Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium

doi:10.1007/s10483-019-2488-9

Abstract

Abstract: The present study aims to investigate the salient features of incompressible, hydromagnetic, three-dimensional flow of viscous fluid subject to the oscillatory motion of a disk. The rotating disk is contained in a porous medium. Furthermore, a time-invariant version of the Maxwell-Cattaneo law is implemented in the energy equation. The flow problem is normalized by obtaining similarity variables. The resulting nonlinear system is solved numerically using the successive over-relaxation method. The main results are discussed through graphical representations and tables. It is perceived that the thermal relaxation time parameter decreases the temperature curves and increases the heat transfer rate. The oscillatory curves for the velocity field demonstrate a decreasing tendency with the increasing porosity parameter values. Two- and three-dimensional flow phenomena are also shown through graphical results.

Key words: dynamic programming, systems of functional equations, common and coincidence solutions, Maxwell-Cattaneo law, time-dependent flow, magnetohydrodynamic (MHD), porous medium, oscillatory disk, numerical solution

2010 MSC Number:

76Bxx
76Sxx

A. RAUF, Z. ABBAS, S. A. SHEHZAD. Utilization of Maxwell-Cattaneo law for MHD swirling flow through oscillatory disk subject to porous medium. Applied Mathematics and Mechanics (English Edition), 2019, 40(6): 837-850.

