Boundary layer flow of MHD Williamson nano fluid flow over a curved stretching surface
Keywords:
Williamson fluid, MHD, FEM, curved stretching sheet and nanofluid.
Abstract
This study explores the effects of heat and mass transfer on the Williamson nanofluid over a porous exponentially curved stretching sheet is discussed. This analysis is carried out subject to the Brownian motion and thermophoresis. The highly nonlinear partial differential equations are converted into nonlinear ordinary differential equations using similarity transformations and finally solved with the help of finite element method. The results are obtained and good agreement with previous published results of the same nature in the limiting case. The effects of prominent physical parameters like, magnetic field parameter, Brownian motion parameter, thermophoresis parameter, Williamson fluid parameter, Prandtl number and Schmidt number on velocity, temperature and concentration is displayed by using graphs. Numerical results of skin-friction coefficient, Nusselt and Sherwood numbers are systematized in the form of tables.
References
[1] Sakiadis BC. Boundary layer behaviour on continuous solid surfaces: Boundary layer equations for two-dimensional and axisymmetric flow. AIChE, 7, (1961), 26-28.
[2] Crane LJ. Flow past a stretching plate, ZAMP, 21, (1970), 645-647.
[3] Sajid M, Ali N, Javed T, Abbas Z. Stretching a curved surface in a viscous fluid. Chinese Physics Letters, 27, (2010), 024703.
[4] Okechi NF, Jalil M, Asghar S. Flow of viscous fluid along an exponentially stretching curved surface. Results in Physics, 7, (2017), 2851-2854.
[5] Hayat T, Saif RS, Ellahi R, Muhammad T, Ahmad B. Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions. Results in Physics, 7, (2017), 2601-2606.
[6] T, Rashid M, Imtiaz M, Alsaedi A. MHD convective flow due to a curved surface with thermal radiation and chemical reaction. Journal of Molecular Liquids, 225, (2017), 482-489.
[7] N.F. Okechi, M. Jalil, S. Asghar, Flow of viscous fluid along an exponentially stretching curved surface, Results in Physics, 7, (2017), 2851-2854.
[8] Williamson, R.V., The flow of pseudoplastic materials. Industrial and Engineering Chemistry Research, 21, No. 11, 1108 (1929).
[9] Liao, S.J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, Journal of Fluid Mechanics, 488, (2003), 189-212.
[10] Nadeem, S, Hussain, S.T., Heat transfer analysis of Williamson fluid over exponentially stretching surface, Appl. Math. Mech.35, (2014), 489-502.
[11] Nadeem, S., Hussain, S.T., Lee, C., Flow of Williamson fluid over a stretching sheet, Braz. J. Chem. Eng., 30, (2013), 619-625.
[12] K. Anantha Kumar, J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, Simultaneous solutions for MHD flow of Williamson fluid over a curved sheet with non-uniform heat source/sink, Heat Transfer Research, 50, (2019), 581-603.
[13] M.M. Bhatti, M.M. Rashidi, Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet, J. Mol. Liq. 221 (2016) 567-573.
[14] M. Bilal, M. Sagheer, S. Hussain, Numerical study of magneto hydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity, Alexandria Engineering Journal, 57, (2018), 3281-3289.
[15] T. Hayat, A. Aziz, T. Muhammad and B. Ahmad, Onmagnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet, J. Magn. Magn. Mater. 408 (2016) 99-106.
[16] O. D. Makinde and A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Ther. Sci. 50 (2011) 1326-1332.
[17] M. M. Rashidi, N. V. Ganesh, A. K. A. Hakeem and B. Ganga, Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation, J. Mol. Liq. 198 (2014) 234-238.
[18] S.U.S. Choi, Enhancing Thermal Conductivity of Fluids with Nanoparticles, ASME, USA, (1995).
[19] J. Buongiorno, Convective transport in nanofluids, ASME J.Heat Tran. 128 (2006) 240–250.
[20] Waris, K.; Gul, T.; Idrees, M.; Islam, S.; Khan, I.; Dennis, L. Thin film Williamson nanofluid flow with varying viscosity and thermal conductivity on a time-dependent stretching sheet, Appl. Sci. 6, (2016), 334.
[21] T. Hayat, A. Shafiq, A. Alsaedi, Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation, Alex. Engr. J. 6 (2016) 035101.
