Darcy-Forchheimer flow by rotating disk with partial slip

doi:10.1007/s10483-020-2608-9

Abstract

Abstract: The viscous dissipation and heat transfer in the Darcy-Forchheimer flow by a rotating disk are examined. The partial slip conditions are invoked. The optimal series solutions are computed via the optimal homotopic analysis method (OHAM). The thermophoresis and Brownian motions are studied. The Darcy-Forchheimer relation characterizes the porous space. The roles of influential variables on the physical quantities are graphically examined. A reduction in the local Nusselt number is observed through thermophoresis and thermal slip parameters. The local Sherwood number depicts an increasing trend for the higher Brownian motion and concentration slip parameters.

Key words: Darcy-Forchheimer flow, nanofluid, viscous dissipation, slip condition, optimal homotopy analysis method (OHAM)

2010 MSC Number:

76S05

T. HAYAT, F. HAIDER, T. MUHAMMAD, A. ALSAEDI. Darcy-Forchheimer flow by rotating disk with partial slip. Applied Mathematics and Mechanics (English Edition), 2020, 41(5): 741-752.

TrendMD

References

[1] CHOI, S. U. S. Enhancing thermal conductivity of fluids with nanoparticles. ASME International Mechanical Engineering Congress and Exposition, 66, 99-105 (1995)
[2] EASTMAN, J. A., CHOI, S. U. S., LI, S., YU, W., and THOMPSON, L. J. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters, 78, 718-720 (2001)
[3] BUONGIORNO, J. Convective transport in nanofluids. ASME Journal of Heat Transfer, 128, 240-250 (2006)
[4] TIWARI, R. K. and DAS, M. K. Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluid. International Journal of Heat and Mass Transfer, 50, 2002-2018 (2007)
[5] ABU-NADA, E. and OZTOP, H. F. Effects of inclination angle on natural convection in enclosures filled with Cu-water nanofluid. International Journal of Heat and Fluid Flow, 30, 669-678 (2009)
[6] HSIAO, K. L. Nanofluid flow with multimedia physical features for conjugate mixed convection and radiation. Computers and Fluids, 104, 1-8 (2014)
[7] HSIAO, K. L. Stagnation electrical MHD nanofluid mixed convection with slip boundary on a stretching sheet. Applied Thermal Engineering, 98, 850-861 (2016)
[8] SHEHZAD, N., ZEESHAN, A., ELLAHI, R., and VAFAI, K. Convective heat transfer of nanofluid in a wavy channel: Buongiorno's mathematical model. Journal of Molecular Liquids, 222, 446-455 (2016)
[9] MAHANTHESH, B., MABOOD, F., GIREESHA, B. J., and GORLA, R. S. R. Effects of chemical reaction and partial slip on the three-dimensional flow of a nanofluid impinging on an exponentially stretching surface. European Physical Journal Plus, 132, 113 (2017)
[10] FAROOQ, M., JAVED, M., KHAN, M. I., ANJUM, A., and HAYAT, T. Melting heat transfer and double stratification in stagnation flow of viscous nanofluid. Results in Physics, 7, 2296-2301 (2017)
[11] KUMAR, K. G., RAMESH, G. K., GIREESHA, B. J., and GORLA, R. S. R. Characteristics of Joule heating and viscous dissipation on three-dimensional flow of Oldroyd B nanofluid with thermal radiation. Alexandria Engineering Journal, 57, 2139-2149 (2018)
[12] HAYAT, T., RASHID, M., ALSAEDI, A., and AHMAD, B. Flow of nanofluid by nonlinear stretching velocity. Results in Physics, 8, 1104-1109 (2018)
[13] USMAN, M., SOOMRO, F. A., HAQ, R. U., WANG, W., and DEFTERLI, O. Thermal and velocity slip effects on Casson nanofluid flow over an inclined permeable stretching cylinder via collocation method. International Journal of Heat and Mass Transfer, 122, 1255-1263 (2018)
[14] IMTIAZ, M., SHAHID, F., HAYAT, T., and ALSAEDI, A. Melting heat transfer in Cu-water and Ag-water nanofluids flow with homogeneous-heterogeneous reactions. Applied Mathematics and Mechanics (English Edition), 40(4), 465-480 (2019) https://doi.org/10.1007/s10483-019-2462-8
