Influences of Zero Mass Flux and Active Conditions on the Predictions of Double Dispersion and Double Diffusive Boundary Layer in Darcy/Non Darcy Nanofluid Flow

Article Preview

Abstract:

Free convective of nanofluid inside dispersive porous medium adjacent to a vertical plate under the effects of the zero mass nanoparticles flux condition and the thermal and solutal dispersions is studied. Buongiorno's model revised is used considering Darcy and non Darcy laminar flows, and isothermal or convective flux outer the wall. Dimensionless governing equations formulated using velocity, temperature, concentration and nanoparticle volume fraction have been solved by finite difference method that implements the 3-stage Lobatto collocation formula. The numerical data obtained with semi or full dispersions cases are compared to predictions made using the non dispersive porous medium. Taking into account the dispersions, the influence of the zero mass nanoparticles flux condition is examined to test the validity of the control active nanoparticle assumption. It is found mainly that the thermal transfers can reach more than 100% in connection with the case where of a semi-dispersion of the porous medium is applied. Realistic condition, i.e. zero mass flux should be addressed for the heat transfer rate rather than the mass transfer rate, discovered markedly different to the active condition. This signifies the importance of considering the zero nanoparticles mass flux and dispersions in the performance characterization of nanofluid flow in porous media.

You might also be interested in these eBooks

Info:

Pages:

49-65

Citation:

Online since:

November 2021

Export:

Price:

Permissions CCC:

Permissions PLS:

Сopyright:

© 2021 Trans Tech Publications Ltd. All Rights Reserved

Share:

Citation:

* - Corresponding Author

[1] R.S. Vajjha, D.K. Das; A review and analysis on influence of temperature and concentration of nanofluids on thermophysical properties, heat transfer and pumping power, International journal of heat and mass transfer 55 15-16 (2012) 4063-4078.

DOI: 10.1016/j.ijheatmasstransfer.2012.03.048

Google Scholar

[2] B. Mahanthesh, B. J. Gireesha, R. S. Reddy Gorla; Nanoparticles effect on 3D flow, heat and mass transfer of nanofluid with nonlinear radiation, thermal-diffusion and diffusion-thermo effects, Journal of Nanofluids 5.5 (2016) 669-678.

DOI: 10.1166/jon.2016.1257

Google Scholar

[3] B.Mahanthesh, S.S Nagavangala, G. Lorenzini; Heat transfer enhancement due to nanoparticles, magnetic field, thermal and exponential space-dependent heat source aspects in nanoliquid flow past a stretchable spinning disk, Journal of Thermal Analysis and Calorimetry (2020) 1-9.

DOI: 10.1007/s10973-020-09927-x

Google Scholar

[4] J. Buongiorno; Convective Transport in Nanofluids, Journal of Heat Transfer 128 (2006) 240-250.

DOI: 10.1115/1.2150834

Google Scholar

[5] Z. Haddad, H.F. Oztop, E. Abu-Nada, A. Mataoui; A review on natural convective heat transfer of nanofluids, Renewable and Sustainable Energy Reviews 16 (7) (2012) 5363–5378.

DOI: 10.1016/j.rser.2012.04.003

Google Scholar

[6] T.G. Myers, H. Ribera, V. Cregan; Does mathematics contribute to the nanofluid debate?, International Journal of Heat and Mass Transfer 111 (2017) 279-288.

DOI: 10.1016/j.ijheatmasstransfer.2017.03.118

Google Scholar

[7] R.A. Mahdi, H.A. Mohammed, K.M. Munisamy, N.H. Saeid; Review of convection heat transfer and fluid flow in porous media with nanofluid, Renewable and Sustainable Energy Reviews 41 (2015) 715-734.

DOI: 10.1016/j.rser.2014.08.040

Google Scholar

[8] M. Chandrasekar, S. Suresh, T. S. kumar; Mechanisms proposed through experimental investigations on thermophysical properties and forced convective heat transfer characteristics of various nanofluids – A review, Renewable and Sustainable Energy Reviews 16 (2012) 3917-3938.

DOI: 10.1016/j.rser.2012.03.013

Google Scholar

[9] S. Kumar, S.K. Prasad, J. Banerjee; Analysis of flow and thermal field in nanofluid using a single phase thermal dispersion model, Applied Mathematical Modelling 34 (2010) 573-592.

DOI: 10.1016/j.apm.2009.06.026

Google Scholar

[10] P. Cheng; Thermal dispersion effects on non-Darcy convection flows in a saturated porous medium, Letters in Heat and Mass Transfer 8 (1981) 267-270.

DOI: 10.1016/0094-4548(81)90041-2

Google Scholar

[11] J.T. Hong, C.L. Tien; Analysis of thermal dispersion effect on vertical plate natural convection in porous media, International Journal of Heat and Mass Transfer 30 (1987) 143-150.

DOI: 10.1016/0017-9310(87)90067-6

Google Scholar

[12] A. Mokmeli, M. Saffar- Avval; Prediction of nanofluid convective heat transfer using the dispersion model, International Journal of Thermal Sciences 49 (2010) 471-478.

DOI: 10.1016/j.ijthermalsci.2009.09.005

Google Scholar

[13] A.V. Kuznetsov, D.A. Nield; Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences 49 (2010) 243-247.

