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MHD Buoyancy Flow of Nanofluids over an Inclined Plate Immersed in Uniform Porous Medium in the Presence of Solar Radiation

Published online by Cambridge University Press:  14 April 2019

Z. Z. Rashed
Affiliation:
Mathematics Department Faculty of Science and ArtsJouf UniversityQurayyatSaudi Arabia
S. E. Ahmed*
Affiliation:
Department of Mathematics Faculty of Science for GirlsKing Khalid UniversityAbhaSaudi Arabia
M. A. Sheremet
Affiliation:
Laboratory on Convective Heat and Mass TransferTomsk State UniversityRussia
*
*Corresponding author (sameh.hassan@sci.svu.edu.eg)
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Abstract

Free convective flow and heat transfer of nanofluid close to the inclined plate immersed in the porous medium under the effects of uniform magnetic field and solar radiation has been studied. Boundary-layer approach, Boussinesq approximation and two-phase nanofluid model have been used for a formulation of the governing equations taking into account convective-radiative heat exchange with an environment. The local similarity method has been adopted for the analysis of the considered phenomenon. The obtained equations have been solved numerically using MATLAB software. The effects of control characteristics on profiles of velocity, temperature and nanoparticles volume fraction as well as Nusselt number have been studied in detail.

Type
Research Article
Copyright
© The Society of Theoretical and Applied Mechanics 2018 