[15] PRAKASH, J., TRIPATHI, D., TIWARI, A. K., SAIT, S. M., and ELLAHI, R. Peristaltic pumping of nanofluids through tapered channel in porous environment: applications in blood flow. Symmetry, 11, 868 (2019)
[16] SARAFRAZ, M. M., POURMEHRANA, O., YANGA, B., ARJOMANDIA, M., and ELLAHI, R. Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. International Journal of Thermal Sciences, 147, 106131 (2020)
[17] NIAZI, M. D. K. and XU, H. Modelling two-layer nanofluid flow in a micro-channel with electro-osmotic effects by means of Buongiorno's model. Applied Mathematics and Mechanics (English Edition), 41(1), 83-104 (2020) https://doi.org/10.1007/s10483-020-2558-7
[18] FORCHHEIMER, P. Wasserbewegung durch boden. Zeitschrift des Vereins Deutscher Ingenieure, 45, 1781-1788 (1901)
[19] MUSKAT, M. The Flow of Homogeneous Fluids Through Porous Media, Edwards, MI (1946)
[20] SEDDEEK, M. A. Influence of viscous dissipation and thermophoresis on Darcy-Forchheimer mixed convection in a fluid saturated porous media. Journal of Colloid and Interface Science, 293, 137-142 (2006)
[21] SADIQ, M. A. and HAYAT, T. Darcy-Forchheimer flow of magneto Maxwell liquid bounded by convectively heated sheet. Results in Physics, 6, 884-890 (2016)
[22] BAKAR, S. A., ARIFIN, N. M., NAZAR, R., ALI, F. M., and POP, I. Forced convection boundary layer stagnation-point flow in Darcy-Forchheimer porous medium past a shrinking sheet. Frontiers in Heat and Mass Transfer, 7, 38 (2016)
[23] UMAVATHI, J. C., OJJELA, O., and VAJRAVELU, K. Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using Darcy-Forchheimer-Brinkman model. International Journal of Thermal Sciences, 111, 511-524 (2017)
[24] HAYAT, T., NAZAR, H., IMTIAZ, M., and ALSAEDI, A. Darcy-Forchheimer flows of copper and silver water nanofluids between two rotating stretchable disks. Applied Mathematics and Mechanics (English Edition), 38(12), 1663-1678 (2017) https://doi.org/10.1007/s10483-017-2289-8
[25] HAYAT, T., AZIZ, A., MUHAMMAD, T., and ALSAEDI, A. An optimal analysis for Darcy-Forchheimer 3D flow of nanofluid with convective condition and homogeneous-heterogeneous reactions. Physics Letterrs A, 382, 2846-2855 (2018)
[26] HAYAT, T., HAIDER, F., MUHAMMAD, T., and ALSAEDI, A. Darcy-Forchheimer squeezed flow of carbon nanotubes with thermal radiation. Journal of Physics and Chemistry of Solids, 120, 79-86 (2018)
[27] ULLAH, M. Z., ALSHOMRANI, A. S., and ALGHAMDI, M. Significance of Arrhenius activation energy in Darcy-Forchheimer 3D rotating flow of nanofluid with radiative heat transfer. Physica A: Statistical Mechanics and Its Applications, 124024 (2019) https://doi.org/10.1016/j.physa.2019.124024
[28] FANG, T. G. and WANG, F. J. Momentum and heat transfer of a special case of the unsteady stagnation-point flow. Applied Mathematics and Mechanics (English Edition), 41(1), 51-82 (2020) https://doi.org/10.1007/s10483-020-2556-9
[29] SAIF, R. S., MUHAMMAD, T., and SADIA, H. Significance of inclined magnetic field in Darcy-Forchheimer flow with variable porosity and thermal conductivity. Physica A: Statistical Mechanics and Its Applications, 124067 (2020) https://doi.org/10.1016/j.physa.2019.124067
[30] VON KÁRMÁN, T. V. Über laminare and turbulente reibung. Zeitschrift für Angewandte Mathematik und Mechanik, 1, 233-252 (1921)
[31] TURKYILMAZOGLU, M. and SENEL, P. Heat and mass transfer of the flow due to a rotating rough and porous disk. International Journal of Thermal Sciences, 63, 146-158 (2013)
[32] RASHIDI, M. M., KAVYANI, N., and ABELMAN, S. Investigation of entropy generation in MHD and slip flow over rotating porous disk with variable properties. International Journal of Heat and Mass Transfer, 70, 892-917 (2014)
