ORIGINAL PAPER
The ‘influence of Hall currents on unsteady-MHD heat transfer flow’ in a conducting channel containing two ionized fluids
More details
Hide details
1
Department of Mathematics, St. Joseph's College for Women (A), Visakhapatnam, India
2
Department of Engineering Mathematics, A.U. College of Engineering, Andhra University, Visakhapatnam - 3, Andhra University, India
Submission date: 2024-02-17
Final revision date: 2024-03-26
Acceptance date: 2024-04-15
Publication date: 2024-09-12
Corresponding author
LINGA RAJU TEMBURU
Department of Engineering Mathematics, A.U. College of Engineering, Andhra University, Visakhapatnam - 3, Andhra University, AUCE, Visakhapatnam-3, 530003, Visakhapatnam urban, India
International Journal of Applied Mechanics and Engineering 2024;29(3):118-149
KEYWORDS
TOPICS
ABSTRACT
We delve into the ‘effects of hall currents on the dynamics of unsteady magnetohydrodynamic flow and heat transfer within a two-fluid system of ionized gases confined within a horizontal channel bounded by parallel conducting plates. Employing a regular perturbation technique, we solve the governing partial differential equations to unveil the distributions of velocity and temperature, alongside profiles depicting heat transfer coefficients. Through a systematic parametric analysis, we explore the interplay among variables such as the Hartmann number, Hall parameter, and ratios involving viscosities, heights, electrical conductivities, and thermal conductivities. The results highlight the profound influence of these parameters on the dynamics of unsteady magnetohydrodynamic (MHD) heat transfer within a flow regime characterized by a dual-ionized fluid’. This influence is particularly pronounced when the lateral plates of the channel are conductive. Significantly, elevated Hartmann numbers and Hall parameters are associated with augmented heat transfer coefficients at both plates, holding other variables constant.
REFERENCES (55)
1.
Shail R. (1973): On laminar two-phase flows in magnetohydrodynamics.– Int. J. Engg. Sci., vol.11, pp.1103-1109.
2.
Cowling T.G.(1962):Magnetohydrodynamics.– Rep. Prog. Phys., vol.25, pp.244.
3.
Hall Edwin (1879): On a new action of the magnet on electric currents.– American Journal of Mathematics, vol.2, No.2, pp. 287-292.
4.
Broer L.J.F. and Peletier L.A. (1960): A Mechanical. Hall Effect.– Appl. Sci. Res., vol.8B, pp.259.
5.
Sato H. (1961): The Hall effect in the viscous flow of ionized gas between parallel plates under transverse magnetic field.– J. Phys. Soc. Japan, vol.16, No.7, pp.1427-1433.
6.
Tani I. (1962): Steady flow of conducting fluids in channels under transverse magnetic fields with consideration of Hall effect.– J. Aerospace Sci., vol.29, pp.297.
7.
Pop I. (1971): The effect of Hall current on hydromagnetic flow near accelerated plate.– J. Math. Phys. Sci., vol.5, pp.375-379.
8.
Cramer Kenneth R. and Pai Shih-I. (1973): Magneto fluid Dynamics for Engineers and Applied Physicists.– McGraw-Hill Company, p.347.
9.
Shercliff J.A. (1979): Thermoelectric magnetohydrodynamics.–J. Fluid Mechanics, vol.91, No.2, pp.231-251.
10.
Sharma R.C. and Neela Rani (1988): Hall effects of thermo-solute instability of a plasma.– Indian J. Pure Appl. Math, vol.19, No.2, pp.202-207.
11.
Niranjan S.S., Soundalgekar V.M. and Takhar H.S. (1990): Free convection effects on HMD horizontal channel flow with Hall currents.– Plasma Sci. IEEE Trans, vol.18, No.2, pp.177-183.
12.
LingaRaju T. and Ramana Rao V.V. (1992): Hall effect in the viscous flow of an ionized gas between two parallel walls under transverse magnetic field in a rotating system.– Acta Physica Hungarica, vol.72, No.1, pp.23-45.
13.
LingaRaju T. and Ramana Rao V.V.(1993): Hall effects on temperature distribution in a rotating ionized hydromagnetic flow between parallel walls.– Int. J. Engg. Sci., vol.31, No.7, pp.1073-1091.
14.
Attia H.A. (1998): Hall current effects on the velocity and temperature fields of an unsteady Hartmann flow.– Can. J. Phys, vol.76, No.9, pp.739-746.
15.
Aboeldahab E.M. and Elbarbary E.M.E. (2001): Hall current effect on magnetohydrodynamic free convection flow past a semi-infinite vertical plate with mass transfer.– Int. J. Engg. Sci., vol.39, pp.1641-1652.
16.
Singh J.K., Begum S.G. and Seth G.S. (2018): Influence of Hall current and wall conductivity on hydromagnetic mixed convective flow in a rotating Darcian channel.– Physics of Fluids, vol.30, No.11, p.12.
17.