[2] Crane LJ. Flow past a stretching plate, ZAMP, 21, (1970), 645-647.
[3] Sajid M, Ali N, Javed T, Abbas Z. Stretching a curved surface in a viscous fluid. Chinese Physics Letters, 27, (2010), 024703.
[4] Okechi NF, Jalil M, Asghar S. Flow of viscous fluid along an exponentially stretching curved surface. Results in Physics, 7, (2017), 2851-2854.
[5] Hayat T, Saif RS, Ellahi R, Muhammad T, Ahmad B. Numerical study of boundary-layer flow due to a nonlinear curved stretching sheet with convective heat and mass conditions. Results in Physics, 7, (2017), 2601-2606.
[6] T, Rashid M, Imtiaz M, Alsaedi A. MHD convective flow due to a curved surface with thermal radiation and chemical reaction. Journal of Molecular Liquids, 225, (2017), 482-489.
[7] N.F. Okechi, M. Jalil, S. Asghar, Flow of viscous fluid along an exponentially stretching curved surface, Results in Physics, 7, (2017), 2851-2854.
[8] Williamson, R.V., The flow of pseudoplastic materials. Industrial and Engineering Chemistry Research, 21, No. 11, 1108 (1929).
[9] Liao, S.J., On the analytic solution of magnetohydrodynamic flows of non-Newtonian fluids over a stretching sheet, Journal of Fluid Mechanics, 488, (2003), 189-212.
[10] Nadeem, S, Hussain, S.T., Heat transfer analysis of Williamson fluid over exponentially stretching surface, Appl. Math. Mech.35, (2014), 489-502.
[11] Nadeem, S., Hussain, S.T., Lee, C., Flow of Williamson fluid over a stretching sheet, Braz. J. Chem. Eng., 30, (2013), 619-625.
[12] K. Anantha Kumar, J.V. Ramana Reddy, V. Sugunamma, N. Sandeep, Simultaneous solutions for MHD flow of Williamson fluid over a curved sheet with non-uniform heat source/sink, Heat Transfer Research, 50, (2019), 581-603.
[13] M.M. Bhatti, M.M. Rashidi, Effects of thermo-diffusion and thermal radiation on Williamson nanofluid over a porous shrinking/stretching sheet, J. Mol. Liq. 221 (2016) 567-573.
[14] M. Bilal, M. Sagheer, S. Hussain, Numerical study of magneto hydrodynamics and thermal radiation on Williamson nanofluid flow over a stretching cylinder with variable thermal conductivity, Alexandria Engineering Journal, 57, (2018), 3281-3289.
[15] T. Hayat, A. Aziz, T. Muhammad and B. Ahmad, Onmagnetohydrodynamic flow of second grade nanofluid over a nonlinear stretching sheet, J. Magn. Magn. Mater. 408 (2016) 99-106.
[16] O. D. Makinde and A. Aziz, Boundary layer flow of a nanofluid past a stretching sheet with a convective boundary condition, Int. J. Ther. Sci. 50 (2011) 1326-1332.
[17] M. M. Rashidi, N. V. Ganesh, A. K. A. Hakeem and B. Ganga, Buoyancy effect on MHD flow of nanofluid over a stretching sheet in the presence of thermal radiation, J. Mol. Liq. 198 (2014) 234-238.
[18] S.U.S. Choi, Enhancing Thermal Conductivity of Fluids with Nanoparticles, ASME, USA, (1995).
[19] J. Buongiorno, Convective transport in nanofluids, ASME J.Heat Tran. 128 (2006) 240–250.
[20] Waris, K.; Gul, T.; Idrees, M.; Islam, S.; Khan, I.; Dennis, L. Thin film Williamson nanofluid flow with varying viscosity and thermal conductivity on a time-dependent stretching sheet, Appl. Sci. 6, (2016), 334.
[21] T. Hayat, A. Shafiq, A. Alsaedi, Hydromagnetic boundary layer flow of Williamson fluid in the presence of thermal radiation and Ohmic dissipation, Alex. Engr. J. 6 (2016) 035101.
How to Cite
Nagaraju Kasula, & M N Raja Shekar. (1). Boundary layer flow of MHD Williamson nano fluid flow over a curved stretching surface. Revista Electronica De Veterinaria, 24(4), 760-772. https://doi.org/10.69980/redvet.v24i4.2438
Issue
Section
Articles
