Stagnation-Point Flow of a Walters’ B Fluid Towards a Vertical Stretching Surface Embedded in a Porous Medium with Elastic-Deformation and Chemical Reaction

Document Type : Full Length Research Article

Authors

1 Department of Mathematics, Federal University of Agriculture, Abeokuta

2 Department of Mathematics, Federal University of Agriculture, Abeokuta.

Abstract

In this paper, an analytical solution is presented for the stagnation-point flow of MHD Walters’ B fluid towards a vertical stretching surface with elastic-deformation and chemical reaction. The higher non-linear ordinary differential equations for the heat and mass transfer are obtained from partial differential equations via similarity transformation techniques and solved by the modern analytical method. The behaviors of the various embedded parameter are addressed and the result justifies among others that the fluid exhibits Newtonian properties in the absence of local Weissenberg number. On the other hand, the presence of local Weissenberg number makes the model possess the Non-Newtonian properties with great industrial application such as plastic film, artificial fibers, and higher molecular-weight liquid used in industries and engineering field, while greater cooling problems commonly encountered in industries and engineering discipline for the cooling of the system or electronics components is observed with higher values of thermal buoyancy effect.

Keywords

Main Subjects

References

[1]    Singh, G., Sharma P.R., Chamkha, A.J., 2010. Effect of volumentric heat generation/absorption on mixed convection stagnation point flow on an iso-thermal vertical plate in porous media. International Journal of Industrial Mathematics, 2(2), pp.59-71.
[2]    Wu, Q., Weinbaum, S., Andreopoulos, Y., 2005. Stagnation point flow in a porous medium. Chemical Engineering Science, 60(1), pp.123-134.
[3]    Akinbo, B.J., Olajuwon, B.I., 2019. Homotopy analysis investigation of heat and mass transfer flow past a vertical porous medium in the presence of heat source. International Journal of Heat and Technology, 37(3), pp. 899-908.
[4]    Akinbo, B.J., Olajuwon, B.I., 2019. Convective heat and mass transfer in electrically conducting flow past a vertical plate embedded in a porous medium in the presence of thermal radiation and thermo diffusion. Computational Thermal Sciences, 11(4), pp. 367–385.
[5]    Akinbo, B.J., Olajuwon, B.I., 2019. Heat and mass transfer in magnetohydrodynamics (MHD) flow over a moving vertical plate with convective boundary condition in the presence of thermal radiation. Sigma Journal Engineering and Natural Science, 37(3), pp. 1031-1053.
[6]    Ellahi, R., Sait, S.M., Shehzad, N., Ayaz, Z., 2020. A hybrid investigation on numerical and analytical  solutions of electro-magnetohydrodynamics flow of nanofluid through porous media with entropy generation. International Journal of Numerical Methods for Heat and Fluid Flow, 30(2), pp. 834-854.
[7]    Shehzad, N.,  Zeeshan, A.,  Ellahi, R., Rashidi, S., 2018. Modelling study on internal energy loss due to entropy generation for non-Darcy Poiseuille flow of silver-water nanofluid: an application of purification. Entropy, 20(11), p.851.
[8]    Zeeshan, A.,  Pervaiz, Z., Shehzad, N.,  Nayak, M.K., Al‑Sulami, H.H., 2021. Optimal thermal performance of magneto‑nanofluid flow in expanding/contracting channel. Journal of Thermal Analysis and Calorimetry, 143, pp.2189-2201
[9]    Shehzad, N., Zeeshan, A.,   Ellahi, R., 2018. Electroosmotic Flow of MHD Power Law Al2O3-PVC Nanofluid in a Horizontal Channel: Couette-Poiseuille Flow Model. Communications in Theoretical Physics, 69(6), pp.655-666.
[10] Mahapatra, T.R., Gupta, A.S., 2004. Stagnation-point flow of a viscoelastic fluid towards a stretching surface. International Journal of Non-Linear Mechanics, 39, pp.811-820.
