Multiple slip effects on inclined MHD Casson fluid flow over a permeable stretching surface and a melting surface

Multiple slip effects on inclined MHD Casson fluid flow over a permeable stretching surface and a melting surface

Shalini JainAmit Parmar 

Department of Mathematics and Statistics, Manipal University Jaipur, Rajasthan 302026, India

Corresponding Author Email: 
Amit.198631@gmail.com
Page: 
585-594
|
DOI: 
https://doi.org/10.18280/ijht.360222
Received: 
10 August 2017
| |
Accepted: 
14 May 2018
| | Citation

OPEN ACCESS

Abstract: 

In this paper, we have investigated the effects of multiple slip on inclined MHD Casson fluid flow over a permeable stretching surface and a melting surface. We have considered first and second order velocity slip, non-linear radiation, non-uniform heat source and non-linear chemical reaction. The analysis is carried out numerically for the momentum, heat and mass equations by solving the bvp4c MATLAB solver. The physical features of non-dimensional Casson fluid parameter, Schmidt number, Eckert number, variable radiation parameter, porosity parameter, variable heat source parameter, Prandtl number, Skin friction coefficient, local Nusselt number and local Sherwood number of velocity, temperature, volume fraction have been discussed and depicted by the graphs and tables. The θ and ϕ profiles were uplifted with the increment of the β, M and Kp parameters on a suction and melting surface whereas the opposite behavior observed on f’ profiles and the f’ profile and momentum boundary layer thickness was depressed with the increment of the L1 and L2 parameters under a suction and a melting surface whereas the reverse behavior observed on θ and ϕ profiles. The impact of various physical parameters of melting surface and porous surface are obtained and observed that the effect of melting surface is higher than porous surface.

Keywords: 

non-linear radiation, non-linear heat source, melting surface, permeable surface, Casson fluid

1. Introduction
2. Mathematical Formulation
3. Results and Discussion
4. Conclusion
Nomenclature
  References

[1] Animasaun IL. (2015). Effects of thermophoresis, variable viscosity and thermal conductivity on free convective heat and mass transfer of non-darcian MHD dissipative Casson fluid flow with suction and nth order of chemical reaction. Journal of the Nigerian Mathematical Society 34: 11-31.

[2] Megaheda AM. (2015). MHD viscous Casson fluid flow and heat transfer with second-order slip velocity and thermal slip over a permeable stretching sheet in the presence of internal heat generation/absorption and thermal radiation. Eur. Phys. J. Plus 130: 81.

[3] Bala P, Reddy A. (2016). Magneto hydrodynamic flow of a Casson fluid over an exponentially inclined permeable stretching surface with thermal radiation and chemical reaction. Ain Shams Engineering Journal 7: 593-602.

[4] Haq RU, Nadeem S, Akbar NS, Khan ZH. (2013). MHD three dimensional Casson fluid flow past a porous linearly stretching sheet. Alexandria Eng. J. 52(4): 577-582. http://dx.doi.org/10.1016/j.aej.2013.08.005

[5] Hari RK, Harshad RP. (2016). Soret and heat generation effects on MHD Casson fluid flow past an oscillating vertical plate embedded through porous medium. Alexandria Engineering Journal 55: 2125–2137.

[6] Haq RU, Nadeem S, Lee C. (2012). MHD flow of a Casson fluid over an exponentially shrinking sheet. Sci. Iran. 19: 1550-1553.

[7] Mukhopadhyaya S, Moindala IC, Hayat T. (2014). MHD boundary layer flow of Casson fluid passing through an exponentially stretching permeable surface with thermal radiation. Chin. Phys. 23: 104701.

[8] Sandeep N, Raju CSK, Saleem S. (2016). Effects of induced magnetic field and homogeneous–heterogeneous reactions on stagnation flow of a Casson fluid. Engineering Science and Technology, an International Journal 19: 875–887.

[9] Sandeep N, Raju CSK, Sugunamma V, Babu MJ, Reddy JVR. (2015). Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface. Eng. Sci. Technol. Int. J. 19(1): 45-52. http://dx.doi.org/10.1016/j.jestch.2015.05.010

[10] Jain S, Parmar A. (2017). Comparative study of flow and heat transfer behavior of Newtonian and non-Newtonian fluids over a permeable stretching surface. Global and stochastic analysis, SI. pp. 41-50.

[11] Jain S, Parmar A. (2017). Study of radiative heat transfer of nano-Williamson fluid flow through a porous medium. Acta Technica 62(2):137-150. 

