Double-diffusive mixed convection flow towards a convectively heated stretching sheet with non-linear thermal radiation

Double-diffusive mixed convection flow towards a convectively heated stretching sheet with non-linear thermal radiation

Mrutyunjay Das Bhupesh K. Mahatha Raj Nandkeolyar Subharthi Sarkar 

Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology, Bhubaneswar 751024, India

Department of Applied Science, Jharkhand Rai University, Ranchi 835222, India

Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, India

Corresponding Author Email: 
sarkar.ism@gmail.com
Page: 
1015-1024
|
DOI: 
https://doi.org/10.18280/ijht.360331
Received: 
13 May 2017
| |
Accepted: 
2 May 2018
| | Citation

OPEN ACCESS

Abstract: 

An investigation of two dimensional double-diffusive mixed convective flow of a viscous, incompressible, electrically conducting and optically thick nanofluid over a convectively heated stretching sheet is carried out taking into account the effects of non-linear thermal radiation and partial hydrodynamic slip. A similarity solution to the governing non-linear partial differential equations subject to the boundary conditions is obtained using the efficient Spectral Local Linearization Method (SLLM). In order to study the behavioral changes in flow profiles by various non-dimensional flow parameters, the numerical solution for fluid velocity, fluid temperature, and species concentration are illustrated through figures, and the numerical values of skin friction, Nusselt number and Sherwood number are presented in tables. Nanofluid models of this kind are useful in several engineering processes requiring efficient heat and mass exchange mechanisms like catalytic and nuclear reactors, metal extraction, cooling systems and many more.

Keywords: 

mixed convection, nanofluid flow, nonlinear thermal radiation, convective heat transfer partial slip, Brownian motion, thermophoresis

1. Introduction
2. Formulation of The Problem
3. Numerical Method and Error Analysis
4. Results and Discussion
5. Conclusions
Acknowledgements

Authors are highly thankful to reviewers whose constructive suggestions helped to present the manuscript in its present form.

  References

[1] Crane LJ. (1970). Flow past a stretching plate. Z. Angrew Math Phys 21: 645-647. https://doi.org/10.1007/BF01587695

[2] Choi SUS. (1995). Enhancing thermal conductivity of fluids with nanoparticles. Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA ASME FED 231/MD 66, pp. 99-105.

[3] Kelson NA, Desseaux A. (2001). Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet. Int J Eng. Sci 39: 1881-1897. https://doi.org/10.1016/S0020-7225(01)00026-X

[4] Bhargava R, Kumar L, Takhar HS. (2003). Finite element solution of mixed convection micropolar flow driven by a porous stretching sheet. Int J Eng. Sci 41: 2161-2178. https://doi.org/10.1016/S0020-7225(03)00209-X

[5] Prasad KV, Vajravelu K. (2009). Heat transfer in the MHD flow of a power law fluid over a non-isothermal stretching sheet. Int J Heat Mass Transf. 52: 4956-4965. https://doi.org/10.1016/j.ijheatmasstransfer.2009.05.022

[6] Shaw S, Kameswaran PK, Sibanda P. (2013). Homogeneous-heterogeneous reactions in micropolar fluid flow from a permeable stretching or shrinking sheet in a porous medium. Boundary Value Problems 2013: 77. https://doi.org/10.1186/1687-2770-2013-77

[7] Seth GS, Sharma R, Kumbhakar B, Chamkha AJ. (2016). Hydromagnetic flow of heat absorbing and radiating fluid over exponentially stretching sheet with partial slip and viscous and Joule dissipation. Eng. Computation 33(3): 907-925. https://doi.org/10.1108/EC-05-2015-0122

[8] Das S, Putra N, Thiesen P, Roetzel W. (2003). Temperature dependence of thermal conductivity enhancement for nanofluids. J Heat Transfer 125: 567-574. https://doi.org/10.1115/1.1571080

[9] Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ. (2001). Anomalously increased effective thermal conductivity of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett 78(6): 718-720. https://doi.org/10.1063/1.1341218

[10] Minsta HA, Roy G, Nguyen CT, Doucet D. (2009). New temperature dependent thermal conductivity data for water-based nanofluids. Int J Therm. Sci. 48: 363-371. https://doi.org/10.1016/j.ijthermalsci.2008.03.009

[11]  Buongiorno J. (2006). Convective transport in nanofluids. J. Heat Transfer 128: 240-250. https://doi.org/10.1115/1.2150834

[12] Buongiorno J. (2009). A benchmark study of thermal conductivity of nanofluids. J Appl Phys 106. https://doi.org/10.1063/1.3245330

[13] Nadeem S, Haq RU, Khan ZH. (2014). Heat transfer analysis of water-based nanofluid over an exponentially stretching sheet. Alexandria Eng. J 53: 219-224. https://doi.org/10.1016/j.aej.2013.11.003

[14] Das M, Mahatha BK, Nandkeolyar R. (2015). Mixed convection and nonlinear radiation in the stagnation point nanofluid flow towards a stretching sheet with homogenous-heterogeneous reactions effects. Procedia Engineering 127: 1018-1025. https://doi.org/10.1016/j.proeng.2015.11.451

[15] Nguyen NT, Wereley ST. (2009). Fundamentals and applications of microuidics. Artech house, London.

[16] Li D. (2008.) Encyclopedia of Microuidics and Nanofluidics. Springer USA.

