Chemical Reaction and Radiation Effects on Non-Newtonian Fluid Flow over a Stretching Sheet with Non-Uniform Thickness and Heat Source

Abstract:

The principle priority of this study is to inspect the performance of two dimensional chemically reacting non-Newtonian fluid bearing Soret, Dufour, thermal radiation, heat source and slip effects. The flow is prompted by a slendering surface with variable thickness. Casson and Williamson fluid models are incorporated in this discussion. Governing equations are evolved and converted into ordinary differential equations using similarity transformations. We adopted homotopy analysis method (HAM) to pick up the solutions. The graphical and tabular results for velocity, temperature, concentration, skin friction factor, local Nusselt number and Sherwood number are secured for both Casson and Williamson fluids. The correspondence between the acquired and previous results reveals that they are in good correlation. It is found that there is a significant increase in the thermal boundary layer thickness when the strength of the Dufour number is increased.

• Periodical: Defect and Diffusion Forum (Volume 387)
• Pages: 319-331
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.387.319
• Online since: September 2018
• Authors: S. Mohammed Ibrahim*, Prathi Vijaya Kumar, Oluwole Daniel Makinde
• Keywords: Casson Fluid, Chemical Reaction, Dufour Effects, HAM, Heat Source, Soret Effect, Stretching Sheet, Thermal Radiation, Williamson Fluid

References

[1] N. Casson, A flow equation for pigment oil suspensions of the printing ink type. In: Mill CC, Rheology of Disperse Systems, Pergamon press, New York, (1959) 84-104.

[2] R. K. Dash, K. N. Mehta, G. Jayaraman, Casson fluid flow in a pipe filled with a homogeneous porous medium, International Journal of Engineering Science, 34(10) (1996) 1145-1156.

DOI: 10.1016/0020-7225(96)00012-2

[3] R. K. Dash, K. N. Mehta, G. Jayaraman, Effect of yield stress on the flow of a Casson fluid in a homogeneous porous medium bounded by a circular tube, Applied Scientific Research, 57(2) (196) 133-149.

DOI: 10.1007/bf02529440

[4] C. S. K. Raju, N. Sandeep, V. Sugunamma, M. Jayachandra Babu, J. V. Ramana Reddy, Heat and mass transfer in magnetohydrodynamic Casson fluid over an exponentially permeable stretching surface, Engineering Science and Technology, an International Journal, 19(1) (2016).

DOI: 10.1016/j.jestch.2015.05.010

[5] M. G. Reddy, B.C. Prasannakumara, O. D. Makinde, Cross diffusion impacts on hydromagnetic radiative peristaltic Carreau-Casson nanofluids flow in an irregular channel, Defect and Diffusion Forum, 377 (2017) 62-83.

DOI: 10.4028/www.scientific.net/ddf.377.62

[6] A. J. Benazir, R. Sivaraj, O. D. Makinde, Unsteady magnetohydrodynamic Casson fluid flow over a vertical cone and flat plate with non-uniform heat source/sink, International Journal of Engineering Research in Africa, 21 (2016) 69-83.

DOI: 10.4028/www.scientific.net/jera.21.69

[7] W. Ibrahim, O. D. Makinde, Magnetohydrodynamic stagnation point flow and heat transfer of Casson nanofluid past a stretching sheet with slip and convective boundary condition, Journal of Aerospace Engineering, 29(2) (2016) Article # 04015037.

DOI: 10.1061/(asce)as.1943-5525.0000529

[8] I. Ullah, S. Shafie, O. D. Makinde, I. Khan, Unsteady MHD Falkner-Skan flow of Casson nanofluid with generative/destructive chemical reaction, Chemical Engineering Science, 172 (2017) 694–706.

DOI: 10.1016/j.ces.2017.07.011

[9] A. S. Eegunjobi, O. D. Makinde, MHD mixed convection slip flow of radiating Casson fluid with entropy generation in a channel filled with porous media. Defect and Diffusion Forum, 374 (2017) 47-66.

DOI: 10.4028/www.scientific.net/ddf.374.47

[10] R. V. Williamson, The flow of pseudoplastic materials, Industrial & Engineering Chemistry, 21(11) (1929) 1108-1111.

DOI: 10.1021/ie50239a035

[11] S. Nadeem, S. T. Hussian, Heat transfer analysis of Williamson fluid over exponentially stretching surface, Applied Mathematics and Mechanics, 35 (2014) 489-502.

DOI: 10.1007/s10483-014-1807-6

[12] S. Nadeem, S. T. Hussain, C. Lee, Flow of a Williamson fluid over a stretching sheet, Brazilian Journal of Chemical Engineering, 30 (2013) 619-625.

DOI: 10.1590/s0104-66322013000300019

[13] M. Y. Malik, T. Salahuddin, Numerical solution of MHD stagnation point flow of Williamson fluid model over a stretching cylinder, International Journal of Nonlinear Sciences and Numerical Simulation, 16 (2015) 161-164.