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References

REFERENCES

Nield, D. A. and Bejan, A., Convection in Porous Media, Springer, New York, 3rd Edition (2006).Google Scholar
Ingham, D. B. and Pop, I. Transport Phenomena in Porous Media, Pergamon Press, Oxford, Vol. II (2002).Google Scholar
Shenoy, A., Sheremet, M. and Pop, I., Convective Flow and Heat Transfer from Wavy Surfaces: Viscous Fluids, Porous Media and Nanofluids, 1st Edition, CRC Press, Boca Raton, Florida, U.S.A. (2016).CrossRefGoogle Scholar
Choi, U. S. and Eastman, J. A., Enhancing Thermal Conductivity of Fluids with Nanoparticles, American Society of Mechanical Engineers, Fluids Engineering Division, New York, U.S.A, 231, pp. 99105 (1995).Google Scholar
Buongiorno, J., “Convective Transport in Nanofluids,” Journal of Heat Transfer, 128, pp. 240250 (2006).CrossRefGoogle Scholar
Nield, D. A. and Kuznetsov, A. V., “The Cheng-Minkowycz Problem for Natural Convection Boundary-Layer Flow in a Porous Medium Saturated by a Nanofluid,” International Journal of Heat and Mass Transfer, 52, pp. 57925795 (2009).CrossRefGoogle Scholar
Cheng, P. and Minkowycz, W. J., “Free Convection about a Vertical Flat Plate Embedded in a Porous Medium with Application to Heat Transfer from a Dike,” Journal of Geophysical Research, 82, pp. 20402044 (1977).CrossRefGoogle Scholar
Kuznetsov, A. V. and Nield, D. A., “Natural Convective Boundary-Layer Flow of a Nanofluid past a Vertical Plate,” International Journal of Thermal Sciences, 49, pp. 243247 (2010).CrossRefGoogle Scholar
Kuznetsov, A. V. and Nield, D A., “Double-Diffusive Natural Convective Boundary-Layer Flow of a Nanofluid past a Vertical Plate,” International Journal of Thermal Sciences, 50, pp. 712717 (2011).CrossRefGoogle Scholar
Khan, W. A. and Aziz, A., “Natural Convection Flow of a Nanofluid over a Vertical Plate with Uniform Surface Heat Flux,” International Journal of Thermal Sciences, 50, pp. 12071214 (2011).CrossRefGoogle Scholar
Khan, W. A. and Aziz, A., “Double-Diffusive Natural Convective Boundary Layer Flow in a Porous Medium Saturated with a Nanofluid over a Vertical Plate: Prescribed Surface Heat, Solute and Nanoparticle Fluxes,” International Journal of Thermal Sciences, 50, pp. 21542160 (2011).CrossRefGoogle Scholar
Aziz, A. and Khan, W. A., “Natural Convective Boundary Layer Flow of a Nanofluid past a Convectively Heated Vertical Plate,” International Journal of Thermal Sciences, 52, pp. 8390 (2012).CrossRefGoogle Scholar
Gorla, R. S. R. and Chamkha, A., “Natural Convective Boundary Layer Flow over a Non-Isothermal Vertical Plate Embedded in a Porous Medium Saturated with a Nanofluid,” Nanoscale Microscale Thermophysical Engineering, 15, pp. 8194 (2011).CrossRefGoogle Scholar
Noghrehabadi, A., Behseresht, A. and Ghalambaz, M., “Natural Convection of Nanofluid over Vertical Plate Embedded in Porous Medium: Prescribed Surface Heat Flux,” Applied Mathematics and Mechanics (English Edition), 34, pp. 669686 (2013).CrossRefGoogle Scholar
Srinivasacharya, D. and Kumar, P. V., “Free Convection of a Nanofluid over an Inclined Wavy Surface Embedded in a Porous Medium with Wall Heat Flux,” Procedia Engineering, 127, pp. 4047 (2015).CrossRefGoogle Scholar
Sheikholeslami, M., Hatami, M. and Domairry, G., “Numerical Simulation of Two Phase Unsteady Nanofluid Flow and Heat Transfer between Parallel Plates in Presence of Time Dependent Magnetic Field,” Journal of the Taiwan Institute of Chemical Engineers, 46, pp. 4350 (2015).CrossRefGoogle Scholar
Sheikholeslami, M. and Ganji, D. D., “Nanofluid Flow and Heat Transfer between Parallel Plates Considering Brownian Motion Using DTM,” Computer Methods in Applied Mechanics and Engineering, 283, pp. 651663 (2015).CrossRefGoogle Scholar
Balazadeh, N., Sheikholeslami, M., Ganji, D. D. and Li, Z., “Semi Analytical Analysis for Transient Eyring-Powell Squeezing Flow in a Stretching Channel Due to Magnetic Field Using DTM,” Journal of Molecular Liquids, 260, pp. 3036 (2018).CrossRefGoogle Scholar
Ghalambaz, M., Noghrehabad, A. and Ghanbarzadeh, A., “Natural Convection of Nanofluids over a Convectively Heated Vertical Plate Embedded in a Porous Medium,” Brazilian Journal of Chemical Engineering, 31, pp. 413427 (2014).CrossRefGoogle Scholar
Rana, P., Bhargava, R. and Beg, O. A., “Numerical Solution for Mixed Convection Boundary Layer Flow of a Nanofluid Along an Inclined Plate Embedded in a Porous Medium,” Computers & Mathematics with Applications, 64, pp. 28162832 (2012).CrossRefGoogle Scholar
Ahmad, S. and Pop, I., “Mixed Convection Boundary Layer Flow from a Vertical Flat Plate Embedded in a Porous Medium Filled with Nanofluids,” International Communications in Heat and Mass Transfer, 37, pp. 987991 (2010).CrossRefGoogle Scholar
Srinivasacharya, D. and Surender, O., “Non-Similar Solution for Natural Convective Boundary Layer Flow of a Nanofluid past a Vertical Plate Embedded in a Doubly Stratified Porous Medium,” International Journal of Heat and Mass Transfer, 71, pp. 431438 (2014).CrossRefGoogle Scholar
