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Effect of Magnetohydrodynamic Second Order Slip Flow Boundary Condition Coefficients on Flow in Parallel Plates

Yıl 2022, Sayı: 41, 23 - 30, 30.11.2022

Öz

In this study, the fully developed velocity profile in magnetohydrodynamic (MHD) flow between microparallel plates was analyzed analytically using all the second-order slipvelocity boundary conditions available in the literature. The heat flux is assumed to be constant. The magnetic field acts perpendicular to the plate surface. The momentum equation is solved analytically using the quadratic slip velocity boundary condition model in slip flow. The extent to which the second-order slip velocity boundary conditions affect the slip flow at the center and at the wall is shown with both graphs and tables. In the study, it was emphasized how effective the magnetic field is especially in the case of second order slip flow, and the percentage of the second order slip flow in the presence/absence of magnetic field was calculated as a percentage.

Kaynakça

  • Cercignani, C. and A. Daneri, Flow of a rarefied gas between two parallel plates. Journal of Applied Physics, 1963. 34(12): p. 3509-3513.
  • Cercignani, C. and S. Lorenzani, Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Physics of Fluids, 2010. 22(6): p. 062004.
  • Deissler, R., An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases. International Journal of Heat and Mass Transfer, 1964. 7(6): p. 681-694.
  • Hadjiconstantinou, N.G., Comment on Cercignani’s second-order slip coefficient. Physics of Fluids, 2003. 15(8): p. 2352-2354.
  • Hsia, Y.-T. and G. Domoto, An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. 1983.
  • Karniadakis, G.E., A. Beskok, and M. Gad-el-Hak, Micro flows: fundamentals and simulation. Appl. Mech. Rev., 2002. 55(4): p. B76-B76.
  • Lorenzani, S., Higher order slip according to the linearized Boltzmann equation with general boundary conditions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011. 369(1944): p. 2228-2236.
  • Mitsuya, Y., Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. 1993.
  • Pitakarnnop, J., et al., A novel experimental setup for gas microflows. Microfluidics and Nanofluidics, 2010. 8(1): p. 57-72.
  • Schamberg, R., The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems. 1947, California institute of technology.
  • Hartmann, J. and F. Lazarus, Hg-dynamics II. Theory of laminar flow of electrically conductive Liquids in a Homogeneous Magnetic Field, 1937. 15(7).
  • Kushwaha, H.M. and S. Sahu, Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions. Heat and Mass Transfer, 2014. 50(12): p. 1649-1659.
  • Wu, L., A slip model for rarefied gas flows at arbitrary Knudsen number. Applied Physics Letters, 2008. 93(25): p. 253103.
  • Singh, G. and A. Chamkha, Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet. Ain Shams Engineering Journal, 2013. 4(4): p. 911-917.
  • Yazdi, M., et al., Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction. International Journal of Heat and Mass Transfer, 2011. 54(15-16): p. 3214-3225.
  • Colin, S., P. Lalonde, and R. Caen, Validation of a second-order slip flow model in rectangular microchannels. Heat transfer engineering, 2004. 25(3): p. 23-30.
  • Rahimi, B. and H. Niazmand, Effects of high-order slip/jump, thermal creep, and variable thermophysical properties on natural convection in microchannels with constant wall heat fluxes. Heat transfer engineering, 2014. 35(18): p. 1528-1538.
  • Roşca, A.V. and I. Pop, Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. International Journal of Heat and Mass Transfer, 2013. 60: p. 355-364.
  • Roşca, N.C. and I. Pop, Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. International Journal of Heat and Mass Transfer, 2013. 65: p. 102-109.
  • Turkyilmazoglu, M., Heat and mass transfer of MHD second order slip flow. Computers & Fluids, 2013. 71: p. 426-434.
  • Aman, S., Q. Al-Mdallal, and I. Khan, Heat transfer and second order slip effect on MHD flow of fractional Maxwell fluid in a porous medium. Journal of King Saud University-Science, 2020. 32(1): p. 450-458.
  • Liu, Y. and B. Guo, Effects of second-order slip on the flow of a fractional Maxwell MHD fluid. Journal of the Association of Arab Universities for Basic and Applied Sciences, 2017. 24: p. 232-241.
  • Majeed, A., et al., Impact of magnetic field and second-order slip flow of Casson liquid with heat transfer subject to suction/injection and convective boundary condition. Journal of Magnetics, 2019. 24(1): p. 81-89.
  • Qayyum, S., et al., Modeling and theoretical investigation of curved parabolized surface of second-order velocity slip flow: Combined analysis of entropy generation and activation energy. Modern Physics Letters B, 2020. 34(33): p. 2050383.
  • Almutairi, F., S. Khaled, and A. Ebaid, MHD flow of nanofluid with homogeneous-heterogeneous reactions in a porous medium under the influence of second-order velocity slip. Mathematics, 2019. 7(3): p. 220.
  • Sayyed, S., B. Singh, and N. Bano, MHD Stagnation-Point Dissipative Flow in a Porous Medium with Joule Heating and Second-Order Slip, in Computing, Communication and Signal Processing. 2019, Springer. p. 601-609.

