Abstract
The combined impact of solar radiation, chemical reaction, Joule heating, viscous dissipation and magnetic field on flow of an electrically conducting nanofluid over a convectively heated stretching sheet embedded in a saturated porous medium is simulated. By using appropriate similarity transformation, the governing nonlinear equations are converted into ODEs and numerical shooting technique with (RK45) method is employed to tackle the problem. The effects of various thermo-physical parameters on the entire flow structure with heat and mass transfer are presented graphically and discussed quantitatively. Special cases of our results are benchmarked with some of those obtained earlier in the literature and are found to be in excellent agreement. It is found that both the temperature and surface concentration gradients are increasing functions of the non-Darcy porous medium parameter. One describing result is the incident solar radiation absorption and its transmission into the working nanofluid by convection.
Compliance with ethical standards
Conflict of interest The authors declare that they have no conflict of interest.
References
Angstrom, A.K. 1924. “Solar and Atmospheric Radiation.” Journal of Roy Meteorol Social 50: 121–127.10.1002/qj.49705021008Search in Google Scholar
Birkoff, G. 1960. Hydrodynamics. New Jersey: Princeton University Press.Search in Google Scholar
Brewster, M. Q. 1972. Thermal Radiative Transfer Properties. New York: John Wiley and Sons.Search in Google Scholar
Chamkha, A.J., and C. Issa. 2000. “Effects of Heat Generation or Absorption and Thermophoresis on Hydromagnetic Flow with Heat and Mass Transfer over a Flat Surface.” International Journal Numerical Method Heat Fluid Flow 10: 432–449.10.1108/09615530010327404Search in Google Scholar
Cheng, W.T., and H.T. Lin. 2002. “Non-Similarity Solution and Correlation of Transient Heat Transfer in Laminar Boundary Layer Flow over a Wedge.” International Journal Engineering Sciences 40: 531–540.10.1016/S0020-7225(01)00081-7Search in Google Scholar
Choi, S.U.S. 1995. “Enhancing Thermal Conductivity of Fluids with Nanoparticles.” In Developments and Applications of Non-Newtonian Flows, FED-Vol. 231, MD-Vol. 66, Eds. D.A. Siginer and H.P. Wang, 99–105. ASME.Search in Google Scholar
Eid, M.R. 2016. “Chemical Reaction Effect on MHD Boundary-Layer Flow of Two-Phase Nanofluid Model over an Exponentially Stretching Sheet with a Heat Generation.” Journal of Molecular Liquid 220: 718–725.10.1016/j.molliq.2016.05.005Search in Google Scholar
Eid, M.R., S.M. Abdel-Gaied, and A.A. Idarous. 2015. “On Effectiveness Chemical Reaction on Viscous Flow of a non-Darcy Nanofluid over a Non-Linearly Stretching Sheet in a Porous Medium.” Jokull Journal 65 (12): 76–92.Search in Google Scholar
Eid, M. R., A. Alsaedi, T. Muhammad, and T. Hayat. 2017. “Comprehensive Analysis of Heat Transfer of Gold-Blood Nanofluid (Sisko-Model) with Thermal Radiation.” Results Physical 7: 4388–4393.10.1016/j.rinp.2017.11.004Search in Google Scholar
Eid, M.R., and K.L. Mahny. 2017. “Unsteady MHD Heat and Mass Transfer of a non-Newtonian Nanofluid Flow of a Two-Phase Model over a Permeable Stretching Wall with Heat Generation/Absorption.” Advancement Powder Technological 28 (11): 3063–3073.10.1016/j.apt.2017.09.021Search in Google Scholar
Eid, M.R., K.L. Mahny, T. Muhammad, and M. Sheikholeslami. 2018. “Numerical Treatment for Carreau Nanofluid Flow over a Porous Nonlinear Stretching Surface.” Results Physical 8: 1185–1193.10.1016/j.rinp.2018.01.070Search in Google Scholar
Eid, M. R., and S.R. Mishra. 2017. “Exothermically Reacting of non-Newtonian Fluid Flow over a Permeable Non-Linear Stretching Vertical Surface with Heat and Mass Fluxes.” Computation Therm Sciences 9 (4): 283–296.10.1615/ComputThermalScien.2017020298Search in Google Scholar
Gnaneswara Reddy, M., K. Venugopal Reddy, and O.D. Makinde. 2016. “Hydromagnetic Peristaltic Motion of a Reacting and Radiating Couple Stress Fluid in an Inclined Asymmetric Channel Filled with a Porous Medium.” Alex Engineering Journal 55 (2): 1841–1853.10.1016/j.aej.2016.04.010Search in Google Scholar
