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  4. Radiative flow of magnetic nanofluids over a moving surface with convective boundary condition

Radiative flow of magnetic nanofluids over a moving surface with convective boundary condition

MMC.
2022;
Volume 9, Number 4
: pp. 791–804
https://doi.org/10.23939/mmc2022.04.791
Received: August 11, 2022
Accepted: September 04, 2022

Mathematical Modeling and Computing, Vol. 9, No. 4, pp. 791–804 (2022)

Authors:
  1. N. S. Wahid
  2. N. M. Arifin
  3. N. S. Khashi'ie
  4. I. Pop
  5. N. Bachok
  6. M. E. H. Hafidzuddin
1
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia
2
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia; Institute for Mathematical Research, Universiti Putra Malaysia
3
Fakulti Teknologi Kejuruteraan Mekanikal dan Pembuatan, Universiti Teknikal Malaysia Melaka
4
Department of Mathematics, Babeş-Bolyai University; Academy of Romanian Scientists
5
Department of Mathematics and Statistics, Faculty of Science, Universiti Putra Malaysia; Institute for Mathematical Research, Universiti Putra Malaysia
6
Centre of Foundation Studies for Agricultural Science, Universiti Putra Malaysia

The influence of convective boundary conditions and heat radiation on magnetic nanofluids (MNFs) flowing through a permeable moving plate is investigated numerically in this study.  The governing partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs) using suitable similarity variables.  The ODEs are solved by implementing the built-in solver in Matlab called bvp4c.  The stability analysis has supported our initial presumption that only the first solution is stable.  The thermal performance between cobalt ferrite nanofluid and manganese-zinc ferrite nanofluid is compared, and it appears that cobalt ferrite nanofluid has a slightly better performance in heat transportation compared to manganese-zinc ferrite nanofluid.  We also considered a higher amount of thermal radiation and Biot number to scrutinize the heat transfer performance of MNF, and we found out that a greater amount of these parameters are effective in improving the heat transfer rate.