TrendMD

References

[1] VON KARMAN, T. Ube Laminare und turbulente Reibung. Zeitschrift für Angewandte Mathematik und Mechanik, 1, 233-252(1921)
[2] COCHRAN, W. G. The flow due to a rotating disk. Mathematical Proceedings of the Cambridge Philosophical Society, 30(3), 365-375(1934)
[3] STUART, J. T. On the effects of uniform suction on the steady flow due to a rotating disk. The Quarterly Journal of Mechanics and Applied Mathematics, 7(4), 446-457(1954)
[4] BENTON, E. R. On the flow due to a rotating disk. Journal of Fluid Mechanics, 24(4), 781-800(1966)
[5] ATTIA, H. A. and HASSAN, A. L. L. Effect of Hall current on the unsteady MHD flow due to a rotating disk with uniform suction or injection. Applied Mathematical Modelling, 25(12), 1089-1098(2001)
[6] TURKYILMAZOGLU, M. Effects of uniform radial electric field on the MHD heat and fluid flow due to a rotating disk. International Journal of Engineering Science, 51, 233-240(2012)
[7] TURKYILMAZOGLU, M. Nanofluid flow and heat transfer due to a rotating disk. Computers and Fluids, 94, 139-146(2014)
[8] TURKYILMAZOGLU, M. MHD fluid flow and heat transfer due to a shrinking rotating disk. Computers and Fluids, 90, 51-56(2014)
[9] XUN, S., ZHAO, J., ZHENG, L., CHEN, X., and ZHANG, X. Flow and heat transfer of Ostwaldde Waele fluid over a variable thickness rotating disk with index decreasing. International Journal of Heat and Mass Transfer, 103, 1214-1224(2016)
[10] YIN, C., ZHENG, L., ZHANG, C., and ZHANG, X. Flow and heat transfer of nanofluids over a rotating disk with uniform stretching rate in the radial direction. Propulsion and Power Research, 6(1), 25-30(2017)
[11] MUSTAFA, M. MHD nanofluid flow over a rotating disk with partial slip effects:Buongiorno model. International Journal of Heat and Mass Transfer, 108, 1910-1916(2017)
[12] AZIZ, A., ALASEDI, A., MUHAMMAD, T., and HAYAT, T. Numerical study for heat generation/absorption in flow of nanofluid by a rotating disk. Results in Physics, 8, 785-792(2018)
[13] MUNAWAR, S., ALI, A., SALEEM, N., and NAQEEB, A. Swirling flow over an oscillatory stretchable disk. Journal of Mechanics, 30(4), 339-347(2014)
[14] CHRISTOV, C. I. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mechanics Research Communications, 36(4), 481-486(2009)
[15] LI, J., ZHENG, L., and LIU, L. MHD viscoelastic flow and heat transfer over a vertical stretching sheet with Cattaneo-Christov heat flux effects. Journal of Molecular Liquids, 221, 19-25(2016)
[16] SHEHZAD, S. A., ABBASI, F. M., HAYAT, T., and AHMED, B. Cattaneo-Christov heat flux model for third-grade fluid flow towards exponentially stretching sheet. Applied Mathematics and Mechanics (English Edition), 37(6), 761-768(2016) https://doi.org/10.1007/s10483-016-2088-6
[17] ABBASI, F. M. and SHEHZAD, S. A. Heat transfer analysis for three-dimensional flow of Maxwell fluid with temperature dependent thermal conductivity:application of Cattaneo-Christov heat flux model. Journal of Molecular Liquids, 220, 848-854(2016)
[18] SHEHZAD, S. A., HAYAT, T., ALASEDI, A., and MERAJ, M. A. Cattaneo-Christov heat and mass flux model for 3D hydromagnetic flow of chemically reactive Maxwell liquid. Applied Mathematics and Mechanics (English Edition), 38(10), 1347-1356(2017) https://doi.org/10.1007/s10483-017-2188-6
[19] MERAJ, M. A., SHEHZAD, S. A., HAYAT, T., ABBASI, F. M., and ALSAEDI, A. Darcy-Forchheimer flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory. Applied Mathematics and Mechanics (English Edition), 38(4), 557-566(2017) https://doi.org/10.1007/s10483-017-2188-6
[20] RAUF, A., ABBAS, Z., SHEHZAD, S. A., ALASEDI, A., and HAYAT, T. Numerical simulation of chemically reactive Powell-Eyring liquid flow with double diffusive Cattaneo-Christov heat and mass flux theories. Applied Mathematics and Mechanics (English Edition), 39(4), 467-476(2018) https://doi.org/10.1007/s10483-018-2314-8
[21] KUMAR, K, A., REDDY, J. V. R., SUGNAMMA, V., and SANDEEP, N. Magnetohydrodynamic Cattaneo-Christov flow past a cone and a wedge with variable heat source/sink. Alexandria Engineering Journal, 57, 435-443(2018)
[22] DARCY, H. R. P. G. Les Fontaines Publiques de la volle de Dijon, Vector Dalmont, Paris (1856)
[23] KHALED, A. R. A. and VAFAI, K. The role of porous media in modeling flow and heat transfer in biological tissues. International Journal of Heat and Mass Transfer, 46(26), 4989-5003(2003)
[24] CHEN, D., MIOSHI, H., AKAI, T., and YAZAWA, T. Colorless transparent fluorescence material:sintered porous glass containing rare-earth and transition-metal ions. Applied Physics Letters, 86(23), 231908(2005)
[25] ATTIA, H. A., ABDEEN, H. A. M., and ELBARAWY, M. M. Time varying rotating disk flow with heat transfer of a non-Newtonian fluid in porous medium. Kragujevac Journal of Science, 36, 33-40(2014)
[26] ALI, N., KHAN, S. U., SAJID, M., and ABBAS, Z. Slip effects in the hydromagnetic flow of a viscoelastic fluid through porous medium over a porous oscillatory stretching sheet. Journal of Porous Media, 20(3), 249-262(2017)
[27] REDDY, P. S., SREEDEVI, P., and CHAMKHA, A. J. MHD boundary layer flow, heat and mass transfer analysis over a rotating disk through porous medium saturated by Cu-water and Ag-water nanofluid with chemical reaction. Powder Technology, 307, 46-55(2017)
[28] HASNAIN, J. and ABBAS, Z. Hydromagnetic convection flow in two immiscible fluids through a porous medium in an inclined annulus. Journal of Porous Medium, 20(11), 977-987(2017)
[29] SIDDIQ, M. K., RAUF, A., SHEHZAD, S. A., ALSAEDI, A., and HAYAT, T. Interaction of convective and Nield-Kuznetsov's conditions in hydromagnetic flow of nanofluid subject to DarcyForchheimer effects. Journal of Porous Media, 20(11), 989-998(2017)
[30] SHEIKHOLESLAMI, M. Numerical simulation of magnetic nanofluid natural convection in porous media. Physics Letter A, 381, 494-503(2017)
[31] SHEIKHOLESLAMI, M. and SHAMLOOEI, M. Magnetic source influence on nanofluid flow in porous medium considering shape factor effect. Physics Letter A, 381, 3071-3078(2017)
[32] KHAN, S. U. and ALI, N. Thermophoresis and heat generation/absorption effects on magnetohydrodynamic flow of Jeffrey fluid over porous oscillatory stretching surface with convective boundary conditions. Journal of Porous Media, 21(6), 555-576(2018)
[33] SHEIKHOLESLAMI, M., LI, Z., and SHAFEE, A. Lorentz forces effect on NEPCM heat transfer during solidifications in a porous energy storage system. International Journal of Heat and Mass Transfer, 127, 655-674(2018)
[34] SHEIKHOLESLAMI, M. Influence of magnetic field on Al2O3-H2O nanofluid force convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM. Journal of Molecular Liquids, 263, 472-488(2018)
[35] SHEIKHOLESLAMI, M. Numerical approach for MHD Al2O3-water nanofluid transportation inside a permeable medium using innovative computer method. Computer Methods in Applied Mechanics and Engineering, 344, 306-318(2019)
[36] SHEIKHOLESLAMI, M. New computational approach for exergy and entropy analysis of nanofluid under the impact of Lorentz force through a porous media. Computer Methods in Applied Mechanics and Engineering, 344, 319-333(2019)