Effect of Magnetohydrodynamic Second Order Slip Flow Boundary Condition Coefficients on Flow in Parallel Plates

Yıl 2022, Sayı: 41, 23 - 30, 30.11.2022

Öz

In this study, the fully developed velocity profile in magnetohydrodynamic (MHD) flow between microparallel plates was analyzed analytically using all the second-order slipvelocity boundary conditions available in the literature. The heat flux is assumed to be constant. The magnetic field acts perpendicular to the plate surface. The momentum equation is solved analytically using the quadratic slip velocity boundary condition model in slip flow. The extent to which the second-order slip velocity boundary conditions affect the slip flow at the center and at the wall is shown with both graphs and tables. In the study, it was emphasized how effective the magnetic field is especially in the case of second order slip flow, and the percentage of the second order slip flow in the presence/absence of magnetic field was calculated as a percentage.

Kaynakça

  • Cercignani, C. and A. Daneri, Flow of a rarefied gas between two parallel plates. Journal of Applied Physics, 1963. 34(12): p. 3509-3513.
  • Cercignani, C. and S. Lorenzani, Variational derivation of second-order slip coefficients on the basis of the Boltzmann equation for hard-sphere molecules. Physics of Fluids, 2010. 22(6): p. 062004.
  • Deissler, R., An analysis of second-order slip flow and temperature-jump boundary conditions for rarefied gases. International Journal of Heat and Mass Transfer, 1964. 7(6): p. 681-694.
  • Hadjiconstantinou, N.G., Comment on Cercignani’s second-order slip coefficient. Physics of Fluids, 2003. 15(8): p. 2352-2354.
  • Hsia, Y.-T. and G. Domoto, An experimental investigation of molecular rarefaction effects in gas lubricated bearings at ultra-low clearances. 1983.
  • Karniadakis, G.E., A. Beskok, and M. Gad-el-Hak, Micro flows: fundamentals and simulation. Appl. Mech. Rev., 2002. 55(4): p. B76-B76.
  • Lorenzani, S., Higher order slip according to the linearized Boltzmann equation with general boundary conditions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2011. 369(1944): p. 2228-2236.
  • Mitsuya, Y., Modified Reynolds equation for ultra-thin film gas lubrication using 1.5-order slip-flow model and considering surface accommodation coefficient. 1993.
  • Pitakarnnop, J., et al., A novel experimental setup for gas microflows. Microfluidics and Nanofluidics, 2010. 8(1): p. 57-72.
  • Schamberg, R., The fundamental differential equations and the boundary conditions for high speed slip-flow, and their application to several specific problems. 1947, California institute of technology.
  • Hartmann, J. and F. Lazarus, Hg-dynamics II. Theory of laminar flow of electrically conductive Liquids in a Homogeneous Magnetic Field, 1937. 15(7).
  • Kushwaha, H.M. and S. Sahu, Analysis of gaseous flow in a micropipe with second order velocity slip and temperature jump boundary conditions. Heat and Mass Transfer, 2014. 50(12): p. 1649-1659.
