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

## Main Article Content

## 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 (NH) condition. The problem is modeled 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 microrotaion reduce 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 are 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.

## Article Details

**Thermal Science**, [S.l.], mar. 2017. ISSN 2334-7163. Available at: <http://thermal-science.tech/journal/index.php/thsci/article/view/2119>. Date accessed: 26 sep. 2017. doi: https://doi.org/10.2298/TSCI150221125H.

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Authors retain copyright of the published article and have the right to use the article in the ways permitted to third parties under the - Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence. Full bibliographic information (authors, article title, journal title, volume, issue, pages) about the original publication must be provided and a link must be made to the article's DOI.

The authors and third parties who wish use the article in a way not covered by the the -Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International (CC BY-NC-ND) licence must obtain a written consent of the publisher. This license allows others to download the paper and share it with others as long as they credit the journal, but they cannot change it in any way or use it commercially.

Authors grant to the publisher the right to publish the article, to be cited as its original publisher in case of reuse, and to distribute it in all forms and media.

Accepted 2017-03-13

Published 2017-03-13

## References

(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