DOI: 10.1016/j.ijthermalsci.2009.07.015

Google Scholar

[14] A.V. Kuznetsov, D.A. Nield; Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences 50 (2011) 712-717.

DOI: 10.1016/j.ijthermalsci.2011.01.003

Google Scholar

[15] D.A. Nield, A.V. Kuznetsov; The Cheng–Minkowycz problem for natural convective boundary-layer flow in a porous medium saturated by a nanofluid, International Journal of Heat and Mass Transfer 52 (2009) 5792–5795.

DOI: 10.1016/j.ijheatmasstransfer.2009.07.024

Google Scholar

[16] D.A. Nield, A.V. Kuznetsov; The Cheng–Minkowycz problem for the double-diffusive natural convective boundary layer flow in a porous medium saturated by a nanofluid, International Journal of Heat and Mass Transfer 54 (2011) 374–378.

DOI: 10.1016/j.ijheatmasstransfer.2010.09.034

Google Scholar

[17] B. Mahanthesh, J. Mackolil; Flow of nanoliquid past a vertical plate with novel quadratic thermal radiation and quadratic Boussinesq approximation: sensitivity analysis, International Communications in Heat and Mass Transfer 120 (2021) 105040.

DOI: 10.1016/j.icheatmasstransfer.2020.105040

Google Scholar

[18] A.V. Kuznetsov, D.A. Nield; Natural convective boundary-layer flow of a nanofluid past a vertical plate: A revised model, International Journal of Thermal Sciences 77 (2014) 126-129.

DOI: 10.1016/j.ijthermalsci.2013.10.007

Google Scholar

[19] A.V. Kuznetsov, D.A. Nield; The Cheng–Minkowycz problem for natural convective boundary layer flow in a porous medium saturated by a nanofluid: A revised model, International Journal of Heat and Mass Transfer 65 (2013) 682–685.

DOI: 10.1016/j.ijheatmasstransfer.2013.06.054

Google Scholar

[20] D.A. Nield, A.V. Kuznetsov; Thermal instability in a porous medium layer saturated by a nanofluid: A revised model, International Journal of Heat and Mass Transfer 68 (2014) 211–214.

DOI: 10.1016/j.ijheatmasstransfer.2013.09.026

Google Scholar

[21] M. Khan, W. A. Khan; MHD boundary layer flow of a power-law nanofluid with new mass flux condition, AIP Advances 6.2 (2016) 025211.

DOI: 10.1063/1.4942201

Google Scholar

[22] N.A. Halim, U.H Rizwan, N. F. M. Noor; Active and passive controls of nanoparticles in Maxwell stagnation point flow over a slipped stretched surface, Meccanica 52.7 (2017) 1527-1539.

DOI: 10.1007/s11012-016-0517-9

Google Scholar

[23] K.U. Rehman, M. Awais, A. Hussain, N. Kousar, M. Y. Malik; Mathematical analysis on MHD Prandtl‐Eyring nanofluid new mass flux conditions, Mathematical Methods in the Applied Sciences 42 (1) (2019) 24-38.

DOI: 10.1002/mma.5319

Google Scholar

[24] F. Awad, N.A.H. Haroun, P. Sibanda, M. Khumalo; On couple stress effects on unsteady nanofluid flow over stretching surfaces with vanishing nanoparticle flux at the wall, Journal of Applied Fluid Mechanics 9.4 (2016) 1937-1944.

DOI: 10.18869/acadpub.jafm.68.235.24940

Google Scholar

[25] M. Ahmad, S.A. Shehzad, A. Iqbal, A., M. Taj; Time-dependent three-dimensional Oldroyd-B nanofluid flow due to bidirectional movement of surface with zero mass flux, Advances in Mechanical Engineering, 12(4) (2020) 1687814020913783.

DOI: 10.1177/1687814020913783

Google Scholar

[26] M. Abd El-Aziz, A. A. Afify; Effect of Hall current on MHD slip flow of Casson nanofluid over a stretching sheet with zero nanoparticle mass flux, Thermophysics and Aeromechanics 26.3 (2019) 429-443.

DOI: 10.1134/s0869864319030119

Google Scholar

[27] B. Mahanthesh, S.A. Shehzad, J. Mackolil, N.S. Shashikumar; Heat transfer optimization of hybrid nanomaterial using modified Buongiorno model: A sensitivity analysis, International Journal of Heat and Mass Transfer 171 (2021) 121081.

DOI: 10.1016/j.ijheatmasstransfer.2021.121081

Google Scholar

[28] A.M. Bouaziz, S. Hanini; Double dispersion for double diffusive boundary layer in non-Darcy saturated porous medium filled by a nanofluid, Journal of Mechanics 32.4 (2016) 441-451.

DOI: 10.1017/jmech.2016.18

Google Scholar

[29] O.D Makinde, A. Aziz; MHD mixed convection from a vertical plate embedded in porous medium with a convective boundary condition, International Journal of Thermal Sciences 49 (2010) 1813-1820.

DOI: 10.1016/j.ijthermalsci.2010.05.015

Google Scholar

[30] J.C Butcher, Numerical methods for ordinary differential equations, John Wiley & Sons, (2016).

Google Scholar

[31] J. Kierzenka, L.F.A Shampine; A BVP solver based on residual control and the Maltab PSE, ACM Transactions on Mathematical Software (TOMS) 27 3 (2001) 299-316.

DOI: 10.1145/502800.502801

Google Scholar