[11] Hayat T, Asad S, Mustafa M., Hamed, H. A., 2014. Heat transfer analysis in the flow of Walters’ B fluid with a convective boundary condition. Chinese Physics B, 23(8), p.084701.
[12] Hakeem, A.K.A., Ganesh, N.V., and Ganga, B., 2014. Effect of heat radiation in a Walter’s liquid B fluid over a stretching sheet with non-uniform heat source/sink and elastic deformation. Journal of King Saud University - Engineering Sciences, 26, pp.168-175
[13] Dhanalaxmi, V., 2017. Heat transfer in a viscoelastic fluid over a stretching sheet with frictional heating and work due to deformation. Global Journal of Pure and Applied Mathematics, 13(9), pp.6061-6080.
[14] Mishra, S.R., Baag, S., Bhatti, M.M., 2018. Study of heat and mass transfer on MHD Walters B’ Nanofluid flow induced by a stretching porous surface. Alexandria Engineering Journal, 57, pp.2435–2443.
[15] Qayyum, S., Hayat, T., Shehzad, S.A., and Alsaedi, A., 2017. Effect of a chemical reaction on magnetohydrodynamic (MHD) stagnation point flow of Walters-B nanofluid with newtonian heat and mass conditions. Nuclear Engineering and Technology, 49, pp.1636-1644
[16] Hayat, T., Abbas, Z., Pop, I., 2008. Mixed convection in the stagnation point flow adjacent to a vertical surface in a viscoelastic fluid. International Journal of Heat and Mass Transfer, 51, pp.3200-3206
[17] Pillai, K.M.C., Sai, K.S., Swamy, N.S., Nataraja, H.R., Tiwari, S.B., Rao, B.N., 2004. Heat transfer in a viscoelastic boundary layer flow through a porous medium. Computational Mechanics, 34, pp. 27-37.
[18] Abel, M.S., Mahesha, N., 2008. Heat transfer in MHD viscoelastic fluid over a stretching sheet with variable thermal conductivity, non-uniform heat source and radiation. Applied Mathematical Modelling, 32(10), pp.1965-1983.
[19] Abel, M.S., Sanjayanand, E., Nandeppanavar, M. M., 2008. Viscoelastic MHD flow and heat transfer over a stretching sheet with viscous and ohmic dissipations. Communications in Nonlinear Science and Numerical Simulation, 13(9), pp.1808-1821.
[20] Abel, M.S., Siddheshwar, P.G., Nandeppanavar, M. 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, 50, pp.960-966.
[21] Cortell R., 2006. Effects of viscous dissipation and work done by deformation on MHD flow and heat transfer of a viscoelastic fluid over a stretching sheet. Physics Letters A, 357, pp.298-305.
[22] Makinde, O. D., 2012. Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation. Meccanica 47, pp. 1173–1184.
[23] Nadeem, S., Mehmood, R., Motsa, S.S., 2003. Numerical investigation on MHD oblique flow of Walter's B type nanofluid over a convective surface. International Journal of Thermal Sciences 92, pp. 162-172
[24] Zeeshan, A., Shehzad, N., Ellahi, R., 2018. Analysis of activation energy in Couette-Poiseuille flow of nanofluid in the presence of chemical reaction and convective boundary conditions. Results in Physics, 8, pp.502-512.
[25] Alamri, S. Z., Ellahi, R., Shehzad, N., Zeeshan, A., 2019. Convective radiative plane Poiseuille flow of nanofluid through porous medium with slip: An application of Stefan blowing. Journal of Molecular Liquids, 273, pp.292-304
[26] Liao S. J., 2003. Beyond perturbation: an introduction to Homotopy Analysis Method. Boca Raton, Fla., USA: Chapman and Hall.
[27] Akinbo, B.J., Olajuwon, B.I., 2021. Radiation and thermal-diffusion interaction on stagnation-point ow of Walters' B uid toward a vertical stretching sheet. International Communications in Heat and Mass Transfer, 126, pp.105471
[28] Akinbo, B.J., Olajuwon, B.I., 2021. Heat transfer analysis in a hydromagnetic Walters' B uid with elastic deformation and Newtonian heating. Heat Transfer, 50, pp.2033-2048.
[29] Shahid, A., Bhatti, M.M., Bég, O.A., Kadir, A., 2018. Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model. Neural Computing and Applications, 30(11), pp.3467-3478.

Files

Cited by

History

  • Receive Date: 03 November 2020
  • Revise Date: 03 June 2022
  • Accept Date: 06 June 2022

Share

How to cite

Statistics