Unsteady Magnetohydrodynamic Mixed Convection Flow over a Rotating Sphere with Sinusoidal Mass Transfer

Document Type : Full Length Research Article

Authors

1 Department of Mathematics, National Institute of Technology, Tiruchirappalli, India

2 Department of Mathematics, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala

Abstract

This paper investigates the unsteady magnetohydrodynamic (MHD) mixed convective fluid flow over a rotating sphere. An implicit finite difference scheme, together with quasi-linearization, is used to find non-similar solutions for the governing equations. The impact of variable physical properties and viscous dissipation are included. It is observed that the skin friction coefficient in the axial direction and the heat transfer coefficient are increasing with an increase in MHD, mixed convection and rotation parameters and with time, whereas the effect is just the opposite for the skin friction coefficient in the rotational direction. The non-uniform slot suction(injection) and the slot movement influence the point of vanishing skin friction to move in the axial direction downstream (upstream).

Keywords

Main Subjects

References

  • Lien, F.S., Chen, C.K. and Cleaver, J.W., 1986. Mixed and Free Convection Over a Rotating Sphere with Blowing and Suction. Journal of Heat Transfer, 108(2), pp.398–404.
  • Kreith, F., Roberts, L.G., Sullivan, J.A. and Sinha, S.N., 1963. Convection Heat Transfer and Flow Phenomena of Rotating Spheres. International Journal of Heat and Mass Transfer, 6(10), pp.881–895.
  • Lee, M.H., Jeng, D.R. and De Witt, K.J., 1978. Laminar Boundary Layer Transfer Over Rotating Bodies in Forced Flow. Transactions of the ASME, 100, pp.496–502.
  • Niazmand, H. and Renksizbulut, M., 2005. Flow Past a Spinning Sphere with Surface Blowing and Heat Transfer. Journal of Fluids Engineering, 127(1), pp.163–171.
  • Safarzadeh, S. and Brahimi, A., 2022. Convection Heat Transfer and Flow Phenomena from a Rotating Sphere in Porous Media. Scientia Iranica, 29(2), pp.588–596.
  • Attia, H.A., 2009. Steady Flow Over a Rotating Disk in Porous Medium with Heat Transfer. Nonlinear Analysis: Modelling and Control, 14(1), pp.21–26.
  • Al-Maliky, R.F., 2013. Numerical Investigation of Laminar Flow Over a Rotating Circular Cylinder. International Journal of Mechanical & Mechatronics Engineering, 13(3), pp.32–44.
  • Towers, P.D. and Garrett, S.J., 2016. Similarity Solutions of Compressible Flow Over a Rotating Cone with Surface Suction. Thermal Science, 20(2), pp.517–528.
  • Schlichting, H. and Gersten, K., 2016. Boundary-Layer Theory, Springer.
  • Mahdy, A., 2018. Simultaneous Impacts of MHD and Variable Wall Temperature on Transient Mixed Casson Nanofluid Flow in the Stagnation Point of Rotating Sphere. Applied Mathematics and Mechanics, 39(9), pp.1327–1340.
  • Rajakumar, J., Saikrishnan, P. and Chamkha, A., 2016. Non-similar Solution of Steady MHD Mixed Convection Flow Over a Rotating Sphere. Computational Thermal Sciences, 8(6), pp.509–523.
  • Rajakumar, J., Saikrishnan, P. and Chamkha, A., 2016. Non-uniform Mass Transfer in MHD Mixed Convection Flow of Water Over a Sphere with Variable Viscosity and Prandtl Number. International Journal of Numerical Methods for Heat & Fluid Flow, 26(7), pp.2235–2251.
  • Revathi, G., Saikrishnan, P. and Chamkha, A., 2013. Non‐similar Solution for Unsteady Water Boundary Layer Flows Over a Sphere with Non‐uniform Mass Transfer. International Journal of Numerical Methods for Heat & Fluid Flow, 23(6), pp.1104–1116.
  • Roy, S. and Saikrishnan, P., 2003. Non-Uniform Slot Injection (Suction) Into Steady Laminar Water Boundary Layer Flow Over a Rotating Sphere. International Journal of Heat and Mass Transfer, 46(18), pp.3389–3396.
  • Saikrishnan, P. and Roy, S., 2002. Steady Nonsimilar Axisymmetric Water Boundary Layers with Variable Viscosity and Prandtl Number. Acta Mechanica, 157(1–4), pp.187–199.
  • Saikrishnan, P. and Roy, S., 2003. Non-uniform Slot Injection (Suction) Into Water Boundary Layers Over (i) a Cylinder and (ii) a Sphere. International Journal of Engineering Science, 41(12), pp.1351–1365.