[12] Jain S. (2006). Temperature distribution in a viscous fluid flow through a channel bounded by a porous medium and a stretching sheet. J. Rajasthan Acad. Phy. Sci. 4: 477-482.

[13] Jain S, Choudhary R. (2015). Effects of MHD on boundary layer flow in porous medium due to exponentially shrinking sheet with slip. Procedia Engineering 127: 1203-1210.

[14] Jain S, Choudhary R. (2017). Combined Effects of sunction/injection on MHD boundary Layer flow of nanofluid over horizontal permeable cylinder with radiation. Journal of advanced research in Dynamical and Control System 11: 88-98.

[15] Jain S, Bohra S. (2017). Heat and mass transfer over a three-dimensional inclined non-linear stretching sheet with convective boundary conditions. Indian Journal of Pure and Applied Physics 55: 847-856.

[16] Chauhan DS, Vyas P. (1995). Heat transfer in hydromagnetic couette flow of compressible Newtonian fluid. J. of Engng. Mech; ASCE 121(1): 57-61.

[17] Chauhan DS, Gupta S. (1999). Heat transfer in couette flow of a compressible Newtonian fluid through a channel with highly permeable layer at the bottom. AMSE periodicals: Mod. Meas.& Contl. B. 67(2): 37-52.

[18] Parmar A. (2017). MHD Falkner-Skan flow of Casson fluid and heat transfer with variable property past a moving wedge. International Journal of Applied and Computational Mathematics 3(1): 611-629. http://dx.doi.org/10.1007/s40819-017-0373-x 

[19] Parmar A. (2017). Unsteady convective boundary layer flow for MHD Williamson fluid over an inclined porous stretching sheet with non-linear radiation and heat source. International Journal of Applied and Computational Mathematics 3(1): 859-881. http://dx.doi.org/10.1007/s40819-017-0373-4

[20] Sandeep N, Sulochana C, Ashwinkumar GP. (2016). Similarity solution of 3D Casson nanofluid flow over a stretching sheet with convective boundary conditions. Journal of the Nigerian Mathematical Society 35: 128-141.

[21] Bhattacharyya K, Uddin MS, Layek GC. (2016). Exact solution for thermal boundary layer in Casson fluid flow over permeable shrinking sheet with variable wall temperature and thermal radiation. Alexandria Engineering Journal 55: 1703-1712.

[22] Mukhopadhyay S. (2013). Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chin Phys. 22: 7.

[23] Bhattacharya K. (2013). Boundary layer stagnation point flow of Casson fluid and heat transfer towards a shrinking/stretching sheet. Front Heat Mass Transfer 4: 1-9.

[24] Animasaun IL, Adebile EA, Fagbade AI. (2016). Casson fluid flow with variable thermo-physical property along exponentially stretching sheet with suction and exponentially decaying internal heat generation using the homotopy analysis method. J. of the Nigerian Mathematical Society 35: 1-17.

[25] Animasaun IL, Sandeep N, Koriko OK. (2016). modified kinematic viscosity model for 3D-Casson fluid flow within boundary layer formed on a surface at absolute zero. J. Mol. Liq. 221: 1197-1206. http:// dx.doi.org/10.1016/j.molliq.2016.06.049

[26] Hayat T, Shehzad SA, Alsaedi A. (2016). Three-dimensional MHD flow of Casson fluid in porous medium with heat generation. J. Appl. Fluid Mech. 9: 215-223.

[27] Hayat T, Ashraf MB, Shehzad SA, Alsaedi A. (2015). Mixed convection flow of Casson nanofluid over a stretching sheet with convectively heated chemical reaction and heat source/sink. J. Appl. Fluid Mech. 8: 803-813.

[28] Makinde OD, Ibrahim W. (2016). Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition. J. Aerosp. Eng., 29(2): 04015037.

[29] Makinde OD. (2012). Computational modelling of MHD unsteady Flow and heat transfer over a flat plate with Navier slip and Newtonian heating. Braz J Chem Eng. 29(1): 159-66.

[30] Daba M, Devaraj P. (2016). Unsteady hydromagnetic chemically reacting mixed convection flow over a permeable stretching surface with slip and thermal radiation. Journal of the Nigerian Mathematical Society. 35: 245-256.

[31] Nadeem S, Mehmood R, Akbar NS. (2015). Partial slip effect on non-aligned stagnation point nanofluid over a stretching convective surface. Chin. Phys. B 24(1): 1–8. 

[32] Ramesh K, Devakar M. (2015). Some analytical solutions for flows of Casson fluid with slip boundary conditions. Ain Shams Eng. J. 6: 967–975.

