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2023 | OriginalPaper | Chapter

Magnetohydrodynamic Mixed Convection Flow in a Vertical Channel Filled with Porous Media

Authors : Nidhi Singh, Manish K. Khandelwal

Published in: Frontiers in Industrial and Applied Mathematics

Publisher: Springer Nature Singapore

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Abstract

The chapter delves into the phenomenon of mixed convection flow in a vertical porous medium channel, driven by thermal buoyancy and an external pressure gradient. It emphasizes the significance of magnetohydrodynamic (MHD) effects on flow stability, particularly under a transverse magnetic field. The study employs linear stability analysis to examine the impact of various parameters, including the Hartmann number, Darcy number, and Rayleigh number, on flow instability. The results reveal that while the magnetic field tends to stabilize the flow, increased media permeability and thermal buoyancy can induce flow instabilities. The chapter offers valuable insights into the behavior of MHD mixed convection flows, which are crucial for applications in heat exchangers, nuclear reactors, and electronic equipment.

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Literature
1.
go back to reference Chen, Y.C., Chung, J.N.: The linear stability of mixed convection in a vertical channel flow. J. Fluid Mech. 325, 29–51 (1996)CrossRefMATH Chen, Y.C., Chung, J.N.: The linear stability of mixed convection in a vertical channel flow. J. Fluid Mech. 325, 29–51 (1996)CrossRefMATH
2.
go back to reference Chen, Y.C., Chung, J.N.: Stability of mixed convection in a differentially heated vertical channel. J. Heat Transf. 120, 127–132 (1998)CrossRef Chen, Y.C., Chung, J.N.: Stability of mixed convection in a differentially heated vertical channel. J. Heat Transf. 120, 127–132 (1998)CrossRef
3.
go back to reference Chen, Y.C., Chung, J.N.: A direct numerical simulation of k and h-type flow transition phenomenon in a heated vertical channel. Phys. Fluids 14, 3327–3346 (2002)CrossRefMATH Chen, Y.C., Chung, J.N.: A direct numerical simulation of k and h-type flow transition phenomenon in a heated vertical channel. Phys. Fluids 14, 3327–3346 (2002)CrossRefMATH
4.
go back to reference Khandelwal, M.K., Bera, P.: Weakly nonlinear stability analysis of non-isothermal Poiseuille flow in a vertical channel. Phys. Fluids 27, 064103-1-24 (2015) Khandelwal, M.K., Bera, P.: Weakly nonlinear stability analysis of non-isothermal Poiseuille flow in a vertical channel. Phys. Fluids 27, 064103-1-24 (2015)
5.
go back to reference Su, Y.C., Chung, J.N.: Linear stability analysis of mixed convection flow in a vertical pipe. J. Fluid Mech. 422, 141–166 (2000)CrossRefMATH Su, Y.C., Chung, J.N.: Linear stability analysis of mixed convection flow in a vertical pipe. J. Fluid Mech. 422, 141–166 (2000)CrossRefMATH
6.
go back to reference Yao, L.S., Rogers, B.B.: The linear stability of mixed convection in a vertical annulus. J. Fluid Mech. 201, 279–298 (1989)CrossRef Yao, L.S., Rogers, B.B.: The linear stability of mixed convection in a vertical annulus. J. Fluid Mech. 201, 279–298 (1989)CrossRef
7.
go back to reference Geindreau, C., Auriault, J.L.: Magnetohydrodynamic flows in porous media. J. Fluid Mech. 466, 343–363 (2002)CrossRefMATH Geindreau, C., Auriault, J.L.: Magnetohydrodynamic flows in porous media. J. Fluid Mech. 466, 343–363 (2002)CrossRefMATH
8.
go back to reference Mc Whirter, J., Crawford, M., Klein, D., Sanders, T.: Modal for inertialess magnetohydrodynamic flow in packed beds. Fus. Technol. 34, 187–197 (1998) Mc Whirter, J., Crawford, M., Klein, D., Sanders, T.: Modal for inertialess magnetohydrodynamic flow in packed beds. Fus. Technol. 34, 187–197 (1998)
9.
go back to reference Bera, P., Khalili, A.: Stability of mixed convection in an anisotropic porous channel. Phys. Fluids 14, 1617–1630 (2002)CrossRefMATH Bera, P., Khalili, A.: Stability of mixed convection in an anisotropic porous channel. Phys. Fluids 14, 1617–1630 (2002)CrossRefMATH
10.