  • Ganapathirao, M., Ravindran, R. and Pop, I., 2013. Non-uniform Slot Suction (Injection) on an Unsteady Mixed Convection Flow Over a Wedge with Chemical Reaction and Heat Generation or Absorption. International Journal of Heat and Mass Transfer, 67, pp.1054–1061.
  • Roy, S. and Nath, G., 1994. Non-uniform Slot Injection (Suction) or Wall Enthalpy into a Steady Nonsimilar Compressible Laminar Boundary Layer. Acta Mechanica, 103, pp.45–61.
  • Ganapathirao, M. and Ravindran, R., 2015. Non-uniform Slot Suction/Injection Into Mixed Convective MHD Flow Over a Vertical Wedge with Chemical Reaction. Procedia Engineering, 127, pp.1102–1109.
  • Subhashini, S.V., Takhar, H.S. and Nath, G., 2007. Non-uniform Mass Transfer or Wall Enthalpy Into a Compressible Flow Over a Rotating Sphere. Heat and Mass Transfer, 43(11), pp.1133–1141.
  • Dewey, C.F. and Gross, J.F., 1967. Exact Similar Solutions of the Laminar Boundary-Layer Equations, Advances in Heat Transfer, Elsevier, 4, pp.317–446.
  • Chamkha, A.J. and Ahmed, S.E., 2012. Unsteady MHD Heat and Mass Transfer by Mixed Convection Flow in the Forward Stagnation Region of a Rotating Sphere at Different Wall Conditions. Chemical Engineering Communications, 199(1), pp.122–141.
  • Eswara, A.T. and Nath, G., 1994. Unsteady Nonsimilar Two-Dimensional and Axisymmetric Water Boundary Layers with Variable Viscosity and Prandtl Number. International Journal of Engineering Science, 32(2), pp.267–279.
  • Roy, S., Takhar, H.S. and Nath, G., 2004. Unsteady MHD Flow on a Rotating Cone in a Rotating Fluid. Meccanica, 39(3), pp.271–283.
  • Anilkumar, D. and Roy, S., 2004. Self-Similar Solution of the Unsteady Mixed Convection Flow in the Stagnation Point Region of a Rotating Sphere. Heat and Mass Transfer, 40(6), pp.487–493.
  • Mahdy, A., Chamkha, A.J. and Nabwey, H.A., 2020. Entropy Analysis and Unsteady MHD Mixed Convection Stagnation-Point Flow of Casson Nanofluid Around a Rotating Sphere. Alexandria Engineering Journal, 59(3), pp.1693–1703.
  • Takhar, H.S. and Nath, G., 2000. Self-Similar Solution of the Unsteady Flow in the Stagnation Point Region of a Rotating Sphere with a Magnetic Field. Heat and Mass Transfer, 36(2), pp.89–96.
  • Sau, A., 1994. Unsteady Non-similar Compressible Boundary Layer Flow over a Rotating Sphere. Acta Mechanica, 106(3–4), pp.207–213.
  • Chen, T.S. and Mucoglu, A., 1977. Analysis of Mixed Forced and Free Convection About a Sphere. International Journal of Heat and Mass Transfer, 20(8), pp.867–875.
  • Devi, C.D.S. and Nath, G., 1988. Unsteady Mixed Convection Over Two-Dimensional and Axisymmetric Bodies. Wärme- Und Stoffübertragung, 22(1–2), pp.83–90.
  • Natarajan, E., Basak, T. and Roy, S., 2008. Natural Convection Flows in a Trapezoidal Enclosure With Uniform and Non-Uniform Heating of Bottom Wall. International Journal of Heat and Mass Transfer, 51(3–4), pp.747–756.
  • Natarajan, E., Basak, T. and Roy, S., 2007. Natural Convection in a Trapezoidal Cavity With Linearly Heated Side Wall (s). In Heat Transfer Summer Conference, 42746 pp. 1021–1030.
  • Hatem, N., Philippe, C., Mbow, C., Kabdi, Z., Najoua, S. and Daguenet, M., 1996. Numerical Study of Mixed Convection Around a Sphere Rotating About Its Vertical Axis in a Newtonian Fluid at Rest and Subject to a Heat Flux. Numerical Heat Transfer, Part A: Applications, 29(4), pp.397–415.
  • Hatzikonstantinou, P., 1990. Effects of Mixed Convection and Viscous Dissipation on Heat Transfer about a Porous Rotating Sphere. ZAMM - Journal of Applied Mathematics and Mechanics, 70(10), pp.457–463.
  • Le Palec, G. and Daguenet, M., 1987. Laminar Three-Dimensional Mixed Convection About a Rotating Sphere in a Stream. International Journal of Heat and Mass Transfer, 30(7), pp.1511–1523.
  • Rajasekaran, R. and Palekar, M.G., 1985. Mixed Convection About a Rotating Sphere. International Journal of Heat and Mass Transfer, 28(5), pp.959–968.
