**ABSTRACT**

The purpose of this study is to investigate the impact of thermal relaxation time on the mixed convection flow of non-Newtonian micropolar fluid over a continuously stretching sheet of variable thickness in the presence of transverse magnetic field. An innovative and modified form of Fourier’s law, namely, Cattaneo-Christov heat flux is employed in the energy equation to study the characteristics of thermal relaxation time. The governing equations are transformed into ODE, using similarity transformations. Fourth order Runge-Kutta numerical method is used to solve these equations. The effects of relevant parameters such as a micro-rotation parameter, magnetic parameter, thermal relaxation parameter, Prandtl number, surface thickness parameter, and mixed convection parameter, on the physical quantities are graphically presented. Results illustrate that fluid temperature enhances with the rise of thermal relaxation parameter, but it reduces with an increase in micro-rotation parameter. The skin friction decreases with a rise in micro-rotation and micro-element parameters. However, variation in the rate of heat transfer is quite significant for small values of thermal relaxation parameter.

**KEYWORDS**

PAPER SUBMITTED: 2018-12-20

PAPER REVISED: 2019-04-07

PAPER ACCEPTED: 2019-04-11

PUBLISHED ONLINE: 2019-05-12

**THERMAL SCIENCE** YEAR

**2020**, VOLUME

**24**, ISSUE

**1**, PAGES [1345 - 1356]

- Eringen, A. C., Theory of micropolar fluids, Journal of Applied Mathematics and Mechanics, 16 (1966), pp. 1-18
- Hassanien, I. A., Gorla, R. S. R., Heat transfer to a micropolar fluid from a non-isothermal stretching sheet with suction and blowing, Acta Mechanica, 84 (1990), pp. 191-199
- Ishak, A., Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect, Meccanica, 45 (2010), pp. 367-373
- Hussanan, A., et al., Heat and mass transfer in a micropolar fluid with Newtonian heating: an exact analysis, Neural Computing and Applications, 29 (2018), pp. 59-67
- Hussanan, A., et al. Unsteady free convection flow of a micropolar fluid with Newtonian heating: Closed form solution, Thermal Science, 21 (2017), pp. 2313-2326
- Khan, W.A., Rashad, A.M., Combined effects of radiation and chemical reaction on heat and mass transfer by MHD stagnation-point flow of a micropolar fluid towards a stretching surface, Journal of the Nigerian Mathematical Society, 36 (2017), pp. 219-238
- Mishra, S. R., et al., Free convective micropolar fluid flow and heat transfer over a shrinking sheet with heat source, Case Studies in Thermal Engineering, 11 (2018), pp. 113-119
- Ashraf, M., Batool, K., MHD flow and heat transfer of a micropolar fluid over a stretchable disk, Journal of Theoretical and Applied Mechanics, 51 (2013), pp. 25-38
- Khan, W. A., et al., MHD fluid flow and heat transfer of micropolar ferrofluids over a stretching sheet, Journal of Nanofluids, 5 (2016), pp. 567-573
- Khan, Z. H., et al., Dual solutions of MHD boundary layer flow of a micropolar fluid with weak concentration over a stretching/shrinking sheet, Communications in Theoretical Physics, 67 (2017), pp. 449
- Hashemi, H., et al., MHD natural convection of a micropolar nanofluid flowing inside a radiative porous medium under LTNE condition with an elliptical heat source, Journal of Molecular Liquids, 271 (2018), pp. 914-925
- Qasim, M., et al., Heat transfer in a micropolar fluid over a stretching sheet with Newtonian heating, Plos One, 8 (2013), pp. e59393
- Turkyilmazoglu, M., Flow of a micropolar fluid due to a porous stretching sheet and heat transfer, International Journal of Non-Linear Mechanics, 83 (2016), pp. 59-64
- Kocic, M. M., et al., Heat transfer in micropolar fluid flow under the influence of magnetic field, Thermal Science, 20 (2016), pp. S1391-S1404
- Waqas, H., et al., MHD forced convective flow of micropolar fluids past a moving boundary surface with prescribed heat flux and radiation, British Journal of Mathematics & Computer Science, 21 (2017), pp. 1-14
- Hussanan, A., et al., Microstructure and inertial characteristics of a magnetite ferrofluid over a stretching/shrinking sheet using effective thermal conductivity model, Journal of Molecular Liquids, 255 (2018), pp. 64-75
- Khan S. U., et al., Soret and Dufour effects on hydromagnetic flow of Eyring-Powell fluid over oscillatory stretching surface with heat generation/absorption and chemical reaction, Thermal Science, 22 (2018), pp. 533-543