nanofluid
thermal radiation
moving surface
suction
convective boundary condition
stability analysis
  1. Moutsoglou A., Bhattacharya A. K.  Laminar and Turbulent Boundary Layers on Moving, Nonisothermal Continuous Flat Surfaces.  Journal of Heat Transfer.  104 (4), 707–714 (1982).
  2. Das K.  Radiation and melting effects on MHD boundary layer flow over a moving surface.  Ain Shams Engineering Journal.  5 (4), 1207–1214 (2014).
  3. Sakiadis B. C.  Boundary-layer behavior on continuous solid surfaces: I. Boundary-layer equations for two-dimensional and axisymmetric flow.  AIChE Journal.  7 (1), 26–28 (1961).
  4. Sakiadis B. C.  Boundary-layer behavior on continuous solid surfaces: II. The boundary layer on a continuous flat surface.  AIChE Journal.  7 (2), 221–225 (1961).
  5. Chappidi P. R., Gunnerson F. S.  Analysis of heat and momentum transport along a moving surface.  International Journal of Heat and Mass Transfer.  32 (7), 1383–1386 (1989).
  6. Afzal N.  Turbulent boundary layer on a moving continous plate.  Fluid Dynamics Research.  17 (4), 181–194 (1996).
  7. Howell T. G., Jeng D. R., De Witt K. J.  Momentum and heat transfer on a continuous moving surface in a power law fluid.  International Journal of Heat and Mass Transfer.  40 (8), 1853–1861 (1997).
  8. Weidman P. D., Kubitschek D. G., Davis A. M. J.  The effect of transpiration on self-similar boundary layer flow over moving surfaces.  International Journal of Engineering Science.  44 (11–12), 730–737 (2006).
  9. Ishak A., Nazar R., Bachok N., Pop I.  Melting heat transfer in steady laminar flow over a moving surface.  Heat and Mass Transfer.  46, 463–468 (2010).
  10. Subhashini S. V., Sumathi R.  Dual solutions of a mixed convection flow of nanofluids over a moving vertical plate.  International Journal of Heat and Mass Transfer.  71, 117–124 (2014).
  11. Das S., Jana R. N.  Natural convective magneto-nanofluid flow and radiative heat transfer past a moving vertical plate.  Alexandria Engineering Journal.  54 (1), 55–64 (2015).
  12. Aladdin N. A. L., Bachok N., Pop I.  Cu-Al$_2$O$_3$/water hybrid nanofluid flow over a permeable moving surface in presence of hydromagnetic and suction effects. Alexandria Engineering Journal.  59 (2), 657–666 (2020).
  13. Waini I., Ishak A., Pop I.  Flow and heat transfer of a hybrid nanofluid past a permeable moving surface.  Chinese Journal of Physics.  66, 606–619 (2020).
  14. Khashi'ie N. S., Arifin N. M., Pop I., Nazar R.  Melting heat transfer in hybrid nanofluid flow along a moving surface.  Journal of Thermal Analysis and Calorimetry.  147, 567–578 (2022).
  15. Anuar N. S., Bachok N., Arifin N. M., Rosali H.  Role of multiple solutions in flow of nanofluids with carbon nanotubes over a vertical permeable moving plate.  Alexandria Engineering Journal.  59 (2), 763–773 (2020).
  16. Wahid N. S., Arifin N. M., Khashi'ie N. S., Pop I., Bachok N., Hafidzuddin M. E. H.  Flow and heat transfer of hybrid nanofluid induced by an exponentially stretching/shrinking curved surface.  Case Studies in Thermal Engineering.  25, 100982 (2021).
  17. Khashi'ie N. S., Arifin N. M., Pop I., Nazar R.  Thermal Marangoni Flow Past a Permeable Stretching/Shrinking Sheet in a Hybrid Cu-Al$_2$O$_3$/Water Nanofluid.  Sains Malaysiana.  49 (1), 211–222 (2020).
  18. Khashi'ie N. S., Arifin N. M., Pop I., Nazar R., Hafidzuddin E. H., Wahi N.  Flow and heat transfer past a permeable power-law deformable plate with orthogonal shear in a hybrid nanofluid.  Alexandria Engineering Journal.  59 (3), 1869–1879 (2020).
  19. Khashi'ie N. S., Wahi N., Arifin N. M., Ghani A. A., Hamzah K. B.  Effect of suction on the MHD flow in a doubly-stratified micropolar fluid over a shrinking sheet.  Mathematical Modeling and Computing.  9 (1), 92–100 (2022).
  20. Hussein A. M., Sharma K. V., Bakar R. A., Kadirgama K.  A review of forced convection heat transfer enhancement and hydrodynamic characteristics of a nanofluid.  Renewable and Sustainable Energy Reviews.  29, 734–743 (2014).
  21. Moita A., Moreira A., Pereira J.  Nanofluids for the Next Generation Thermal Management of Electronics: A Review.  Symmetry.  13 (8), 1362 (2021).
  22. Genc S., Derin B.  Synthesis and rheology of ferrofluids: a review.  Current Opinion in Chemical Engineering.  3, 118–124 (2014).
  23. Odenbach S.  Recent progress in magnetic fluid research.  Journal of Physics: Condensed Matter.  16 (32), R1135–R1150 (2004).
  24. Khan W. A., Khan Z. H., Haq R. U.  Flow and heat transfer of ferrofluids over a flat plate with uniform heat flux.  The European Physical Journal Plus.  130, 86 (2015).
  25. Raj K., Moskowitz R.  Commercial applications of ferrofluids.  Journal of Magnetism and Magnetic Materials.  85 (1–2), 233–245 (1990).
  26. Marszałł M. P.  Application of Magnetic Nanoparticles in Pharmaceutical Sciences.  Pharmaceutical Research.  28, 480–483 (2011).
  27. Kumar A., Subudhi S.  Preparation, characteristics, convection and applications of magnetic nanofluids: A review.  Heat and Mass Transfer.  54, 241–265 (2018).
