Swirling Flow of an Oldroyd-B Fluid over a Rotating Disk

Abstract

n the name of ALLAH, the Most Glorious and the Most Merciful Lord, the creator and all praises to ALLAH who guide me in darkness, helps me in troubles and empowers me to view tentative blocks as stepping stones to the stars to reach the eventual stage with courage. I am nothing without my ALLAH but I can achieve everything with assistance. All of my reverence and commitment goes to our Prophet Hazrat Muhammad SAWW the source of humanity, kindness and guidance for the whole creatures and who advised the mankind to pursue knowledge from cradle to grave. First and foremost I would like to express my special appreciation and thanks to my PhD advisor Prof. Dr. Masood Khan, you have been a tremendous mentor for me. I would like to thank you for encouraging my research and for allowing me to grow as a research scientist. Your advice on both research as well as on my career have been invaluable. In short, your tireless work, unique way of research and devotion to your profession cannot be expressed in words. I would like to thank my mother and father, whose love, prayers and guidance are with me to follow my dreams. I am very thankful to my loving parents for their guidance, support and encouragement. I owe my heartiest gratitude for their assistance and never ending prayers for success. I highly commend the cooperative behavior of my brothers and sisters who endeavored for my edification and betterment. I gratefully acknowledge the Department of Mathematics, Quaid-i-Azam university Islamabad for this wonderful facilitation sources that made my PhD work possible. My sincere thanks also goes to chairman Department of Mathematics, Prof. Dr. Tariq Shah, who provide me the opportunity for this milestone achievement. I thank my fellow labmates in for the stimulating discussions, for the sleepless nights we were working together, and for all the fun we have had in the last four years. A very special thank you to Dr. Jawad Ahmed for his invaluable advice and feedback on my research and for always being so supportive of my work. My time at Quaid-i-Azam University was also enriched by the graduates and fellows Dr. Awais Ahmed, Dr. Zahoor Iqbal, Dr. Aamir Hamid, Mahnoor Sarfraz, Muhammad Yasir. In the end I would like to thank to all my research fellows and to those people who directly and indirectly helped me during my research work.