[33] Ibrahim W, Shanker B. (2014). Unsteady MHD mixed convective boundary layer slip flow and heat transfer with thermal radiation and viscous dissipation. Heat Transfer - Asian Res. 43(5): 412–26.

[34] Krishnamurthya MR, Prasannakumara BC, Gireesh BJ, Reddy RS. (2016). Effect of chemical reaction on MHD boundary layer flow and melting heat transfer of Williamson Nano fluid in porous medium. Eng. Science and Technology, an Int J. 19: 53–61 2.

[35] Palani S, Kumar BR, Kameswaran PK. (2016). Unsteady MHD flow of an UCM fluid over a stretching surface with higher order chemical reaction. Ain Shams Engg J. 7: 399–408.

[36] Nadeem S, Hussain ST. (2014). Flow and heat transfer analysis of Williamson Nanofluid. Appl Nanosci. 4(8): 1005–1012.

[37] Khan WA, Pop I. (2010). Boundary-layer flow of a Nanofluid past a stretching sheet. Int. J. Heat Mass Transf. 53: 2477-2483.

[38] Gorla RSR., Sidawi I. (1994). Free convection on a vertical stretching surface with suction and blowing. Appl. Sci Res. 52: 247-257.

[39] Wang Y. (1989). Free convection on a vertical stretching surface. J. Appl. Math Mech. 69: 418-420.

[40] Andersson HI, Hansen OR, Holmedal B. (1994). Diffusion of a chemically reactive species from a stretching sheet. Int. J. Heat Mass Trans. 37: 659–64.

[41] Prasad KV, Sujatha A, Vajravelu K., Pop I. (2012). MHD flow and heat transfer of a UCM fluid over a stretching surface with variable thermos-physical properties. Meccanica 47: 1425–39.

[42] Mukhopadhyay S, Golam AM, Wazed AP (2013). Effects of transpiration on unsteady MHD flow of an UCM fluid passing through a stretching surface in the presence of a first order chemical reaction. Chin Phys B. 22: 124701.

[43] Sandeep N, Krishna PM, Reddy JVR, Sugunamma. V. (2016). Dual solutions for unsteady flow of Powell-Eyring fluid past an inclined stretching sheet. J. of Naval Architecture and Marine Eng. 13: 89-99.

[44] Rajani D, Hemalatha K, Madhavi MVDNS. (2017). Effects of higher order chemical reactions and slip boundary conditions on nanofluid flow. Int. J. of Eng. Res. and Application 7(5): 36-45 

[45] Rahman MM, Al-Lawatia M. (2010). Effects of higher order chemical reaction on micropolar fluid flow on a power law permeable stretched sheet with variable concentration in a porous medium. The Canadian J. of Chemical Eng. 88(1): 23-32. http://dx.doi.org/10.1002/cjce.20244

[46] Mallikarjuna B, Bhuvanavijaya R. (2013). Effect of higher order chemical reaction on MHD non-Darcy convective heat and mass transfer over a vertical plate in a rotating system embedded in a fluid saturated porous medium with non-uniform heat source/sink. Proceedings of the 22th National and 11th International ISHMT-ASME Heat and Mass Transfer Conference, pp. 28-31.

[47] Sharma BR, Borgohain D. (2014). Influence of the order of chemical reaction and soret effect on mass transfer of a binary fluid mixture in porous media. Int. J. of Innovative Res. in Sci., Eng. and Technology 3: 7.

[48] Arifuzzaman SM, Rana BMJ, Ahmed R, Ahmmed F. (2017). Cross diffusion and MHD effects on a high order chemically reactive micropolar fluid of naturally convective heat and mass transfer past through an infinite vertical porous medium with a constant heat sink. AIP Conference Proceedings 1851: 020006. https://doi.org/10.1063/1.4984635

[49] Raju CSK, Kumar RVMSSK, Varma SVK., Madak AG, Prasad PD. (2017). Transpiration effects on MHD flow over a stretched cylinder with Cattaneo–Christov heat flux with suction or injection. Arabian J. for Science and Eng. 1–8.

[50] Raju CSK, Priyadarshini P, Ibrahim SM. (2017). Multiple slip and cross diffusion on MHD Carreau–Casson fluid over a slandering sheet with non-uniform heat source/sink. Int. J. of Applied and Computational Mathematics 3(1): 203–224. 

[51] Sivakumar N, Prasad DP, Raju CSK, Varma SVK, Shehzad SA. (2017). Partial slip and dissipation on MHD radiative ferro-fluid over a non-linear permeable convectively heated stretching sheet. Results in Physics 7: 1940-1949.