[17] Ramzan M, Bilal M, Chung JD. (2017). Effects of thermal and solutal stratification on Jeffrey magneto-nanofluid along an inclined stretching cylinder with thermal radiation and heat generation/absorption. International Journal of Mechanical Sciences 131: 317-324. https://doi.org/10.1016/j.ijmecsci.2017.07.012

[18] Ramzan M, Yousaf F, Farooq M, Chung JD. (2016). Mixed convective viscoelastic nanofluid flow past a porous media with Soret—DuFour effects. Communications in Theoretical Physics 66(1): 133. https://doi.org/10.1088/0253-6102/66/1/133

[19] Turkyilmazoglu M. (2017). Condensation of laminar film over curved vertical walls using single and two-phase nanofluid models. European Journal of Mechanics-B/Fluids 65: 184-191. https://doi.org/10.1016/j.euromechflu.2017.04.007

[20] Aziz A. (2009). A similarity solution for laminar thermal boundary over a flat plate with a convective boundary condition. Comm Nonlinear Sci and Num Simul 15: 1064-1068. https://doi.org/10.1016/j.cnsns.2008.05.003

[21] Noghrehabadi A, Pourrajab R, Ghalambaz M. (2013a). Flow and heat transfer of nanofluids over stretching sheet taking into account partial slip and thermal convective boundary conditions. Heat Mass Transf. 49: 1357-1366. https://doi.org/10.1007/s00231-013-1179-y

[22] Noghrehabadi A, Saffarian MR, Pourrajab R, Ghalambaz M. (2013b). Entropy analysis for nanofluid flow over a stretching sheet in the presence of heat generation/absorption and partial slip. J Mech Sci Tech 27: 927-937. https://doi.org/10.1007/s12206-013-0104-0

[23] Turkyilmazoglu M. (2016). Magnetic field and slip effects on the flow and heat transfer of stagnation point Jeffrey fluid over deformable surfaces. Zeitschrift für Naturforschung A 71(6): 549-556. https://doi.org/10.1515/zna-2016-0047

[24] Turkyilmazoglu M. (2017). Mixed convection flow of magnetohydrodynamic micropolar fluid due to a porous heated/cooled deformable plate: exact solutions. International Journal of Heat and Mass Transfer 106: 127-134. https://doi.org/10.1016/j.ijheatmasstransfer.2016.10.056

[25] Ramzan M, Bilal M, Farooq U, Chung JD. (2016). Mixed convective radiative flow of second grade nanofluid with convective boundary conditions: An optimal solution. Results in Physics 6: 796-804. https://doi.org/10.1016/j.rinp.2016.10.011

[26] Ramzan M, Bilal M, Chung JD, Mann AB. (2017). On MHD radiative Jeffery nanofluid flow with convective het and MSS boundary conditions. Neural Computing and Applications 1-10. 

[27] Makinde OD, Aziz A. (2011). Boundary layer flow of a nanofluid past a stretching sheet with convective boundary condition. Int J of Therm. Sci 50: 1326-1332. https://doi.org/10.1016/j.ijthermalsci.2011.02.019

[28] Makinde OD, Khan WA, Khan ZH. (2013). Buoyancy effects on MHD stagnation point flow and heat transfer of a nanofluid past a convectively heated stretching/shrinking sheet. Int J Heat Mass Transf. 62: 526-533. https://doi.org/10.1016/j.ijheatmasstransfer.2013.03.049

[29] Bhaskar Reddy N, Poornima T, Sreenivasulu P. (2014). Influence of variable thermal conductivity on MHD boundary layer slip flow of ethyleneglycol based Cu nanofluids over a stretching sheet with convective boundary condition. Int J Eng Math Article ID 905158. http://dx.doi.org/10.1155/2014/905158

[30] Uddin MJ, Khan WA, Ismail AIM. (2012). Scaling group transformation for MHD boundary layer slip flow of a nanofluid over a convectively heated stretching sheet with heat generation. Math Prob in Eng. 20. http://dx.doi.org/10.1155/2012/934964

[31] Mahatha BK, Nandkeolyar R, Nagaraju G, Das M. (2015). MHD stagnation point flow of a nanofluid with velocity slip, non-linear radiation and Newtonian heating. Procedia Eng. 127: 1010-1017. https://doi.org/10.1016/j.proeng.2015.11.450

[32] Ramzan M, Chung JD, Ullah N. (2017). Radiative magnetohydrodynamic nanofluid flow due to gyrotactic microorganisms with chemical reaction and non-linear thermal radiation. International Journal of Mechanical Sciences 130: 31-40. https://doi.org/10.1016/j.ijmecsci.2017.06.009

[33] Ramzan M, Bilal M, Kanwal S, Chung JD. (2017). Effects of variable thermal conductivity and non-linear thermal radiation past an Eyring Powell nanofluid flow with chemical reaction. Communications in Theoretical Physics 67(6): 723. https://doi.org/10.1088/0253-6102/67/6/723

[34] Uddin Md J, Hoque AKMF. (2018). Convective heat transfer flow of nanofluid in an isosceles triangular shaped enclosure with an uneven bottom wall. Chem Eng Trans 66: 403-408. https://doi.org/10.3303/CET1866068

[35] Bubbico R, Celatab GP, D’Annibaleb F, Mazzarottaa B, Menalea C (2015). Comparison of the heat transfer efficiency of nanofluids. Chem Eng Trans 43: 703-708. https://doi.org/10.3303/CET1543118

[36] Motsa SS. (2013). A new spectral local linearization method for nonlinear boundary layer flow problems. J Applied Math 1-15. http://dx.doi.org/10.1155/2013/423628

[37] Trefethen LN. (2000). Spectral Methods in Matlab, SIAM. https://doi.org/10.1137/1.9780898719598