On the stability of the flow and heat transfer over a moving thin needle with prescribed surface heat flux |
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| Institution: | 1. Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka, Hang Tuah Jaya, 76100 Durian Tunggal, Melaka, Malaysia;2. School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia;3. Department of Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania;1. Department of Mathematics, Quaid-I-Azam University, 45320, Islamabad 44000, Pakistan;2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80257, Jeddah 21589, Saudi Arabia;3. Department of Mechanical Engineering, Imperial College London, London SW7 2AZ, UK;4. Department of Mechanical Engineering, University of Engineering & Technology Peshawar, Pakistan;5. Department of Mathematics, Riphah International University, Islamabad 44000, Pakistan;1. College of Science, Hunan City University, Yiyang 413000, China;2. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;3. Department of Mathematics and Statistics, Riphah International University I-14, Islamabad 44000, Pakistan;4. Department of Studies and Research in Mathematics, Davangere University, Davangere, Karnataka, India;5. Department of Mathematics, COMSATS Islamabad, Sahiwal 57000, Pakistan;6. CECOS University of IT & Emerging Sciences, Peshawar, Pakistan;7. Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Kingdom of Saudi Arabia;1. Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal 57000, Pakistan;2. Department of Mathematics, COMSATS Institute of Information Technology, Islamabad 44000, Pakistan;3. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan;4. NAAM Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;1. Department of Mathematics & Statistics, Riphah International University, Islamabad, Pakistan.;2. Department of Mathematics, Quaid-I-Azam University, Islamabad 44000, Pakistan |
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| Abstract: | The steady flow and heat transfer over a moving thin needle with prescribed surface heat flux is studied. The similarity equations are obtained by using similarity transformation technique. The problem is solved numerically using the boundary value problem solver (bvp4c) in Matlab software. The plots of the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are presented and their behaviors are discussed for different values of the needle size and the velocity ratio parameter. Results show that the decreasing of the needle size enhance the skin friction coefficient and the local Nusselt number on the needle surface. It is found that dual solutions exist (upper and lower branches) for a certain range of the velocity ratio parameter. A stability analysis of the solutions are performed and it shows that the upper branch solution is stable, while the lower branch solution is unstable. |
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