Hayat, T., A. Aziz, T. Muhammad, and A. Alsaedi. 2016. “On Magnetohydrodynamic Three-Dimensional Flow of Nanofluid over a Convectively Heated Nonlinear Stretching Surface.” International Journal Heat Massachusetts Transfer 100: 566–572.10.1016/j.ijheatmasstransfer.2016.04.113Search in Google Scholar
Hayat, T., F. Haider, T. Muhammad, and A. Alsaedi. 2017a. “On Darcy-Forchheimer Flow of Viscoelastic Nanofluids: A Comparative Study.” Journal of Molecular Liquid 233: 278–287.10.1016/j.molliq.2017.03.035Search in Google Scholar
Hayat, T., M.I. Khan, S. Qayyum, and A. Alsaedi. 2017b. “Modern Developments about Statistical Declaration and Probable Error for Skin Friction and Nusselt Number with Copper and Silver Nanoparticles.” Chinese Journal of Physics 55 (6): 2501–2513.10.1016/j.cjph.2017.08.028Search in Google Scholar
Hayat, T., M.I. Khan, S. Qayyum, and A. Alsaedi. 2018. “Entropy Generation in Flow with Silver and Copper Nanoparticles.” Colloid Surf A: Physchem Engineering Aspe 539: 335–346.10.1016/j.colsurfa.2017.12.021Search in Google Scholar
Hayat, T., T. Muhammad, A. Alsaedi, and M. S. Alhuthali. 2015. “Magnetohydrodynamic Three-Dimensional Flow of Viscoelastic Nanofluid in the Presence of Nonlinear Thermal Radiation.” Journal Magnetic Magnetic Materials 385: 222–229.10.1016/j.jmmm.2015.02.046Search in Google Scholar
Hayat, T., S. Qayyum, M.I. Khan, and A. Alsaedi. 2017c. “Current Progresses about Probable Error and Statistical Declaration for Radiative Two Phase Flow Using AgH2O and CuH2O Nanomaterials.” International Journal Hydrogen Energy 42 (49): 29107–29120.10.1016/j.ijhydene.2017.09.124Search in Google Scholar
Hunt, A.J. 1978. “Small Particle Heat Exchangers.” Journal Renew Sustain Energy. Lawrence Berkeley laboratory report no. LBL-7841.10.2172/6070780Search in Google Scholar
Kafoussias, N.G., and N.D. Nanousis. 1977. “Magnetohydrodynamic Laminar Boundary Layer Flow over a Wedge with Suction or Injection.” Canad Journal Physical 75: 733–741.10.1139/p97-024Search in Google Scholar
Kandasamy, R., I. Muhaimin, and H. Ishak, Ruhaila. 2008. “Thermophoresis and Chemical Reaction Effects on non-Darcy Mixed Convective Heat and Mass Transfer past a Porous Wedge with Variable Viscosity in the Presence of Suction or Injection.” Nucl. Eng. Design 238: 2699–2705.10.1016/j.nucengdes.2008.05.010Search in Google Scholar
Keshavarz, M.M., and H. Majid. 2012. “Modeling of Turbulent Forced Convective Heat Transfer and Friction Factor in a Tube for Fe3O4 Magnetic Nanofluid with Computational Fluid Dynamics.” International Communicable Heat Massachusetts Transfer 39: 1293–1299.10.1016/j.icheatmasstransfer.2012.07.003Search in Google Scholar
Khan, M.I., S. Qayyum, T. Hayat, M. Waqas, M.I. Khan, and A. Alsaedi. 2018. “Entropy Generation Minimization and Binary Chemical Reaction with Arrhenius Activation Energy in MHD Radiative Flow of Nanomaterial.” Journal of Molecular Liquid 259: 274–283.10.1016/j.molliq.2018.03.049Search in Google Scholar
Makinde, O.D., and A. Aziz. 2011. “Boundary Layer Flow of a Nanofluid past a Stretching Sheet with a Convective Boundary Condition.” International Journal Therm Sciences 50: 1326–1332.10.1016/j.ijthermalsci.2011.02.019Search in Google Scholar
Makinde, O.D., and A.S. Eegunjobi. 2016. “Entropy Analysis of Thermally Radiating Magnetohydrodynamics Slip Flow of Casson Fluid in a Microchannel Filled with Saturated Porous Media.” Journal Porous Medica 19 (9): 799–810.10.1615/JPorMedia.v19.i9.40Search in Google Scholar
Makinde, O.D., W.A. Khan, and J.R. Culham. 2016. “MHD Variable Viscosity Reacting Flow over a Convectively Heated Plate in a Porous Medium with Thermophoresis and Radiative Heat Transfer.” International Journal Heat Massachusetts Transfer 93: 595–604.10.1016/j.ijheatmasstransfer.2015.10.050Search in Google Scholar