  28. Kole M., Khandekar S.  Engineering applications of ferrofluids: A review.  Journal of Magnetism and Magnetic Materials.  537, 168222 (2021).
  29. Rashad A. M.  Impact of anisotropic slip on transient three dimensional MHD flow of ferrofluid over an inclined radiate stretching surface.  Journal of the Egyptian Mathematical Society.  25 (2), 230–237 (2017).
  30. Sampath Kumar P. B., Gireesha B. J., Mahanthesh B., Gorla R. S. R.  Radiative nonlinear 3D flow of ferrofluid with Joule heating, convective condition and Coriolis force.  Thermal Science and Engineering Progress.  3, 88–94 (2017).
  31. Hassan M., Fetecau C., Majeed A., Zeeshan A.  Effects of iron nanoparticles' shape on convective flow of ferrofluid under highly oscillating magnetic field over stretchable rotating disk.  Journal of Magnetism and Magnetic Materials.  465, 531–539 (2018).
  32. Shafii M. B., Keshavarz M.  Experimental study of internal forced convection of ferrofluid flow in non-magnetizable/magnetizable porous media.  Experimental Thermal and Fluid Science.  96, 441–450 (2018).
  33. Özdemir M. R., Sadaghiani A. K., Motezakker A. R., Parapari S. S., Park H. S., Acar H. Y., Koşar A.  Experimental studies on ferrofluid pool boiling in the presence of external magnetic force.  Applied Thermal Engineering.  139, 598–608 (2018).
  34. Zhang X., Zhang Y.  Experimental study on enhanced heat transfer and flow performance of magnetic nanofluids under alternating magnetic field.  International Journal of Thermal Sciences.  164, 106897 (2021).
  35. Lee A., Jeon Y., Chinnasamy V., Cho H.  Investigation of forced convective heat transfer with magnetic field effect on water/ethylene glycol-cobalt zinc ferrite nanofluid.  International Communications in Heat and Mass Transfer.  128, 105647 (2021).
  36. Wahid N. S., Arifin N. M., Khashi'ie N. S., Pop I., Bachok N., Hafidz Hafidzuddin M. E.  Mixed Convection Magnetic Nanofluid Flow past a Rotating Vertical Porous Cone.  Journal of Applied Fluid Mechanics.  15 (4), 1207–1220 (2022).
  37. Ho C. J., Liu W. K., Chang Y. S., Lin C. C.  Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: An experimental study.  International Journal of Thermal Sciences.  49 (8), 1345–1353 (2010).
  38. Merkin J. H.  On dual solutions occurring in mixed convection in a porous medium.  Journal of Engineering Mathematics.  20, 171–179 (1986).
  39. Harris S. D., Ingham D. B., Pop I.  Mixed Convection Boundary-Layer Flow Near the Stagnation Point on a Vertical Surface in a Porous Medium: Brinkman Model with Slip.  Transport in Porous Media.  77, 267–285 (2009).
  40. Kameswaran P. K., Sibanda P., Murti A. S. N.  Nanofluid Flow over a Permeable Surface with Convective Boundary Conditions and Radiative Heat Transfer.  Mathematical Problems in Engineering.  2013, 201219 (2013).
  41. Sheremet M. A., Pop I., Rosca A. V.  The influence of thermal radiation on unsteady free convection in inclined enclosures filled by a nanofluid with sinusoidal boundary conditions.  International Journal of Numerical Methods for Heat & Fluid Flow.  28 (8), 1738–1753 (2018).
  42. Ahmed N., Tassaddiq A., Alabdan R., Khan U., Noor S., Mohyud-Din S. T., Khan I.  Applications of Nanofluids for the Thermal Enhancement in Radiative and Dissipative Flow over a Wedge.  Applied Sciences.  9 (10), 1976 (2019).
  43. Rosseland S.  Astrophysik auf Atomtheoretischer Grundlage. Springer Berlin, Heidelberg (1931).
  44. Bataller R. C.  Radiation effects in the Blasius flow.  Applied Mathematics and Computation.  198 (1), 333–338 (2008).
  45. Cortell R.  Effects of viscous dissipation and radiation on the thermal boundary layer over a nonlinearly stretching sheet.  Physics Letters A.  372 (5), 631–636 (2008).
  46. Ishak A.  Thermal boundary layer flow over a stretching sheet in a micropolar fluid with radiation effect.  Meccanica.  45, 367–373 (2010).
  47. Ishak A., Yacob N. A., Bachok N.  Radiation effects on the thermal boundary layer flow over a moving plate with convective boundary condition.  Meccanica.  46, 795–801 (2011).
  48. Magyari E., Pantokratoras A.  Note on the effect of thermal radiation in the linearized Rosseland approximation on the heat transfer characteristics of various boundary layer flows.  International Communications in Heat and Mass Transfer.  38 (5), 554–556 (2011).
  49. Khashi'ie N. S., Arifin N. M., Pop I.  Magnetohydrodynamics (MHD) boundary layer flow of hybrid nanofluid over a moving plate with Joule heating.  Alexandria Engineering Journal.  61 (3), 1938–1945 (2022).
  50. Zainal N. A., Nazar R., Naganthran K., Pop I.  MHD flow and heat transfer of hybrid nanofluid over a permeable moving surface in the presence of thermal radiation.  International Journal of Numerical Methods for Heat & Fluid Flow.  31 (3), 858–879 (2021).
  51. Mohd Rohni A., Ahmad S., Pop I.  Boundary layer flow over a moving surface in a nanofluid beneath a uniform free stream.  International Journal of Numerical Methods for Heat & Fluid Flow.  21 (7), 828–846 (2011).