Milica N., Zivojin S., Jelena P. and Milos K. (2020): Unsteady fluid flow and heat transfer through a porous medium in a horizontal channel with an inclined magnetic field.– Transactions of FAMENA, vol.44, No.4, pp.31-46. DOI:
https://doi.org/10.21278/TOF.4....
18.
Jitendra K.S. and Suneetha K. (2021): Energy dissipation and Hall effect on MHD convective flow of nanofluid within an asymmetric channel with arbitrary wall thickness and conductance.- The European Physical Journal Plus,vol.136, article number 1074, DOI:
https://doi.org/10.1140/epjp/s....
19.
Jitendra K.S., Suneetha K. and Gauri S.S. (2022): Scrutiny of induced magnetic field and Hall current impacts on transient hydromagnetic nano fluid flow within two vertical alternative magnetized surfaces.– Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engg.,vol.237, No.4.pp.1595-1606. DOI:
https://doi.org/10.1177/095440....
20.
Jitendra K.S. and Vishwanath S. (2022): Hall and induced magnetic field effects on MHD buoyancy-driven flow of WaltersB fluid over a magnetised convectively heated inclined surface.– International Journal of Ambient Energy, vol.43, No.1, pp.4444-4453. DOI:
https://doi.org/10.1080/014307....
21.
Jitendra K.S., Gauri S.S. and Syed M.H. (2023): Thermal performance of hydromagnetic nanofluid flow within an asymmetric channel with arbitrarily conductive walls filled with Darcy-Brinkman porous medium.– Journal of Magnetism and Magnetic Materials, vol.582, article number 171034, DOI:
https://doi.org/10.1016/j.jmmm....
22.
Jitendra K.S., Hanumantha, Suneetha K. and Syed M.H. (2023): Exploration of heat and mass transport in oscillatory hydromagnetic nano fluid flow within two verticals alternatively conducting surfaces.– ZAMM,vol.103, No.12, pp. 1-20, DOI:
https://doi.org/10.1002/zamm.2....
23.
Thatcher (1973): Electromagnetic Flow Meters For Liquid Metals, In Modern Development In Flow Measurement.– Clayton, C.G. (ed). London Peter Peregrinus Ltd., pp. 359-380.
24.
Chwla T.C. and Ishii M. (1980): Two-fluid model of two-phase flow in a pin bundle of a nuclear reactor.– Int. J. Heat Mass Transfer, vol.23, pp.991-1001.
25.
Dunn P.F. (1980): Single-phase and two-phase magnetohydrodynamic pipe flow.– Int. Journal of Heat and Mass Transfer, vol.23, pp.373.
26.
Dobran F. (1981): On the consistency conditions of averaging operators in 2-phase flow models and on the formulation of magnetohydrodynamic 2-phase flow.– Int. J. Eng. vol.19,No.10, pp.1353-1368.
27.
Mitra P. (1982): Unsteady flow of two electrically conducting fluids between two rigid parallel plates.– Bulletin of the Calcutta Mathematical Society, vol.74, pp.87-95.
28.
Lohrasbi J. and SahaiV. (1988): Magnetohydrodynamic heat transfer in two phase flow between parallel plates.– Appl. Sci. Res., vol.45, pp.53-66.
29.
Setayesh A. and Sahai V. (1990): Heat transfer in developing magnetohydrodynamic Poiseuille flow and variable transport properties.– Int. J. Heat Mass Transfer, vol.33, No.8,pp.1711.
30.
Malashetty M.S. and LeelaV. (1992): Magnetohydrodynamic heat transfer in two phase flow.– Int. J. of Engg. Sci., vol.30, pp.371-377.
31.
Chamkha A.J. (2000): Unsteady laminar hydromagnetic fluid-particle flow and heat transfer in channels and circular pipes.– Int. J. of Heat and Fluid Flow, vol.21, pp.740-746.
32.
Umavathi J.C., Chamkha A.J., Mateen A. and Kumar J.P. (2008): Unsteady magneto-hydrodynamic two fluid flow and heat transfer in a horizontal channel.– Heat and Technology, vol.26, No.2, pp.121-133.
33.
Tsuyoshi Inoue and InutsukaShu-Ichiro (2008): Two-fluid MHD simulations of converging Hi flows in the interstellar medium I:Methodology and basic results.– The Astr. Phys. J., vol.687, pp.303-310.
34.
Hussameddine S.K., Martin J.M. and Sang W.J. (2008): Analytical prediction of flow field in magnetohydrodynamic based micro fluidic devices.– J. of Fluids Engg, vol.130,No.9, pp.6-10.
35.
Srivastava K.M. (2009): Effect of Hall current on the instability of an anisotropic plasma.–Jet. J. Plasma Phys., vol.12, No.1, pp.33-43.
36.
Stamenkovic M.Z., Nikodjevic D.D, Blagojevic B.D. and Savic S. (2010): MHD flow and heat transfer of two immiscible fluids between moving plates.– Transactions of the Canadian Society for Mechanical Engg., vol.34, No.3-4, pp.351-372.
37.
