Examining the behavior of MHD micropolar fluid over curved stretching surface based on the modified Fourier law

Document Type : Article

Authors

1 Department of Mathematics and Statistics, International Islamic University, Islamabad, 44000, Pakistan

2 Department of Mathematics, FBAS, Air University, Islamabad, Pakistan

Abstract

The present study describes MHD micropolar fluid as a result of curved stretching surface with Cattaneo-Christov theory of heat diffusion. The new heat model with the relaxation time is employed in this paper, in spite of classical theory of heat flux presented by Fourier. The curvilinear coordinates are used to model the governing equations. The nonlinear PDE’s are changed into ODE’s by using suitable transformation. The nonlinear ODE’s are solved with the help of OHAM by using BVPh2. The variation of several parameters are indicated and examined graphically. We observed that the pressure and velocity rises by enhancing the radius of curvature.

Keywords


References:
1. Fourier, J.B.J., Analytical Theory of Heat, F. Didot (1822).
2. Cattaneo, C. "Sulla conduzione del calore", Atti Sem. Mat. Fis. Univ. Modena, 3, pp. 83-101 (1948).
3. Christov, C.I. "On frame indi erent formulation of the Maxwell-Cattaneo model of nite-speed heat conduction", Mechanics Research Communications, 36(4), pp. 481-486 (2009).
4. Ciarletta, M. and Straughan, B. "Uniqueness and structural stability for the Cattaneo-Christov equations", Mechanics Research Communications, 37(5), pp. 445-447 (2010).
5. Ostoja-Starzewski, M. "A derivation of the Maxwell- Cattaneo equation from the free energy and dissipation potentials", International Journal of Engineering Science, 47(7-8), pp. 807-810 (2009).
6. Shahid, A., Bhatti, M.M., Beg, O.A., and Kadir, A. "Numerical study of radiative Maxwell viscoelastic magnetized ow from a stretching permeable sheet with the Cattaneo-Christov heat flux model", Neural Computing and Applications, 30, pp. 3467-3478 (2018). https://doi.org/10.1007/s00521-017-2933-8.
7. Alamri, S.Z., Khan A.A., Azeez, M., and Ellahi, R. "Effect of mass transfer on MHD second grade fluid towards stretching cylinder: A novel perspective of Cattaneo-Christov heat flux model", Physics Letter A, 383, pp. 276-281 (2019).
8. Eringen, A.C. "Theory of micropolar fluids", Journal of Mathematics and Mechanics, 16(1), pp. 1-18 (1966).
9. Je ery, G.B. "The motion of ellipsoidal particles immersed in a viscous fluid", Proc. R. Soc. Lond. A, 102(715), pp. 161-179 (1922).
10. Ericksen, J.L. "Anisotropic fluids", Arch. Ration. Mech. Anal, 4(1), pp. 231-237 (1960).
11. Crane, L.J. "Flow past a stretching plate", Zeitschrift fur Angewandte Mathematik und Physik ZAMP, 21(4), pp. 645-647 (1970).
12. Wang, C.Y. "The three-dimensional ow due to a stretching at surface", AIP Phys. Fluid, 27, pp. 1915- 1917 (1984).
13. Waqas, M., Farooq, M., Khan, M.I., Alsaedi, A., Hayat, T., and Yasmeen, T. "Magnetohydrodynamic (MHD) mixed convection flow of micropolar liquid due to nonlinear stretched sheet with convective condition", International Journal of Heat and Mass Transfer, 102, pp. 766-772 (2016).
14. Khan, W.A. and Pop, I. "Boundary-layer flow of a nano fluid past a stretching sheet", Int. J. Heat Mass Transf., 53, pp. 2477-2483 (2010).
15. Khan, A.A., Bukhari, S.R., and Marin, M. "Effect of chemical reaction on third grade MHD fluid flow under the influence of heat and mass transfer with variable reactive index", Heat Transfer Research, 50(11), pp. 1061-1080 (2019).
16. Turkyilmazoglu, M. "Dual and triple solution for MHD skip flow of non-Newtonian uid over a shrinking surface", Comp & Fluid, 70, pp. 53-58 (2012).
17. Hayat, T. and Qasim, M. "Effect of thermal radiation on unsteady magnetohydrodynamic flow of micropolar fluid with heat and mass transfer", Naturforsch, 65(a), pp. 950-960 (2010).
18. Turkyilmazoglu, M. "Flow of a micropolar uid due to a porous stretching sheet and heat transfer", International Journal of Non-Linear Mechanics, 83, pp. 59-64(2016).
19. Keimanesh, R. and Aghanaja , C. "Analysis of radiation heat transfer of a micropolar uid with variable properties over a stretching sheet in the presence of magnetic field", J. Heat Mass Transf., 1, pp. 9-19 (2016).
20. Saleh, S.H.M., Ari n, N.M., Nazar, R., and Pop, I. "Unsteady micropolar uid over a permeable curved stretching shrinking surface", Mathematical Problems in Engineering, 2017, pp. 1-12 (2017).https://doi.org/10.1155/2017/3085249.
21. Turkyilmazoglu, M. "Latitudinally deforming rotating sphere", Applied Mathematical Modelling, 71, pp. 1-11 (2019).
22. Turkyilmazoglu, M. "Convergence accelerating in the homotopy analysis method: A new approach", Advances in Applied Mathematics and Mechanics, 10(4), pp. 925-947 (2018).
23. Naveed, M., Abbas, Z., and Sajid, M. "MHD flow of micropolar fluid due to a curved stretching sheet with thermal radiation", Journal of Applied fluid Mechan- ics, 9(1), pp. 131-138 (2016).
Volume 28, Issue 1
Transactions on Mechanical Engineering (B)
January and February 2021
Pages 223-230
  • Receive Date: 24 July 2018
  • Revise Date: 30 June 2019
  • Accept Date: 12 October 2019