Khan, Z. H., Culham, J. R., Khan, W. A. and Pop, I., “Triple Convective-Diffusion Boundary Layer along a Vertical Flat Plate in a Porous Medium Saturated by a Water-Based Nanofluid,” International Journal of Thermal Sciences, 90, pp. 5361 (2015).CrossRefGoogle Scholar
Mansour, M. A. and Ahmed, S. E., “A Numerical Study on Natural Convection in Porous Media-Filled an Inclined Triangular Enclosure with Heat Sources Using Nanofluid in the Presence of Heat Generation Effect,” Engineering Science and Technology, an International Journal, 18, pp. 485495 (2015).CrossRefGoogle Scholar
Bondareva, N. S., Sheremet, M. A., Oztop, H. F. and Abu-Hamdeh, N., “Heatline Visualization of MHD Natural Convection in an Inclined Wavy Open Porous Cavity Filled with a Nanofluid with a Local Heater,” International Journal of Heat and Mass Transfer, 99, pp. 872881 (2016).CrossRefGoogle Scholar
Sheremet, M. A. and Pop, I., “Natural Convection in a Square Porous Cavity with Sinusoidal Temperature Distributions on Both Side Walls Filled with a Nanofluid: Buongiorno's Mathematical Model,” Transport in Porous Media, 105, pp. 411429 (2014).CrossRefGoogle Scholar
Sheikholeslami, M., Chamkha, A. J., Rana, P. and Moradi, R., “Combined Thermophoresis and Brownian Motion Effects on Nanofluid Free Convection Heat Transfer in an L-Shaped Enclosure,” Chinese Journal of Physics, 55, pp. 23562370 (2017).CrossRefGoogle Scholar
Sheikholeslami, M. and Ghasemi, A., “Solidification Heat Transfer of Nanofluid in Existence of Thermal Radiation by Means of FEM,” International Journal of Heat and Mass Transfer, 123, pp. 418431 (2018).CrossRefGoogle Scholar
Sheikholeslami, M., Li, Z. and Shamlooei, M., “Nanofluid MHD Natural Convection through a Porous Complex Shaped Cavity Considering Thermal Radiation,” Physics Letters A, 382, pp. 16151632 (2018).CrossRefGoogle Scholar
Murthy, P. V. S. N., Ram Reddy, Ch., Chamkha, A. J. and Rashad, A. M., “Magnetic Effect on Thermally Stratified Nanofluid Saturated Non-Darcy Porous Medium under Convective Boundary Condition,” International Communications in Heat and Mass Transfer, 47, pp. 4148 (2013).CrossRefGoogle Scholar
Reddy, J. V. R., Sugunamma, V., Sandeep, N. and Sulochana, C., “Influence of Chemical Reaction, Radiation and Rotation on MHD Nanofluid Flow past a Permeable Flat Plate in Porous Medium,” Journal of the Nigerian Mathematical Society, 35, pp. 4865 (2016).CrossRefGoogle Scholar
Reddy, P. S., Chamkha, A. J. and Al-Mudhaf, A., “MHD Heat and Mass Transfer Flow of a Nanofluid over an Inclined Vertical Porous Plate with Radiation and Heat Generation/Absorption,” Advanced Powder Technology, 28, pp. 10081017 (2017).CrossRefGoogle Scholar
Sheikholeslami, M., “Numerical Simulation of Magnetic Nanofluid Natural Convection in Porous Media,” Physics Letters, A381, pp. 494503 (2017).CrossRefGoogle Scholar
Shit, G. C., Haldar, R. and Mandal, S., “Entropy Generation on MHD Flow and Convective Heat Transfer in a Porous Medium of Exponentially Stretching Surface Saturated by Nanofluids”, Advanced Powder Technology, 28, pp. 15191530 (2017).CrossRefGoogle Scholar
Sheikholeslami, M. and Shehzad, S. A., “CVFEM Simulation for Nanofluid Migration in a Porous Medium Using Darcy Model,” International Journal of Heat and Mass Transfer, 122, pp. 12641271 (2018).CrossRefGoogle Scholar
Sheikholeslami, M. and Shehzad, S. A., “Simulation of Water Based Nanofluid Convective Flow Inside a Porous Enclosure via Non-Equilibrium Model,” International Journal of Heat and Mass Transfer, 120, pp. 12001212 (2018).CrossRefGoogle Scholar
Fathalah, K. A. and Elsayed, M. M., “Natural Convection Due to Solar Radiation over a Non- Absorbing Plate with and Without Heat Losses”, International Journal of Heat and Fluid Flow, 2, pp. 4145 (1980).CrossRefGoogle Scholar
Chamkha, A. J., “Solar Radiation Assisted Natural Convection in a Uniform Porous Medium Supported by a Vertical Flat Plate,” Journal of Heat Transfer, 119, pp. 8996 (1997).CrossRefGoogle Scholar
Chamkha, A. J., Issa, C. and Khanafer, K., “Natural Convection from an Inclined Plate Embedded in a Variable Porosity Porous Medium Due to Solar Radiation,” International Journal of Thermal Sciences, 41, pp. 7381 (2002).CrossRefGoogle Scholar
Kandasamy, R., Muhaimin, I. and Mohamad, R., “Thermophoresis and Brownian Motion Effects on MHD Boundary-Layer Flow of a Nanofluid in the Presence of the Thermal Dtratification Due to Solar Radiation,” International Journal of Mechanical Sciences, 70, pp. 146154 (2013).CrossRefGoogle Scholar
Acharya, N., Das, K. and Kundu, P. K., “Framing the Effects of Solar Radiation on Magneto-Hydrodynamics Bioconvection Nanofluid Flow in Presence of Gyrotactic Microorganisms,” Journal of Molecular Liquids, 222, pp. 2837 (2016).CrossRefGoogle Scholar
Hayat, T., Waqas, M., Shehzad, S. A. and Alsaedi, A., “A Model of Solar Radiation and Joule Heating in MagnetohyDrodynamic (MHD) Convective Flow of Thixotropic Nanofluid,” Journal of Molecular Liquids, 215, pp. 704710 (2016).CrossRefGoogle Scholar
Sparrow, E. M. and Yu, H. S., “Local Non-Similarity Thermal Boundary-Layer Solutions,” Journal of Heat Transfer, 93, pp. 328334 (1971).CrossRefGoogle Scholar