go back to reference Bera, P., Khalili, A.: Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium. Phys. Fluids 18, 124103 (2006)CrossRefMATH Bera, P., Khalili, A.: Influence of Prandtl number on stability of mixed convective flow in a vertical channel filled with a porous medium. Phys. Fluids 18, 124103 (2006)CrossRefMATH
11.
go back to reference Kumar, J., Bera, P., Khalili, A.: Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel. Int. J. Heat Mass Transf. 53, 5261–5271 (2010)CrossRefMATH Kumar, J., Bera, P., Khalili, A.: Influence of inertia and drag terms on the stability of mixed convection in a vertical porous-medium channel. Int. J. Heat Mass Transf. 53, 5261–5271 (2010)CrossRefMATH
12.
go back to reference Bera, P., Khandelwal, M.K.: A thermal non-equilibrium perspective on instability mechanism of nonisothermal poiseuille flow in a vertical porous medium channel. Int. J. Ther. Sci. 105, 159–173 (2016)CrossRef Bera, P., Khandelwal, M.K.: A thermal non-equilibrium perspective on instability mechanism of nonisothermal poiseuille flow in a vertical porous medium channel. Int. J. Ther. Sci. 105, 159–173 (2016)CrossRef
13.
go back to reference Khandelwal, M.K., Bera, P.: A thermal non equilibrium perspective on mixed convection in a vertical channel, Int. J. Ther. Sci. 56, 23–34 (2012) Khandelwal, M.K., Bera, P.: A thermal non equilibrium perspective on mixed convection in a vertical channel, Int. J. Ther. Sci. 56, 23–34 (2012)
14.
go back to reference Sharma, A.K., Khandelwal, M.K., Bera, P.: Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium. J. Fluid Mech. 857, 469–507 (2018)CrossRefMATH Sharma, A.K., Khandelwal, M.K., Bera, P.: Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium. J. Fluid Mech. 857, 469–507 (2018)CrossRefMATH
15.
go back to reference Khandelwal, M.K., Sharma, A.K., Bera, P.: Instability of mixed convection in a differentially heated channel filled with porous medium: a finite amplitude analysis. Phys. Fluids 33, 024109 (2021)CrossRef Khandelwal, M.K., Sharma, A.K., Bera, P.: Instability of mixed convection in a differentially heated channel filled with porous medium: a finite amplitude analysis. Phys. Fluids 33, 024109 (2021)CrossRef
16.
go back to reference Wallace, W.E., Pierce, C.I., Swayer, W.: Experiments on the flow of mercury in porous media in a transverse magnetic field. Technical Report, TN 23, U7, No. 7259. US Bureau of Mines Wallace, W.E., Pierce, C.I., Swayer, W.: Experiments on the flow of mercury in porous media in a transverse magnetic field. Technical Report, TN 23, U7, No. 7259. US Bureau of Mines
17.
go back to reference Raptis, A., Perdikis, C.: Magnetohydrodynamics effects on mass transfer flow through porous medium. Astrophys. Space Sci. 113, 53–58 (1985)CrossRef Raptis, A., Perdikis, C.: Magnetohydrodynamics effects on mass transfer flow through porous medium. Astrophys. Space Sci. 113, 53–58 (1985)CrossRef
18.
go back to reference Ram, G., Mishra, R.S.: Unsteady flow through magnetohydrodynamic porous media. Indian J. Pure Appl. Maths 8, 637–647 (1977)MATH Ram, G., Mishra, R.S.: Unsteady flow through magnetohydrodynamic porous media. Indian J. Pure Appl. Maths 8, 637–647 (1977)MATH
19.
go back to reference Tawil, M.A.E., Kamel, M.H.: MHD flow under stochastic porous media. Energy Conserv. Manag. 35, 991–997 (1994)CrossRef Tawil, M.A.E., Kamel, M.H.: MHD flow under stochastic porous media. Energy Conserv. Manag. 35, 991–997 (1994)CrossRef
20.
go back to reference Yih, K.A.: The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mech. 130, 147–158 (1998)CrossRefMATH Yih, K.A.: The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mech. 130, 147–158 (1998)CrossRefMATH
21.
go back to reference Prescott, P.J., Incropera, F.P.: Magnetically damped convection during solidification of a binary metal alloy. J. Heat Transf. 115, 302–310 (1993)CrossRef Prescott, P.J., Incropera, F.P.: Magnetically damped convection during solidification of a binary metal alloy. J. Heat Transf. 115, 302–310 (1993)CrossRef
22.
go back to reference Rudriah, N., Ramaiah, B.K., Rajasekhar, B.M.: Hartmann flow over a permeable bed. Intl J. Eng. Sci. 13, 1–24 (1975)CrossRefMATH Rudriah, N., Ramaiah, B.K., Rajasekhar, B.M.: Hartmann flow over a permeable bed. Intl J. Eng. Sci. 13, 1–24 (1975)CrossRefMATH
23.