- Khan S. U., et al., Numerical computations on flow and heat transfer of Casson fluid due to oscillatory moving surface, Thermal Science, Doi: doi.org/10.2298/TSCI171130091U.
- Qasim M., et al., Second law analysis of unsteady MHD viscous flow over a horizontal stretching sheet heated non-uniformly in the presence of Ohmic heating: Utilization of Gear-Generalized Differential Quadrature Method, Entropy, 21 (2019), pp. 240(1-25)
- Hussanan, A., et al., MHD flow and heat transfer in a casson fluid over a nonlinearly stretching sheet with Newtonian heating, Heat Transfer Research, 49 (2018), pp. 1185-1198
- Lee, L.L., Boundary layer over a thin needle, Physics of Fluids, 10 (1967), pp. 822-828
- Wang, C.Y., Mixed convection on a vertical needle with heated tip, Physics of Fluids, 2 (1990), pp. 622-625
- Ahmad, S., et al., Mixed convection boundary layer flow along vertical moving thin needles with variable heat flux, Heat and Mass Transfer, 44 (2008), pp. 473-479
- Fang, T., et al., Boundary layer flow over a stretching sheet with variable thickness, Applied Mathematics and Computation, 218 (2012), pp. 7241-7252
- Subhashini, S. V., et al., Dual solutions in a thermal diffusive flow over a stretching sheet with variable thickness, International Communications in Heat and Mass Transfer, 48 (2013), pp. 61-66
- Abdel-wahed, M. S., et al., Flow and heat transfer over a moving surface with non-linear velocity and variable thickness in a nanofluids in the presence of Brownian motion, Applied Mathematics and Computation, 254 (2015), pp. 49-62
- Acharya, N., et al., Ramification of variable thickness on MHD TiO2 and Ag nanofluid flow over a slendering stretching sheet using NDM, The European Physical Journal Plus, 131 (2016), pp. 1-16
- Kumar, R., et al., Radiative heat transfer study for flow of non-Newtonian nanofluid past a Riga plate with variable thickness, Journal of Molecular Liquids, 248 (2017), pp. 143-152
- Prasad, K. V., et al., MHD flow and heat transfer in a nanofluid over a slender elastic sheet with variable thickness, Results in Physics, 7 (2017), pp. 1462-1474
- Liu, L., Liu, F., Boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness, Applied Mathematics Letters, 79 (2018), pp. 92-99
- Cattaneo, C., Sulla conduzione del calore, Atti Semin. Mat. Fis. Univ, Modena Reggio Emilia, 3 (1948), pp. 83-101
- Christov, C. I., On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction, Mechanics Research Communications, 36 (2009), pp. 481-486
- Tibullo, V., Zampoli, V., A uniqueness result for the Cattaneo-Christov heat conduction model applied to incompressible fluids, Mechanics Research Communications, 38 (2011), pp. 77-99
- Mustafa, M., Cattaneo-Christov heat flux model for rotating flow and heat transfer of upper convected Maxwell fluid, AIP Advances, 5 (2015), pp. 047109-1-10
- Rubab, K., Mustafa, M., Cattaneo-Christov heat flux model for MHD three- dimensional flow of Maxwell fluid over a stretching sheet, Plos One, 11 (2016), pp. e0153481
- Reddy, M. G., Influence of Lorentz force, Cattaneo-Christov heat flux and viscous dissipation on the flow of micropolar fluid past a nonlinear convective stretching vertical surface, Nonlinear Engineering, 2017 (2017), pp. 1-10
- Khan S. U., et al., Some generalized results for Maxwell fluid flow over porous oscillatory surface with modified Fourier and Fick's theories, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40 (2018), pp. 474(1-12)
- Kundu, P. R., et al., Framing the Cattaneo-Christov heat flux phenomena on CNT-based Maxwell nanofluid along stretching sheet with multiple slips, Arabian Journal for Science and Engineering, 43 (2018), pp. 1177-1188
- Sharma, S., et al., Magnetic field effect on flow parameters of blood along with magnetic particles in a cylindrical tube, Journal of Magnetism and Magnetic Materials, 377 (2015), pp. 395-401
- Ahmed, N., Dutta, M., Transient mass transfer flow past an impulsively started infinite vertical plate with ramped plate velocity and ramped temperature, International Journal of the Physical Sciences, 8 (2013), pp. 254-263
- Atlas, M., et al., Entropy generation and unsteady Casson fluid flow squeezing between two parallel plates subject to Cattaneo-Christov heat and mass flux, The European Physical Journal Plus, 134 (2019), pp. 1-17
- Afridi, M. I., et al., Entropy generation minimization in mhd boundary layer flow over a slendering stretching sheet in the presence of frictional and Joule heating, Journal of the Korean Physical Society, 73 (2018), pp. 1-7