Stamenkovic Ź.M., Nikodijevic D.D., Kocic M.M. and Nikodijevic J.D. (2012): MHD flow and heat transfer of two immiscible fluids with induced magnetic field.– Thermal Science: Int. Scientific Journal, vol.16, No.2, pp.323-336.
38.
LingaRaju T. and Valli M. (2014): MHD two-layered unsteady fluid flow and heat transfer through a horizontal channel between parallel plates in a rotating system.– Int. J. Appl. Mech. and Engg., vol.19, No.1, pp.97-121.
https://doi.org/10.2478/ijame-....
39.
Selimli S., Resebli Z. and Arcakhoglu E. (2015): Combined effects of magnetic and electric field on hydrodynamic and thermo-physical parameters of magneto-viscous fluid flow.– Int. J. Heat Mass Trans., vol.86, pp.426-432.
40.
Kalra G.L., KathuriaS.N., Hosking R.J. and Lister G.G. (1970): Effect of Hall current and resistivity on the stability of a gas-liquid system.– J. Plasma Phys., vol.4, No.3, pp.451-469. Doi:10.1017/S0022377800005158.
41.
Hyun S. and Kennel C.F. (2009): Small amplitude waves in a hot relativistic two-fluid plasma.– J. Plasma Phy., vol.20, No.2, pp.281-287.
42.
Sharma P.R. and Sharma Kalpana (2014): Unsteady MHD two-fluid flow and heat transfer through a horizontal channel.– Int. J. of Engineering Science Invention Research and Development, vol.1, No.3, pp.65-72.
43.
Joseph K.M., Peter A., Asie P.E. and Usman S. (2015): The unsteady MHD free convective two immiscible fluid flows in a horizontal channel with heat and mass transfer.– Int. J. of Mathematics and Computer Research, vol.3, No.5, pp.954-972.
44.
Sivakamini L. and Govindarajan A. (2019): Unsteady MHD flow of two immiscible fluids under chemical reaction in a horizontal channel.– AIP conference proceedings 2112.020157
https://doi.org/10.1063/1.5112..., published online: 24 June 2019.
45.
Gireesha B.J., Mahantesh B., Thammanna G.T. and Sampath Kumar P.B.(2018): Hall effects on dusty nanofluid two-phase transient flow past a stretching sheet using KVL model.– Journal of Molecular Liquids, vol.256, pp.139-147.
https://doi.org/10.1016/j.moll....
46.
Linga Raju T. (2019): MHD heat transfer two-ionized fluids flow between parallel plates with Hall currents.– Journal of Results in Engineering, Elsevier Publication. vol.4, p.100043,
https://doi.org/10.1016/j.rine....
47.
LingaRaju T. (2021): Electro-magneto hydrodynamic two fluid flow of ionized-gases with Hall and rotation effects.–Int. J. Appl. Mech., vol.26, No.4, pp.128-144, DOI: 10.2478/ijame-2021-0054.
48.
Linga Raju T. and GowriSankaraRao V. (2021): Effect of Hall current on unsteady magneto hydrodynamic two-ionized fluid flow and heat transfer in a channel.– Int. J. of Applied Mechanics and Engg., vol.26, No.2, pp. 84-106.
https://doi.org/10.2478/ijame-....
49.
Linga Raju T. and GowriSankaraRao V. (2023): An unsteady electro-magnetohydrodynamic two-liquid plasma flow along a channel of insulating porous plates with Hall currents.– Int. J. of Applied Mechanics and Engg., vol.28, No.2, pp.90-112, DOI: 10.59441/ijame/168933.
50.
Linga Raju T. and Valli Naga M. (2023): Effect of hall currents on the MHD two-layered plasma heat transfer flow via a channel of porous plates.– Journal of Engineering Physics and Thermo Physics.,vol.96, No.5. pp.1-12, DOI 10.1007/s10891-023-02794-x.
51.
Linga Raju T. and VenkatRao B. (2022): Unsteady electro-magneto hydrodynamic flow and heat transfer of two ionized fluids in a rotating system with Hall currents.– Int. J. of Applied Mechanics and Engg., vol.27, No.1. pp.125-145, DOI: 10.2478/ijame-2022-0009.
52.
Linga Raju T. and VenkatRao B. (2022): The Hall effect on MHD 2-fluid unsteady heat transfer flow of plasma in a rotating system via a straight channel between conducting plates.– Int. J. of Applied Mechanics and Engg.,vol.27, No.3. pp.137-162, DOI: 10.2478/ijame-2022-0041.
53.
LingaRaju T. and Satish P. (2023): Hall and rotation effects on magnetohydrodynamics two fluids slip flow of ionized gases via parallel conduit.– Heat Transfer, vol.52, No.7. pp.137-162, DOI:10.1002/htj.22909.
54.
Linga Raju T. and Satish P. (2023): Slip regime MHD 2-liquid plasma heat transfer flow with hall currents between parallel plates.– Int. J. Appl. Mech. and Engg., vol.28, No.3. pp.65-85,
https://doi.org/10.59441/ijame....
55.
Spitzer L. Jr. (1956): Physics of Fully Ionized Gases.– Inter science Publishers, N. Y.