International Journal of Nonlinear Analysis and Applications

Viscous dissipation and thermal radiation effects on the flow of Maxwell nanofluid over a stretching surface

Document Type : Research Paper

Authors

1 Department of Humanities and Sciences(Mathematics), CVR College of Engineering, Hyderabad, Telangana State, India

2 Department of Mathematics, GITAM University, Hyderabad, Telangana State, India

3 Department of Humanities and Sciences(Mathematics), CVR College of Engineering, Hyderabad,Telangana State, India.

Abstract

An analysis is made to examine the viscous dissipation and thermal effects on magneto hydrodynamic mixed convection stagnation point flow of Maxwell nanofluid passing over a stretching surface. The governing partial differential equations are transformed into a system of ordinary differential equations by utilizing similarity transformations. An effective shooting technique of Newton is utilize to solve the obtained ordinary differential equations. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. The effects of sundry parameters on the velocity, temperature and concentration distributions are examined and presented in the graphical form. These non-dimensional parameters are the velocity ratio parameter $(A)$, Biot number $(Bi$), Lewis number $(Le)$, magnetic parameter $(M)$, heat generation/absorption coefficients $\left(A^*,B^*\right)$, visco-elastic parameters $\left(\beta\right)$, Prandtl number $(Pr)$, Brownian motion parameter $(Nb)$,  Eckert number $\left(Ec\right)$, Radiation parameter $\left(R\right)$ and local Grashof number $(Gc;\ Gr).$
An analysis is made to examine the viscous dissipation and thermal effects on magneto hydrodynamic mixed convection stagnation point flow of Maxwell nanofluid passing over a stretching surface. The governing partial differential equations are transformed into a system of ordinary differential equations by utilizing similarity transformations. An effective shooting technique of Newton is utilize to solve the obtained ordinary differential equations. Furthermore, we compared our results with the existing results for especial cases. which are in an excellent agreement. The effects of sundry parameters on the velocity, temperature and concentration distributions are examined and presented in the graphical form. These non-dimensional parameters are the velocity ratio parameter $(A)$, Biot number $(Bi$), Lewis number $(Le)$, magnetic parameter $(M)$, heat generation/absorption coefficients $\left(A^*,B^*\right)$, visco-elastic parameters $\left(\beta\right)$, Prandtl number $(Pr)$, Brownian motion parameter $(Nb)$,  Eckert number $\left(Ec\right)$, Radiation parameter $\left(R\right)$ and local Grashof number $(Gc;\ Gr).$

Keywords

[1] S. U. S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, ASME-Publications-Fed. 231 (1995)
99–106.
[2] J. Buongiorno, Convective transport in nanofluids, J. Heat Trans. 128 (3) (2006) 240–250.
[3] A. V. Kuznetsov and D. A. Nield, Natural convective boundary-layer flow of a nanofluid past a vertical plate, Int.
J. Thermal Sci. 49(2) (2010) 243–247.
[4] W. A. Khan and I. Pop, Flow and heat transfer over a continuously moving at plate in a porous medium, J. Heat
Trans. 133(5) (2011) 054501.
[5] L. Zheng, C. Zhang, X. Zhang, and J. Zhang, Flow and radiation heat transfer of a nanofluid over a stretching
sheet with velocity slip and temperature jump in porous medium, J. Franklin Inst. 350(5) (2013) 990–1007.
[6] H. S. Takhar, R. S. R. Gorla, and V. M. Soundalgekar, Short communication radiation effects on MHD free
convection flow of a gas past a semi-infinite vertical plate, Int. J. Numerical Meth. Heat Fluid Flow, 6(2) (1996)
77–83.
[7] A. Y. Ghaly and M. E. E. Elsayed, Radiation effect on MHD free-convection flow of a gas at a stretching surface
with a uniform free stream, J. Appl. Math. 2(2) (2002) 93-103.
[8] S. P. A. Devi and M. Kayalvizhi, Analytical solution of MHD flow with radiation over a stretching sheet embedded
in a porous medium, Int. J. Appl. Math. Mech. 6(7) (2010) 82-106.
[9] O. D. Makinde, W. A. Khan, and Z. H. Khan. Buoyancy effects on MHD stagnation point flow and heat transfer
of a nanofluid past a convectively heated stretching/shrinking sheet, Int. J. Heat Mass Trans.62 (2013) 526–533.
[10] H. I. Andersson, MHD flow of a viscoelastic fluid past a stretching surface, Acta Mech. 5(1) (1992) 227–230.
[11] M. I. Char, Heat and mass transfer in a hydromagnetic flow of the viscoelastic fluid over a stretching sheet, J.
Math. Anal. Appl. 186(3) (1994) 674–689.
[12] H. Markovitz and B. D. Coleman, Incompressible second-order fluids, Adv. Appl. Mech. 8 (1964) 69–101.
[13] K. R. Rajagopal, A note on unsteady unidirectional flows of a non-newtonian fluid, Int. J. Non-Linear Mech.
17(5-6) (1982) 369–373.
[14] K. R. Rajagopal and A. S. Gupta. An exact solution for the flow of a non-newtonian fluid past an infinite porous
plate, Mecc. 19(2) (1984) 158–160.
[15] A. M. Siddiqui, P. N. Kaloni and O. P. Chandna, Hodograph transformation methods in non-Newtonian fluids, J.
Engin. Math. 19(3) (1985) 203–216.
[16] A. M. Siddiqui and P. N. Kaloni, Certain inverse solutions of a non-newtonian fluid, Int. J. Non-linear Mech.
21(6) (1986) 459–473.
[17] O. P. Chandna and P. V. Nguyen, Hodograph method in non-Newtonian MHD transverse fluid flows, J. Engin.
Math. 23(2) (1989) 119–139.
[18] P. V. Nguyen and O. P. Chandna, Non-Newtonian MHD orthogonal steady plane fluid flows, Int. J. Engin. Sci.
30(4) (1992) 443–453.
[19] R. Cortell, Heat transfer in a fluid through a porous medium over a permeable stretching surface with thermal
radiation and variable thermal conductivity, Canadian J. Chemical Engin. 90(5) (2012) 1347–1355.[20] D. P. Bhatta, S. R. Mishra and J. K. Dash, Unsteady squeezing flow of water-based nanofluid between two parallel
disks with slip effects: Analytical approach, Heat Trans. Asian Res. 48(5) (2019) 1575–1594.
[21] M. Farooq, S. Ahmad, M. Javed and A. Anjum, Melting heat transfer in squeezed nanofluid flow through Darcy
Forchheimer medium, J. Heat Trans. 141(1) (2019) 012402.
[22] M. Gholinia, K. Hosseinzadeh, H. Mehrzadi, D. Ganji and A. Ranjbar, Investigation of MHD Eyring Powell fluid
flow over a rotating disk under effect of homogeneous-heterogeneous reactions, Case Stud. Thermal Engin. 13
(2019) 100356.
[23] G.Narender, G.Sreedhar Sarma and K.Govardhan, Heat and Mass Transfer of a nanofluid over a stretching sheet
with viscous dissipation effect, J. Heat Mass Trans. Res. 6(2) (2019) 117–124.
[24] W. Ibrahim and R. U. Haq. Magnetohydrodynamic (MHD) stagnation point flow of nanofluid past a stretching
sheet with convective boundary condition, J. Brazilian Soc. Mech. Sci. Engin. 38(4) (2016) 1155–1164.
International Journal of Nonlinear Analysis and Applications
Volume 12, Issue 2
November 2021
Pages 1267-1287
  • Receive Date: 17 October 2019
  • Revise Date: 14 March 2020
  • Accept Date: 24 March 2020