  • Rajasekaran, R. and Palekar, M.G., 1985. Viscous Dissipation Effects on Mixed Convection About a Rotating Sphere. International Journal of Engineering Science, 23(8), pp.789–795.
  • Tieng, S.M. and Yan, A.C., 1992. Investigation of Mixed Convection About a Rotating Sphere by Holographic Interferometry. Journal of Thermophysics and Heat Transfer, 6(4), pp.727–732.
  • Patil, P.M., Benawadi, S. and Shanker, B., 2022. Influence of Mixed Convection Nanofluid Flow over a Rotating Sphere in the Presence of Diffusion of Liquid Hydrogen and Ammonia. Mathematics and Computers in Simulation, 194, pp.764–781.
  • Sathyakrishna, M., Roy, S. and Nath, G., 2001. Unsteady Two-Dimensional and Axisymmetric MHD Boundary-Layer Flows. Acta Mechanica, 150(1–2), pp.67–77.
  • Turkyilmazoglu, M., 2011. Numerical and Analytical Solutions for the Flow and Heat Transfer near the Equator of an MHD Boundary Layer over a Porous Rotating Sphere. International Journal of Thermal Sciences, 50(5), pp.831–842.
  • Kazem, S., Tameh, M.S. and Rashidi, M.M., 2019. An Improvement To The Unsteady MHD Rotating Flow Over a Rotating Sphere Near the Equator via Two Radial Basis Function Schemes. The European Physical Journal Plus, 134(12), p.611.
  • Vajravelu, K., Li, R., Dewasurendra, M. and Prasad, K.V., 2017. Mixed Convective Boundary Layer MHD Flow Along a Vertical Elastic Sheet. International Journal of Applied and Computational Mathematics, 3(3), pp.2501–2518.
  • Ghani, M. and Rumite, W., 2021. Keller-Box Scheme to Mixed Convection Flow over a Solid Sphere with the Effect of MHD. MUST: Journal of Mathematics Education, Science and Technology, 6(1), pp.97–120.
  • Chamkha, A.J. and Ahmed, S.E., 2011. Unsteady MHD Heat and Mass Transfer by Mixed Convection Flow in the Forward Stagnation Region of a Rotating Sphere in the Presence of Chemical Reaction and Heat Source. In Proceedings of the World Congress on Engineering, 1 pp.133–138.
  • Sahaya Jenifer, A., Saikrishnan, P. and Lewis, R.W., 2021. Unsteady MHD Mixed Convection Flow of Water over a Sphere ‎with Mass Transfer. Journal of Applied and Computational Mechanics, 7(2), pp.935–942.
  • Gul, T., Ali, B., Alghamdi, W., Nasir, S., Saeed, A., Kumam, P., Mukhtar, S., Kumam, W. and Jawad, M., 2021. Mixed Convection Stagnation Point Flow of the Blood Based Hybrid Nanofluid around a Rotating Sphere. Scientific Reports, 11(1), pp.1–15.
  • Calabretto, S.A., Levy, B., Denier, J.P. and Mattner, T.W., 2015. The Unsteady Flow Due to an Impulsively Rotated Sphere, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 471(2181), p.20150299.
  • Mahdy, A.E.N., Hady, F.M. and Nabwey, H.A., 2021. Unsteady Homogeneous-Heterogeneous Reactions in MHD Nanofluid Mixed Convection Flow Past a Stagnation Point of an Impulsively Rotating Sphere. Thermal Science, 25(1 Part A), pp.243–256.
  • Almakki, M., Mondal, H., Mburu, Z. and Sibanda, P., 2022. Entropy Generation in Double Diffusive Convective Magnetic Nanofluid Flow in Rotating Sphere with Viscous Dissipation. Journal of Nanofluids, 11(3), pp.360-372.
  • Das, K., Kundu, P.K. and Sk, M.T., 2022. Magnetophoretic Effect on the Nanofluid Flow Over Decelerating Spinning Sphere with the Presence of induced Magnetic Field. Journal of Nanofluids, 11(1), pp.135-141.
  • Mahmood, Z., Alhazmi, S.E., Khan, U., Bani-Fwaz, M.Z. and Galal, A.M., 2022. Unsteady MHD Stagnation Point Flow of Ternary Hybrid Nanofluid over a Spinning Sphere with Joule Heating. International Journal of Modern Physics B, 36(32), p.2250230.
  • Bellman, R.E. and Kalaba, R.E., 1965. Quasilinearization and Nonlinear Boundary Value Problems, The RAND Corporation, American Elsevier Publishing Company, Inc., New York.
  • Inouye, K. and Tate, A., 1974. Finite-Difference Version of Quasi-Linearization Applied to Boundary-Layer Equations. AIAA Journal, 12(4), pp.558–560.
  • Varga, S., 2000. Matrix Iterative Analysis, Springer-Verlag Berlin Heidelberg.

Files

Cited by

History

  • Receive Date: 16 March 2021
  • Revise Date: 04 January 2023
  • Accept Date: 10 January 2023

Share

How to cite

Statistics