THERMAL SCIENCE

International Scientific Journal

UNSTEADY FREE CONVECTION FLOW OF A MICROPOLAR FLUID WITH NEWTONIAN HEATING: CLOSED FORM SOLUTION

ABSTRACT
This article investigates the unsteady free convection flow of a micropolar fluid over a vertical plate oscillating in its own plane with Newtonian heating condition. The problem is modelled in terms of partial differential equations with some physical conditions. Closed form solutions in terms of exponential and complementary error functions of Gauss are obtained by using the Laplace transform technique. They satisfy the governing equations and impose boundary and initial conditions. The present solution in the absence of microrotation reduces to well-known solutions of Newtonian fluid. Graphs are plotted to study the effects of various physical parameters on velocity and microrotation. Numerical results for skin friction and wall couple stress is computed in tables. Apart from the engineering point of view, the present article has strong advantage over the published literature as the exact solutions obtained here can be used as a benchmark for comparison with numerical/ approximate solutions and experimental data.
KEYWORDS
PAPER SUBMITTED: 2015-02-21
PAPER REVISED: 2015-07-29
PAPER ACCEPTED: 2015-07-29
PUBLISHED ONLINE: 2015-09-06
DOI REFERENCE: https://doi.org/10.2298/TSCI150221125H
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2017, VOLUME 21, ISSUE Issue 6, PAGES [2313 - 2326]
REFERENCES
  1. Eringen, A. C., Theory of micropolar fluids, Journal of Applied Mathematics and Mechanics, 16 (1966), pp. 1-18
  2. Eringen, A. C., Theory of thermomicropolar fluids, Journal of Mathematical Analysis and Applications, 38 (1972), pp. 480-496
  3. Hsu, P. T., et al., Mixed convection of micropolar fluids along a vertical wavy surface, Acta Mechanica, 144 (2000), pp. 231-247
  4. Damseh, R. A., et al., Unsteady natural convection heat transfer of micropolar fluid over a vertical surface with constant heat flux, Turkish Journal of Engineering and Environmental Sciences, 31 (2007), pp. 225-233
  5. Agarwal, R. S., et al., Numerical solution of flow and heat transfer of a micropolar fluid at a stagnation point on a porous stationary wall, Indian Journal of Pure and Applied Mathematics, 21 (1990), pp. 567-573
  6. Kim, Y. J., Thermal boundary layer flow of a micropolar fluid past a wedge with constant wall temperature, Acta Mechanica, 138 (1999), pp. 113-121
  7. Kim, Y. J., Kim, T. A., Convective micropolar boundary layer flows over a wedge with constant surface heat flux, International Journal of Applied Mechanics and Engineering, 8 (2003), pp. 147- 153
  8. Rahman, M. M., Sultana, Y., Radiative heat transfer flow of micropolar fluid with variable heat flux in a porous medium, Nonlinear Analysis, Modelling and Control, 13 (2008), pp. 71-87
  9. Reddy, M. G., Magnetohydrodynamics and radiation effects on unsteady convection flow of micropolar fluid past a vertical porous plate with variable wall heat flux, ISRN Thermodynamics, 2012 (2012), pp. 1-8
  10. Pal, D., Talukdar, B., Perturbation technique for unsteady MHD mixed convection periodic flow, heat and mass transfer in micropolar fluid with chemical reaction in the presence of thermal radiation, Central European Journal of Physics, 10 (2012), pp. 1150-1167
  11. Bakier, A. Y., Natural convection heat and mass transfer in a micropolar fluid-saturated non-darcy porous regime with radiation and thermophoresis effects, Thermal Science, 15 (2011), pp. 317-326
  12. Rashidi, M. M., et al., A generalized differential transform method for combined free and forced convection flow about inclined surfaces in porous media, Chemical Engineering Communications, 199 (2012), pp. 257-282