DOI: 10.1515/ijnsns-2014-0035

[14] F. Mabood, S. M. Ibrahim, G. Lorenzini, E. Lorenzini, Radiation effects on Williamson nanofluid flow over a heated surface with magnetohydrodynamics, International Journal of Heat and Technology, 35(1) (2017) 196-204.

DOI: 10.18280/ijht.350126

[15] T. Hayat, U. Khalid, M. Qasim, Steady flow of a Williamson fluid past a porous plate, Asia-Pacific Journal of Chemical Engineering, 7(2) (2012) 302-306.

DOI: 10.1002/apj.496

[16] A. Zaib, K. Bhattacharyya, M. Khalid, S. Shafie, Thermal radiation effect on a mixed convection flow and heat transfer of the Williamson fluid past an exponentially shrinking permeable sheet with a convective boundary condition, Journal of Applied Mechanics and Technical Physics, 58 (2017).

DOI: 10.1134/s0021894417030063

[17] O. E. Tewfik, E. R. G. Eckert, L. S. Jurewicz, Diffusion-thermo effects on heat transfer from a cylinder in cross flow, AIAA Journal, 1 (1963) 1537-1543.

DOI: 10.2514/3.1852

[18] A. Postelnicu, Influence of a magnetic field on heat and mass transfer by natural convection from vertical surfaces in porous media considering Soret and Dufour effects, International Journal of Heat and Mass Transfer, 47 (2004) 1467-1472.

DOI: 10.1016/j.ijheatmasstransfer.2003.09.017

[19] O. D. Makinde, On MHD mixed convection with Soret and Dufour effects past a vertical plate embedded in a porous medium, Latin American Applied Research, 41 (2011) 63-68.

DOI: 10.15373/2249555x/june2013/133

[20] O. D. Makinde, P. O. Olanrewaju, Unsteady mixed convection with Soret and Dufour effects past a porous plate moving through a binary mixture of chemically reacting fluid, Chemical Engineering Communications, 198(7) (2011) 920-938.

DOI: 10.1080/00986445.2011.545296

[21] G. Sreedevi, D. R. V. Prasada Rao, O. D. Makinde, G. V. Ramana Reddy, Soret and Dufour effects on MHD flow with heat and mass transfer past a permeable stretching sheet in presence of thermal radiation, Indian Journal of Pure & Applied Physics, 55 (8) (2017).

DOI: 10.1002/htj.21723

[22] [P. O. Olanrewaju, O. D. Makinde, Effects of thermal diffusion and diffusion thermo on chemically reacting MHD boundary layer flow of heat and mass transfer past a moving vertical plate with suction /injection, Arabian Journal of Science and Engineering, 36 (2011).

DOI: 10.1007/s13369-011-0143-8

[23] Y. Wang, Analysis of viscous flow due to a stretching sheet with surface slip and suction, Nonlinear Analysis: Real world Applications. 10(1) (2009) 375-380.

DOI: 10.1016/j.nonrwa.2007.09.013

[24] M. C. Kemparaju, M. S. Abel, M. Mahantesh, Heat transfer in MHD flow over a stretching sheet with velocity and thermal slip condition, Advances in Physics, 49 (2015) 25-33.

[25] L. Lee, Boundary layer flow over a thin layer, Physics of Fluids, 10 (1967) 820-822.

[26] M. J. Babu, N. Sandeep, MHD non-Newtonian fluid flow over a slendering stretching sheet in the presence of cross diffusion effects, Alexandria Engineering Journal, 55 (2016) 2193-2201.

DOI: 10.1016/j.aej.2016.06.009

[27] S. J. Liao, Homotopy analysis method in nonlinear differential equations, Springer & Higher Education Press, Heidelberg, (2012).

[28] S. M. Ibrahim, G. Lorenzini, P. V. Kumar, C. S. K. Raju, Influence of chemical reaction and heat source on dissipative MHD mixed convection flow of a Casson nanofluid over a nonlinear permeable stretching sheet, International Journal of Heat and Mass Transfer, 111 (2017).

DOI: 10.1016/j.ijheatmasstransfer.2017.03.097

[29] M. Sajid, Homotopy analysis of stretching flows with partial slip, International Journal of Nonlinear Science, 8 (2009) 284-290.

[30] S. M. Ibrahim, P. V. Kumar, G. Lorenzini, E. Lorenzini, F. Mabood, Numerical study of the onset of chemical reaction and heat source on dissipative mhd stagnation point flow of Casson nanofluid over a nonlinear stretching sheet with velocity slip and convective boundary conditions, Journal of Engineering Thermophysics, 26 (2017).

DOI: 10.1134/s1810232817020096

[31] M. M. Khader, A. M. Megahed, Numerical solution for boundary layer flow due to a nonlinearly stretching sheet with variable thickness and slip velocity, The European Physical Journal Plus, 128 (2013) 100-108.

DOI: 10.1140/epjp/i2013-13100-7

[32] C. S. Reddy, K. Naikoti, M. M. Rashid, MHD flow and heat transfer characteristics of Williamson nanofluid over a stretching sheet with variable thickness and variable thermal conductivity, Transactions of A. Razmadze Mathematical Institute, 171 (2017).

DOI: 10.1016/j.trmi.2017.02.004