Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (7): 957-968.doi: https://doi.org/10.1007/s10483-017-2218-6

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Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

T. HAYAT1,2, A. KIRAN1, M. IMTIAZ1, A. ALSAEDI2   

  1. 1. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;
    2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  • 收稿日期:2016-10-25 修回日期:2017-02-23 出版日期:2017-07-01 发布日期:2017-07-01
  • 通讯作者: M. IMTIAZ, E-mail:mi qau@yahoo.com E-mail:mi qau@yahoo.com

Melting heat and thermal radiation effects in stretched flow of an Oldroyd-B fluid

T. HAYAT1,2, A. KIRAN1, M. IMTIAZ1, A. ALSAEDI2   

  1. 1. Department of Mathematics, Quaid-i-Azam University, Islamabad 44000, Pakistan;
    2. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
  • Received:2016-10-25 Revised:2017-02-23 Online:2017-07-01 Published:2017-07-01
  • Contact: M. IMTIAZ E-mail:mi qau@yahoo.com

摘要:

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature, and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.

关键词: nonlinear Galerkin method, Kuramoto-Sivashinsky equation, infinite dimensional dynamical systems, melting heat transfer, magnetohydrodynamic (MHD), Oldroyd-B fluid, thermal radiation, heat generation/absorption, mixed convection

Abstract:

The incompressible flow of a non-Newtonian fluid with mixed convection along a stretching sheet is analyzed. The heat transfer phenomenon is discussed through thermal radiation. The effects of the melting heat transfer and heat generation/absorption are also taken. Suitable transformations are utilized to attain the nonlinear ordinary differential expressions. The convergent series solutions are presented. The fluid flow, temperature, and surface heat transfer rate are examined graphically. It is observed that the velocity decreases when the relaxation time increases while increases when the retardation time is constant. The results also reveal that the temperature distribution reduces when the radiation parameter increases.

Key words: magnetohydrodynamic (MHD), nonlinear Galerkin method, Kuramoto-Sivashinsky equation, infinite dimensional dynamical systems, melting heat transfer, thermal radiation, Oldroyd-B fluid, mixed convection, heat generation/absorption

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