  13. Si, X., et al., Flow and heat transfer of a micropolar fluid in a porous channel with expanding or contracting walls, International Journal of Heat and Mass Transfer, 67 (2013), pp. 885-895
  14. Alam, M. S., Hossain, S. M. C., A new similarity approach for an unsteady two-dimensional forced convective flow of a micropolar fluid along a wedge, Journal of Applied Mathematics and Mechanics, 9 (2013), pp. 75-89
  15. Aurangzaib, et al., Unsteady MHD mixed convection flow with heat and mass transfer over a vertical plate in a micropolar fluid-saturated porous medium, Journal of Applied Science and Engineering, 16 (2013), pp. 141-150
  16. Hakiem, M. A. E., Heat transfer from moving surfaces in a micropolar fluid with internal heat generation, Journal of Engineering and Applied Sciences, 1 (2014), pp. 30-36
  17. Rashidi, M. M., et al., Lie group solution for free convective flow of a nanofluid past a chemically reacting horizontal plate in a porous media, Mathematical Problems in Engineering, 2014 (2014), pp. 1-21
  18. Rashidi, M. M., et al., Free convective heat and mass transfer for MHD fluid flow over a permeable vertical stretching sheet in the presence of the radiation and buoyancy effects, Ain Shams Engineering Journal, 5 (2014), pp. 901-912
  19. Ali et al., On combined effect of thermal radiation and viscous dissipation in hydromagnetic micropolar fluid flow between two stretchable disks, Thermal Science, 10.2298/TSCI15032 5096A
  20. Merkin, J. H., Natural convection boundary layer flow on a vertical surface with Newtonian heating, International Journal of Heat and Fluid Flow, 15 (1994), pp. 392-398
  21. Chaudhary, R. C., Jain, P., Unsteady free convection boundary layer flow past an impulsively started vertical surface with Newtonian heating, Romanian Journal of Physics, 51 (2006), pp. 911-925
  22. Mebine, P., Adigio, E. M., Unsteady free convection flow with thermal radiation past a vertical porous plate with Newtonian heating, Turkish Journal of Physics, 33 (2009), pp. 109-119
  23. Narahari, M., Ishak, A., Radiation effects on free convection flow near a moving vertical plate with Newtonian heating, Journal of Applied Sciences, 11 (2011), pp. 1096-1104
  24. Abid, H., et al., Natural convection flow past an oscillating plate with Newtonian heating, Heat Transfer Research, 45 (2014), pp. 119-137
  25. Abid H., et al., Unsteady boundary layer MHD free convection flow in a porous medium with constant mass diffusion and Newtonian heating, The European Physical Journal Plus, 129 (2014), pp. 1-16
  26. Qasim, M., et al., Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating, Plos One, 8 (2013), pp. e59393
  27. Salleh, M. Z., et al., Boundary layer flow and heat transfer over a stretching sheet with Newtonian heating, Journal of the Taiwan Institute of Chemical Engineers, 41 (2010), pp. 651-655
  28. Salleh, M. Z., et al., Forced convection heat transfer over a circular cylinder with Newtonian heating, Journal of Engineering Mathematics, 69 (2011), pp. 101-110
  29. Das, S., et al., Radiation effects on unsteady free convection flow past a vertical plate with Newtonian heating, International Journal of Computer Applications, 41 (2012), pp. 36-41
  30. Kasim, A. R. M., et al., Natural convection boundary layer flow of a viscoelastic fluid on solid sphere with Newtonian heating, World Academy of Science, Engineering and Technology, 64 (2012), pp. 628-633
  31. Uddin, M. J., et al., MHD free convective boundary layer flow of a Nanofluid past a flat vertical plate with Newtonian heating boundary condition, Plos One, 7 (2012), pp. e49499
  32. Sherief, H. H., et al., Exact solution for the unsteady flow of a semi-infinite micropolar fluid, Acta Mechanica Sinica, 27 (2011), pp. 354-359

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence