Heat source/sink and Newtonian heating effects on convective micropolar fluid flow over a stretching/shrinking sheet with slip flow model

Heat source/sink and Newtonian heating effects on convective micropolar fluid flow over a stretching/shrinking sheet with slip flow model

Muhammad Kamran

Department of Mathematics and Statistics, Curtin University of Technology, GPO Box U1987, Perth WA 6845 Australia

Corresponding Author Email: 
muhammad.kamran@curtin.edu.au
Page: 
473-482
|
DOI: 
https://doi.org/10.18280/ijht.360212
Received: 
1 November 2017
|
Accepted: 
28 April 2018
|
Published: 
30 June 2018
| Citation

OPEN ACCESS

Abstract: 

The purpose of this study is to analyse the combined effects of the heat generation(source)/ absorption (sink) and Newtonian heating on the mixed convective micropolar fluid flow past over a stretching/shrinking porous sheet. Slip flow model is also taken into account in this investigation. The governing flow behaviour is designed by coupled partial differential equations and then transformed into a system of coupled nonlinear ordinary differential equations with the mixed derivative boundary conditions. A semi-analytical approach named Homotopy Analysis Method (HAM) is applied to solve this transformed system of nonlinear equations. Influences of the pertinent dimensionless parameters on the prescribed velocities and temperature profiles along with the physical quantities are presented in the graphical and tabular illustrations. For special cases, it is found that the obtained solutions are excellent in agreement with the available results. In this study, it is observed that when the sheet stretches or shrinks, the temperature of the micropolar fluid flow increases with an increase in the heat generation and Newtonian heating parameters and it decreases with an increase in the heat absorption parameter and the Prandtl number. This investigation of the heat generation and absorption on the micropolar fluid flow with slip flow effects has shown the useful information which could be helpful for crystal growing in the industry and the processes to polish the artificial heart valves and the internal cavities.

Keywords: 

micropolar fluid, stretching/shrinking sheet, slip flow model, Newtonian heating

1. Introduction
2. Governing Equations
3. Series Solution
4. Results and Discussion
5. Conclusions
Acknowledgement
Nomenclature
  References

[1] Eringen AC. (1964). Simple microfluids. International Journal of Engineering Science 2: 205–217. https://doi.org/10.1016/0020-7225(64)90005-9

[2] Eringen AC. (1965). Theory of micropolar fluids. Purdue University Lafayette in School of Aeronautics and Astronautics, USA, Technical Report 27.

[3] Eringen AC. (1972). Theory of thermomicrofluids. Journal of Mathematical Analysis and Applications 38: 480–496. https://doi.org/10.1016/0022 -247X(72)90106-0

[4] Eringen AC. (2001). Microcontinuum Field Theories: II Fluent Media, Springer-Verlag, New York, Inc.

[5] Lukaszewicz G. (1999). Micropolar Fluids: Theory and Applications. Springer Science & Business Media, New York. https://doi.org/10.1007/978-1-4612-0641-5

[6] Kelson NA, Farrell TW. (2001). Micropolar flow over a porous stretching sheet with strong suction or injection. International Communications of Heat and Mass Transfer 28(4): 479–488. https://doi.org/10.1016/S0735-1933(01)00252-4

[7] Kelson NA, Desseaux A. (2001). Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet. International Journal of Engineering Science 39(16): 1881–1897. https://doi.org/10.1016/S0020-7225(01)00026-X

[8] Bhargava R, Kumar L, Takhar HS. (2003). Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet. International Journal of Engineering Science 41(18): 2161–2178. https://doi.org/10.1016/S0020-7225(03)00209-X

[9] Ahmed SE, Ahmed KH, Mohammed HA, Sivasankaran S. (2014). Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids. Applied Mathematicsand Computation 238: 149–162. https://doi.org/10.1016/j.amc.2014.03.106

[10] Chand R, Rana GC, Hussein AK. (2015). Effect of suspended particles on the onset of thermal convection in a nanofluid layer for more realistic boundary conditions. International Journal of Fluid Mechanics Research 42: 375–390. https://doi.org/10.1615/InterJFluidMechRes.v42.i5.10

[11] Turkyilmazoglu M. (2014). A note on micropolar fluid flow and heat transfer over a porous shrinking sheet. International Journal of Heat and Mass Transfer 72: 388-391. https://doi.org/10.1016/j.ijheatmasstransfer.2014.01.039

