MHD flow of viscoelastic nanofluid over a stretching sheet in a porous medium with heat source and chemical reaction

MHD flow of viscoelastic nanofluid over a stretching sheet in a porous medium with heat source and chemical reaction

Kharabela Swain  Sampada Kumar Parida  Gouranga Charan Dash 

Department of Mathematics, Radhakrishna Institute of Technology and Engineering, Bhubaneswar 752057, India

Department of Mathematics, Siksha ’O’ Anusandhan (Deemed to be University), Bhubaneswar 751030, India

Corresponding Author Email: 
kharabela1983@gmail.com
Page: 
7-21
|
DOI: 
https://doi.org/10.3166/ACSM.42.7-21
Received: 
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Accepted: 
| | Citation

OPEN ACCESS

Abstract: 

The present study investigates the heat and mass transfer of MHD viscoelastic (Walters’ B’ model) nanofluid flow over a stretching sheet embedded in a saturated porous medium subject to thermal slip and temperature jump. A simulation model is established through the analysis on relevant constraints such as stretching of bounding surface keeping the origin fixed and thermal slip and temperature jump on the boundary. The numerical solutions are obtained by Runge-Kutta fourth order method with shooting technique. The affects of important thermo-physical parameters on the velocity, temperature, concentration and surface criteria are displayed and analyzed through graphs and tables. As a result of the analysis, the following observations are made. Elasticity of the base fluid in the presence of nanoparticle acts adversely to the growth of velocity as well as thermal boundary layers. Brownian diffusion, thermophoresis and heat source enhance the fluid temperature resulting the cooling of the stretching surface. Further, positive values of heat and mass fluxes for different values of elastic, magnetic and permeability parameters indicate that heat and mass transfer occur from the stretching surface to the fluid. These recommendations are useful to limit the parameters to design viable heat exchangers

Keywords: 

MHD, viscoelastic, nanofluid, chemical reaction, heat source/sink

1. Introduction
2. Mathematical analysis
3. Skin friction, heat and mass transfer coefficients
4. Method of solution
5. Results and discussion
6. Conclusion
Nomenclature
  References

Abel S., Siddheshwar P. G., Nandeppanavar M. (2007). Heat transfer in a viscoelastic boundary layer flow over a stretching sheet with viscous dissipation and non-uniform heat source. International Journal of Heat and Mass Transfer, Vol. 50, pp. 960-966. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2006.08.010

Buongiorno J. (2006). Convective transport in nanofluids. J. Heat Transfer ASME, Vol. 128, No. 3, pp. 240-250. http://dx.doi.org/10.1115/1.2150834

Carragher P., Crane L. J. (1982). Heat transfer on a continuous stretching sheet. Zeit ANGEW Math. Phys, Vol. 62, pp. 564-565. http://dx.doi.org/10.1002/zamm.19820621009

Crane L. J. (1970). Flow past a stretching plate. Zeit ANGEW Math. Phys, Vol. 21, pp. 645-647. http://dx.doi.org/10.1007/BF01587695

Daniel Y. S. (2015). Presence of heat generation/absorption on boundary layer slip flow of nanofluid over a porous stretching sheet. American Journal of Heat and Mass Transfer, Vol. 2, No. 1, pp. 15-30. http://dx.doi.org/10.7726/ajhmt.2015.1002

Dessie H., Kishan N. (2014). MHD effects on heat transfer over stretching sheet embedded in porous medium with variable viscosity, viscous dissipation and heat source/sink. Ain Shams Engineering Journal, Vol. 5, pp. 967-977. http://dx.doi.org/10.1016/j.asej.2014.03.008

Farooq M., Khan M. I., Waqas M., Hayat T., Khan M. I. (2016). MHD stagnation point flow of viscoelastic nanofluid with non-linear radiation effects. Journal of Molecular Liquids, Vol. 221, pp. 1097-1103. http://dx.doi.org/10.1016/j.molliq.2016.06.077

Hayat T., Awais M., Imtiaz A. (2016). Heat source/sink in a magneto-hydrodynamic non-newtonian fluid flow in a porous medium: Dual solutions. PLoS One, Vol. 11, No. 9, pp. e0162205. http://dx.doi.org/10.1371/journal.pone.0162205

Kar M., Sahoo S. N., Rath P. K., Dash G. C. (2014). Heat and mass transfer effects on a dissipative and radiative visco-elastic MHD flow over a stretching porous sheet. Arabian Journal for Science and Engineering, Vol. 39, No. 5, pp. 3393-3401. http://dx.doi.org/10.1007/s13369-014-0991-0

Khan W. A., Pop I. (2010). Boundary layer flow of a nanofluid past a stretching sheet. Int. J. Heat and Mass Transfer, Vol. 53, pp. 2477-2483. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2010.01.032

Nandy S. K., Pop I. (2014). Effects of magnetic field and thermal radiation on stagnation flow and heat transfer of nanofluid over a shrinking surface. International Communications in Heat and Mass Transfer, Vol. 53, pp. 50–55. http://dx.doi.org/10.1016/j.icheatmasstransfer.2014.02.010

Nayak M. K., Dash G. C., Singh L. P. (2016). Heat and mass transfer effects on MHD viscoelastic fluid over a stretching sheet through porous medium in presence of chemical reaction. Propulsion and Power Research, Vol. 5, No. 1, pp. 70-80. http://dx.doi.org/10.1016/j.jppr.2016.01.006

Nield D. A., Kuznetsov A. V. (2009). Thermal instability in a porous medium layer saturated by a nanofluid. International Journal of Heat and Mass Transfer, Vol. 52, pp. 5796-5801. http://dx.doi.org/10.1016/j.ijheatmasstransfer.2009.07.023

Popoola A., Ismail G. B., Olajuwon B. (2016). Heat and mass transfer on MHD Viscoelastic fluid flow in the presence of thermal diffusion and chemical reaction. International Journal of Heat and Technology, Vol. 34, No. 1, pp. 15-26. http://dx.doi.org/10.18280/ijht.340103

Rajagopal K. R., Na T. Y., Gupta A. S. (1987). A non similar boundary layer on a stretching sheet in a non-Newtonian fluid with uniform free stream. J. Math. Phys. Sci., Vol. 21, No. 2, pp. 189-200.

Rashidi M. M., Ali M., Rostami B., Rostami P., Xie G. (2015). Heat and mass transfer for MHD viscoelastic fluid flow over a vertical stretching sheet with considering Soret and Dufour effects. Mathematical Problems in Engineering, Vol. 2015, Article ID 861065. http://dx.doi.org/10.1155/2015/861065

Reddy M. G., Padma P., Shankar B. (2015). Effects of viscous dissipation and heat source on unsteady MHD flow over a stretching sheet. Ain Shams Engineering Journal, Vol. 6, pp. 1195-1201.

Rout P. K., Sahoo S. N., Dash G. C., Mishra S. R. (2016). Chemical reaction effect on MHD free convection flow in a micropolar fluid. Alexandria Engineering Journal, Vol. 55, pp. 2967-2973. http://dx.doi.org/10.1016/j.aej.2016.04.033

Sakiadis B. C. (1961). Boundary layer behaviours on continuous solid surface. AIChE J, Vol. 7, No. 2, pp. 221-5.

Tripathy R., Mishra S. R., Dash G. C. (2016). Numerical analysis of hydromagnetic micropolar fluid along a stretching sheet embedded in porous medium with non-uniform heat source and chemical reaction. Engineering Science and Technology, an International Journal, Vol. 19, No. 3, pp. 1573-1581. http://dx.doi.org/10.1016/j.jestch.2016.05.012