[33] TURKYILMAZOGLU, M. Nanofluid flow and heat transfer due to a rotating disk. Computers and Fluids, 94, 139-146 (2014)
[34] HATAMI, M., SHEIKHOLESLAMI, M., and GANJI, D. D. Laminar flow and heat transfer of nanofluids between contracting and rotating disks by least square method. Powder Technology, 253, 769-779 (2014)
[35] MUSTAFA, M., KHAN, J. A., HAYAT, T., and ALSAEDI, A. On Bödewadt flow and heat transfer of nanofluids over a stretching stationary disk. Journal of Molecular Liquids, 211, 119-125 (2015)
[36] SHEIKHOLESLAMI, M., HATAMI, M., and GANJI, D. D. Numerical investigation of nanofluid spraying on an inclined rotating disk for cooling process. Journal of Molecular Liquids, 211, 577-583 (2015)
[37] DOH, D. H. and MUTHTAMILSELVAN, M. Thermophoretic particle deposition on magnetohydrodynamic flow of micropolar fluid due to a rotating disk. International Journal of Mechanical Sciences, 130, 350-359 (2017)
[38] QAYYUM, S., IMTIAZ, M., ALSAEDI, A., and HAYAT, T. Analysis of radiation in a suspension of nanoparticles and gyrotactic microorganism for rotating disk of variable thickness. Chinese Journal of Physics, 56, 2404-2423 (2018)
[39] XU, H. Modelling unsteady mixed convection of a nanofluid suspended with multiple kinds of nanoparticles between two rotating disks by generalized hybrid model. International Communications in Heat and Mass Transfer, 108, 104275 (2019)
[40] MAJEED, A. H., BILAL, S., MAHMOOD, R., and MALIK, M. Y. Heat transfer analysis of viscous fluid flow between two coaxially rotated disks embedded in permeable media by capitalizing non-Fourier heat flux model. Phyisca A: Statistical Mechanics and Its Applications, 540, 123182 (2020)
[41] LIAO, S. J. An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15, 2003-2016 (2010)
[42] MALVANDI, A., HEDAYATI, F., and DOMAIRRY, G. Stagnation point flow of a nanofluid toward an exponentially stretching sheet with nonuniform heat generation/absorption. Journal of Thermodynamics, 2013, 764827 (2013)
[43] ABBASBANDY, S., HAYAT, T., ALSAEDI, A., and RASHIDI, M. M. Numerical and analytical solutions for Falkner-Skan flow of MHD Oldroyd-B fluid. International Journal of Numerical Methods for Heat and Fluid Flow, 24, 390-401 (2014)
[44] TURKYILMAZOGLU, M. An effective approach for evaluation of the optimal convergence control parameter in the homotopy analysis method. Filomat, 30, 1633-1650 (2016)
[45] AWAIS, M., SALEEM, S., HAYAT, T., and IRUM, S. Hydromagnetic couple-stress nanofluid flow over a moving convective wall: OHAM analysis. Acta Astronautica, 129, 271-276 (2016)
[46] HAQ, R. U., HAMOUCH, Z., HUSSAIN, S. T., and MEKKAOUI, T. MHD mixed convection flow along a vertically heated sheet. International Journal of Hydrogen Energy, 42, 15925-15932 (2017)
[47] AWAIS, M., AWAN, S. E., IQBAL, K., KHAN, Z. A., and RAJA, M. A. Z. Hydromagnetic mixed convective flow over a wall with variable thickness and Cattaneo-Christov heat flux model: OHAM analysis. Results in Physics, 8, 621-627 (2018)
[48] GUPTA, S., KUMAR, D., and SINGH, J. MHD mixed convective stagnation point flow and heat transfer of an incompressible nanofluid over an inclined stretching sheet with chemical reaction and radiation. International Journal of Heat and Mass Transfer, 118, 378-387 (2018)
[49] ULLAH, I., RAHIM, M. T., KHAN, H., and QAYYUM, M. Analysis of various semi-numerical schemes for magnetohydrodynamic (MHD) squeezing fluid flow in porous medium. Propulsion and Power Research, 8, 69-78 (2019)
[50] NAZ, R., TARIQ, S., and ALSULAMI, H. Inquiry of entropy generation in stratified Walters' B nanofluid with swimming gyrotactic microorganisms. Alexandria Engineering Journal, 59, 247-261 (2020)