[12] Turkyilmazoglu M. (2016). Flow of a micropolar fluid due to a porous stretching sheet and heat transfer. International Journal of Non-Linear Mechanics 83: 59-64. https://doi.org/10.1016/j.ijnonlinmec.2016.04.004

[13] Pal D, Mandal G. (2017). Thermal radiation and MHD effects on boundary layer flow of micropolar nanofluid past a stretching sheet with non-uniform heat source/sink International Journal of Mechanical Sciences 126: 308–318. https://doi.org/10.1016/j.ijmecsci.2016.12.023

[14] Wu L. (2008). A slip model for rarefied gas flows at arbitrary Knudsen number. Applied Physics Letters 93(25): 253103. https://doi.org/10.1063/1.3052923

[15] Burgdorfer A. (1959). The influence of the molecular mean free path on the performance of hydrodynamic gas lubricated bearings. ASME Journal of Basic Engineering 81: 94–100.

[16] Hsia YT, Domoto GA. (1983). An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. Journal of Lubrication Technology 105(1): 120–129. https://doi.org/10.1115/1.3254526

[17] Mitsuya Y. (1993). Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. Journal of Tribology 115(2): 289–289. https://doi.org/10.1115/1.2921004

[18] Fukui S, Kaneko R. (1990). A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems. Journal of Tribology 112(1): 78–83. https://doi.org/10.1115/1.2920234

[19] Fang T, Yao S, Zhang J, Aziz A. (2010). Viscous flow over a shrinking sheet with a second order slip flow model. Communications in Nonlinear Science and Numerical Simulation 15(7): 1831–1842. https://doi.org/10.1016/j.cnsns.2009.07.017

[20] Nandeppanavar MM, Vajravelu K, Abel MS, Siddalingappa MN. (2012). Second order slip flow and heat transfer over a stretching sheet with non-linear Navier boundary condition International Journal of Thermal Sciences 58: 143–150. https://doi.org/10.1016/j.ijthermalsci.2012.02.019

[21] Singh G, Chamkha AJ. (2013). Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet. Ain Shams Engineering Journal 4(4): 911–917. https://doi.org/10.1016/j.asej.2013.02.006

[22] Rosca NC, Pop I. (2013). Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. International Journal of Heat and Mass Transfer 65: 102–109. https://doi.org/10.1016/j.ijheatmasstransfer.2013.05.061

[23] Rosca NC, Pop I. (2014). Boundary layer flow past a permeable shrinking sheet in a micropolar fluid with a second order slip flow model. European Journal of Mechanics-B/Fluids 48: 115–122. https://doi.org/10.1016/j.euromechflu.2014.05.004

[24] Sharma R, Ishak A, Pop I. (2016). Stagnation point flow of a micropolar fluid over a stretching/ shrinking sheet with second-order velocity slip. Journal of Aerospace Engineering 29(5): 04016025. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000616

[25] Ibrahim W. (2017). MHD boundary layer flow and heat transfer of micropolar fluid past a stretching sheet with second-order slip. Journal of the Brazilian Society of Mechanical Sciences and Engineering 39(3): 791–799. https://doi.org/10.1007/s40430-016-0621-8

[26] Kamran, M., Wiwatanapataphee B. (2018). Chemical reaction and Newtonian heating effects on steady convection flow of a micropolar fluid with second order slip at the boundary. European Journal of Mechanics-B/Fluids 71: 138–150. https://doi.org/10.1016/j.euromechflu.2018.04.005

[27] Merkin JH. (1994). Natural-convection boundary-layer flow on a vertical surface with Newtonian heating. International Journal of Heat and Fluid Flow 15(5): 392–398. https://doi.org/10.1016/0142-727X(94)90053-1

[28] Ahmadi G. (1976). Self-similar solution of incompressible micropolar boundary layer flow over a semi-infinite plate. International Journal of Engineering Science 14(7): 639–646. https://doi.org/10.1016/0020-7225(76)90006-9

[29] Liao S. (2003). Beyond perturbation: Introduction to the Homotopy Analysis Method. CRC Press. https://doi.org/10.1201/9780203491164

[30] Narahari M, Kamran M. (2016). MHD natural convection flow past an impulsively started infinite vertical porous plate with Newtonian heating in the presence of radiation. International Journal of Numerical Methods for Heat & Fluid Flow 26(6): 1932–1953. https://doi.org/10.1108/HFF-03-2015-0086