  • Wu, L., A slip model for rarefied gas flows at arbitrary Knudsen number. Applied Physics Letters, 2008. 93(25): p. 253103.
  • Singh, G. and A. Chamkha, Dual solutions for second-order slip flow and heat transfer on a vertical permeable shrinking sheet. Ain Shams Engineering Journal, 2013. 4(4): p. 911-917.
  • Yazdi, M., et al., Slip MHD liquid flow and heat transfer over non-linear permeable stretching surface with chemical reaction. International Journal of Heat and Mass Transfer, 2011. 54(15-16): p. 3214-3225.
  • Colin, S., P. Lalonde, and R. Caen, Validation of a second-order slip flow model in rectangular microchannels. Heat transfer engineering, 2004. 25(3): p. 23-30.
  • Rahimi, B. and H. Niazmand, Effects of high-order slip/jump, thermal creep, and variable thermophysical properties on natural convection in microchannels with constant wall heat fluxes. Heat transfer engineering, 2014. 35(18): p. 1528-1538.
  • Roşca, A.V. and I. Pop, Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip. International Journal of Heat and Mass Transfer, 2013. 60: p. 355-364.
  • Roşca, N.C. and I. Pop, Mixed convection stagnation point flow past a vertical flat plate with a second order slip: heat flux case. International Journal of Heat and Mass Transfer, 2013. 65: p. 102-109.
  • Turkyilmazoglu, M., Heat and mass transfer of MHD second order slip flow. Computers & Fluids, 2013. 71: p. 426-434.
  • Aman, S., Q. Al-Mdallal, and I. Khan, Heat transfer and second order slip effect on MHD flow of fractional Maxwell fluid in a porous medium. Journal of King Saud University-Science, 2020. 32(1): p. 450-458.
  • Liu, Y. and B. Guo, Effects of second-order slip on the flow of a fractional Maxwell MHD fluid. Journal of the Association of Arab Universities for Basic and Applied Sciences, 2017. 24: p. 232-241.
  • Majeed, A., et al., Impact of magnetic field and second-order slip flow of Casson liquid with heat transfer subject to suction/injection and convective boundary condition. Journal of Magnetics, 2019. 24(1): p. 81-89.
  • Qayyum, S., et al., Modeling and theoretical investigation of curved parabolized surface of second-order velocity slip flow: Combined analysis of entropy generation and activation energy. Modern Physics Letters B, 2020. 34(33): p. 2050383.
  • Almutairi, F., S. Khaled, and A. Ebaid, MHD flow of nanofluid with homogeneous-heterogeneous reactions in a porous medium under the influence of second-order velocity slip. Mathematics, 2019. 7(3): p. 220.
  • Sayyed, S., B. Singh, and N. Bano, MHD Stagnation-Point Dissipative Flow in a Porous Medium with Joule Heating and Second-Order Slip, in Computing, Communication and Signal Processing. 2019, Springer. p. 601-609.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Hatice Şimşek 0000-0003-0041-3406

Erken Görünüm Tarihi 2 Ekim 2022
Yayımlanma Tarihi 30 Kasım 2022
Yayımlandığı Sayı Yıl 2022 Sayı: 41

Kaynak Göster

APA Şimşek, H. (2022). Effect of Magnetohydrodynamic Second Order Slip Flow Boundary Condition Coefficients on Flow in Parallel Plates. Avrupa Bilim Ve Teknoloji Dergisi(41), 23-30. https://doi.org/10.31590/ejosat.1093275