists of seven sections. The section 1.1 gives the detail of the project and the section 1.2 covers the nomenclature of the project. The section 1.3 covers general terms and concepts, the section 1.4 covers types of the ‡uids and the section 1.5 covers some important de…nitions. The section 1.6 consists objects of the project, and the last section 1.7 shows research publications from the project / research work. Chapter 2. This chapter covers literature review, it contains some detail research work already done about the MHD ‡ow and heat transfer through a porous medium over a shrinking surface with suction. Ali & Rakan (College of Science Alzul…) Fluids Over Stretcing / Shrinking Sheet 14/07/1436 12 / 48
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