Masuda, H., A. Ebata, K. Teramae, and N. Hishinuma. 1993. “Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles.” Netsu Bussei (Japan) 7 (4): 227–233.10.2963/jjtp.7.227Search in Google Scholar
Muhammad, T., A. Alsaedi, T. Hayat, and S.A. Shehzad. 2017a. “A Revised Model for Darcy-Forchheimer Three-Dimensional Flow of Nanofluid Subject to Convective Boundary Condition.” Results Physical 7: 2791–2797.10.1016/j.rinp.2017.07.052Search in Google Scholar
Muhammad, T., A. Alsaedi, S.A. Shehzad, and T. Hayat. 2017b. “A Revised Model for Darcy-Forchheimer Flow of Maxwell Nanofluid Subject to Convective Boundary Condition.” Chinese Journal of Physics 55 (3): 963–976.10.1016/j.cjph.2017.03.006Search in Google Scholar
Mushtaq, A., M. Mustafa, T. Hayat, and A. Alsaedi. 2014. “Nonlinear Radiative Heat Transfer in the Flow of Nanofluid Due to Solar Energy: A Numerical Study.” Journal Taiwan Instit Chemical Engineering 45: 1176–1183.10.1016/j.jtice.2013.11.008Search in Google Scholar
Muthucumaraswamy, R. 2012. “Chemical Reaction Effects on Vertical Oscillating Plate with Variable Temperature.” Chemical Industrial Chemical Engineering Quart 16: 167–173.10.2298/CICEQ091231024MSearch in Google Scholar
Muthucumaraswamy, R., and K. Manivannan. 2011. “First Order Chemical Reaction on Isothermal Vertical Oscillating Plate with Variable Mass Diffusion.” International Journal Pure Applications Sciences Technological 3: 19–26.Search in Google Scholar
Nield, D. A., and A. Bejan. 2013. Convection in Porous Media, 3rd ed. New-York: Springer-Verlag.10.1007/978-1-4614-5541-7Search in Google Scholar
Qayyum, S., M.I. Khan, T. Hayat, and A. Alsaedi. 2018. “Comparative Investigation of Five Nanoparticles in Flow of Viscous Fluid with Joule Heating and Slip Due to Rotating Disk.” Physical B: Cond Matter 534: 173–183.10.1016/j.physb.2018.01.044Search in Google Scholar
Raptis, A. 1998. “Radiation and Free Convection Flow through a Porous Medium.” International Communicable Heat Massachusetts Transfer 25: 289–295.10.1016/S0735-1933(98)00016-5Search in Google Scholar
Sparrow, E. M., and R. D. Cess. 1978. Radiation Heat Transfer. Washington: Hemisphere.Search in Google Scholar
Yurusoy, M., and M. Pakdemirli. 1999. “Exact Solutions of Boundary Layer Equations of a Special non-Newtonian Fluid over a Stretching Sheet.” Mechanisms Researcher Communicable 26: 171–176.10.1016/S0093-6413(99)00009-9Search in Google Scholar
Yurusoy, M., M. Pakdemirli, and O.F. Noyan. 2001. “Lie Group Analysis of Creeping Flow of a Second Grade Fluid.” International Journal Non-Linear Mechanisms 36: 955–960.10.1016/S0020-7462(00)00060-3Search in Google Scholar
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Articles in the same Issue
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Articles in the same Issue
- Experiment and Dynamic Simulation of PIG Motion during Pigging Operation in a Slope Pipeline
- Solar Radiation Effect on a Magneto Nanofluid Flow in a Porous Medium with Chemically Reactive Species
- Mathematical Modeling of Ethane Cracking Furnace of Olefin Plant with Coke Formation Approach
- Entropy Generation and Activation Energy Impact on Radiative Flow of Viscous Fluid in Presence of Binary Chemical Reaction
- Exploration of Chemical Reaction Effects on Entropy Generation in Heat and Mass Transfer of Magneto-Jeffery Liquid
- Response Surface Methodology Optimization for Photodegradation of Methylene Blue in a ZnO Coated Flat Plate Continuous Photoreactor
- Modeling of Fluid Bed Reactor of Ethylene Di Chloride Production in Abadan Petrochemical Based on Three-Phase Hydrodynamic Model
- Optimization and Reaction Kinetics Studies on Copper-Cobalt Catalyzed Liquid Phase Hydrogenation of 5-Hydroxymethylfurfural to 2,5-Dimethylfuran
- Role of Fe(III) and Oxalic Acid in the photo-Fenton System for 3-Methylphenol Degradation in Aqueous Solution under Natural and Artificial Light
- Assessment of the Efficiency of Aliquat 336+Rice Bran Oil for Separation of Acrylic Acid from Aqueous Solution Using Reactive Extraction