›› 2014, Vol. 23 ›› Issue (7): 74701-074701.doi: 10.1088/1674-1056/23/7/074701

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink

Dinesh Rajotia, R. N. Jat   

  1. Department of Mathematics, University of Rajasthan, Jaipur 302004, India
  • 收稿日期:2013-09-13 修回日期:2013-11-20 出版日期:2014-07-15 发布日期:2014-07-15
  • 基金资助:
    Project supported by the C.S.I.R., India in the form of Junior Research Fellowship (JRF) (Grant No. 09/149(0593) /2011-EMR-I).

Three-dimensional magnetohydrodynamics axisymmetric stagnation flow and heat transfer due to an axisymmetric shrinking/stretching sheet with viscous dissipation and heat source/sink

Dinesh Rajotia, R. N. Jat   

  1. Department of Mathematics, University of Rajasthan, Jaipur 302004, India
  • Received:2013-09-13 Revised:2013-11-20 Online:2014-07-15 Published:2014-07-15
  • Contact: Dinesh Rajotia, R. N. Jat E-mail:rajotia.dinesh@gmail.com;khurkhuria_rnjat@yahoo.com
  • About author:47.15.Cb; 47.65.-d; 44.20.+b
  • Supported by:
    Project supported by the C.S.I.R., India in the form of Junior Research Fellowship (JRF) (Grant No. 09/149(0593) /2011-EMR-I).

摘要: The present work is concerned with the effects of viscous dissipation and heat source/sink on a three-dimensional magnetohydrodynamic boundary layer axisymmetric stagnation flow, and the heat transfer of an electrically conducting fluid over a sheet, which shrinks or stretches axisymmetrically in its own plane where the line of the symmetry of the stagnation flow and that of the shrinking (stretching) sheet are, in general, not aligned. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations and then solved numerically by a shooting technique. This investigation explores the conditions of the non-existence, existence and uniqueness of the solutions of the similar equations numerically. It is noted that the range of the velocity ratio parameter, where the similarity solution exists, is increased with the increase of the value of the magnetic parameter. Furthermore, the study reveals that the non-alignment function affects the shrinking sheet more than the stretching sheet. In addition, the numerical results of the velocity profile, temperature profile, skin-friction coefficient, and rate of heat transfer at the sheet are discussed in detail with different parameters.

关键词: axisymmetric shrinking/stretching sheet, stagnation-point flow, magnetic effect, heat transfer

Abstract: The present work is concerned with the effects of viscous dissipation and heat source/sink on a three-dimensional magnetohydrodynamic boundary layer axisymmetric stagnation flow, and the heat transfer of an electrically conducting fluid over a sheet, which shrinks or stretches axisymmetrically in its own plane where the line of the symmetry of the stagnation flow and that of the shrinking (stretching) sheet are, in general, not aligned. The governing equations are transformed into ordinary differential equations by using suitable similarity transformations and then solved numerically by a shooting technique. This investigation explores the conditions of the non-existence, existence and uniqueness of the solutions of the similar equations numerically. It is noted that the range of the velocity ratio parameter, where the similarity solution exists, is increased with the increase of the value of the magnetic parameter. Furthermore, the study reveals that the non-alignment function affects the shrinking sheet more than the stretching sheet. In addition, the numerical results of the velocity profile, temperature profile, skin-friction coefficient, and rate of heat transfer at the sheet are discussed in detail with different parameters.

Key words: axisymmetric shrinking/stretching sheet, stagnation-point flow, magnetic effect, heat transfer

中图分类号:  (Laminar boundary layers)

  • 47.15.Cb
47.65.-d (Magnetohydrodynamics and electrohydrodynamics) 44.20.+b (Boundary layer heat flow)