go back to reference Takashima, M.: The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of a transverse magnetic field. Fluid Dyn. Res. 14, 121–134 (1994)CrossRef Takashima, M.: The stability of natural convection in a vertical layer of electrically conducting fluid in the presence of a transverse magnetic field. Fluid Dyn. Res. 14, 121–134 (1994)CrossRef
24.
go back to reference Hudoba, A., Molokov, S.: Linear stability of buoyant convective flow in a vertical channel with internal heat sources and a transverse magnetic field. Phys. Fluids 28(114103), 1–19 (2016) Hudoba, A., Molokov, S.: Linear stability of buoyant convective flow in a vertical channel with internal heat sources and a transverse magnetic field. Phys. Fluids 28(114103), 1–19 (2016)
25.
go back to reference Kolyshkin, A.A.: On the stability convection generated by internal heat sources in a magnetic field. Can. J. Phys. 66, 990–993 (1988)CrossRef Kolyshkin, A.A.: On the stability convection generated by internal heat sources in a magnetic field. Can. J. Phys. 66, 990–993 (1988)CrossRef
26.
go back to reference Stuart, J.T.: On the stability of viscous flow between parallel planes in the presence of co-planner magnetic field. Proc. Royal Soc. Lond. A 221,189-XX (1954) Stuart, J.T.: On the stability of viscous flow between parallel planes in the presence of co-planner magnetic field. Proc. Royal Soc. Lond. A 221,189-XX (1954)
27.
go back to reference Lock, R.C.: The stability of the flow of an electrically conducting fluid between parallel plane under transverse magnetic field. Proc. R. Soc. A 233, 105–125 (1955) Lock, R.C.: The stability of the flow of an electrically conducting fluid between parallel plane under transverse magnetic field. Proc. R. Soc. A 233, 105–125 (1955)
28.
go back to reference Hunt, J.C.R.: On the stability of parallel flows with parallel magnetic fields. Proc. R. Soc. A 293, 342–358 (1966) Hunt, J.C.R.: On the stability of parallel flows with parallel magnetic fields. Proc. R. Soc. A 293, 342–358 (1966)
29.
go back to reference Satake, S., Sone, K., Furumi, K., Kunugi, T.: Direct numerical simulation of turbulent mixed convection in a vertical channel in a wall normal magnetic field. Fusion Eng. Des. 87, 798–802 (2012)CrossRef Satake, S., Sone, K., Furumi, K., Kunugi, T.: Direct numerical simulation of turbulent mixed convection in a vertical channel in a wall normal magnetic field. Fusion Eng. Des. 87, 798–802 (2012)CrossRef
30.
go back to reference Saleh, H., Hashim, I.: Flow reversal of fully-developed mixed MHD convection in vertical channels. Chin. Phys. Lett. 27, 024401–024403 (2010)CrossRef Saleh, H., Hashim, I.: Flow reversal of fully-developed mixed MHD convection in vertical channels. Chin. Phys. Lett. 27, 024401–024403 (2010)CrossRef
31.
go back to reference Shankar, B.M., Kumar, J., Shivakumara, I.S.: Magnetohydrodynamic instability of mixed convection in a differentially heated vertical channel. Eur. Phys. J. Plus 134(53), 1–12 (2019) Shankar, B.M., Kumar, J., Shivakumara, I.S.: Magnetohydrodynamic instability of mixed convection in a differentially heated vertical channel. Eur. Phys. J. Plus 134(53), 1–12 (2019)
32.
go back to reference Singh, N., Khandelwal, M.K., Yu, P.: Instability of mixed convection flow in a differentially heated channel under a magnetic field with internal heating. Phys. Fluids 33, 094102 (2021)CrossRef Singh, N., Khandelwal, M.K., Yu, P.: Instability of mixed convection flow in a differentially heated channel under a magnetic field with internal heating. Phys. Fluids 33, 094102 (2021)CrossRef
33.
go back to reference Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer, New York (2013) Nield, D.A., Bejan, A.: Convection in Porous Media, 4th edn. Springer, New York (2013)
34.
go back to reference Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge (2004)CrossRefMATH Drazin, P.G., Reid, W.H.: Hydrodynamic Stability. Cambridge University Press, Cambridge (2004)CrossRefMATH
Metadata
Title
Magnetohydrodynamic Mixed Convection Flow in a Vertical Channel Filled with Porous Media
Authors
Nidhi Singh
Manish K. Khandelwal
Copyright Year
2023
Publisher
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-19-7272-0_24

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