ORIGINAL ARTICLE
Hall current and Dufour effect on the flow of a viscous fluid in the presence of suction, chemical reaction, and heat source: Laplace transform procedure
Chinmoy Rath,
Anita Nayak,
Chinmoy Rath
Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar, India
Search for more papers by this authorCorresponding Author
Anita Nayak
Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar, India
Correspondence Anita Nayak, Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar-751024, India.
Email: [email protected]
Search for more papers by this authorChinmoy Rath,
Anita Nayak,
Chinmoy Rath
Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar, India
Search for more papers by this authorCorresponding Author
Anita Nayak
Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar, India
Correspondence Anita Nayak, Department of Mathematics, School of Applied Sciences, Kalinga Institute of Industrial Technology (KIIT) Deemed to be University, Bhubaneswar-751024, India.
Email: [email protected]
Search for more papers by this authorFirst published: 19 February 2024
Abstract
The present investigation explores the transient magnetohydrodynamics gravity-driven flow of a viscous, incompressible, electrically conducting fluid past a permeable exponentially accelerated vertical plate in the presence of thermal radiation and suction. Due to several applications in different areas, the influence of Hall current, Dufour number, heat source parameter, and chemically reactive species diffusion are vital and are incorporated in the study, which is the novelty of the present work. The model equations are derived and resolved by utilizing an analytical technique called the Laplace transform procedure. Various properties of the flow due to the influence of different vital parameters have been depicted with the help of graphs. The computed gradients of velocity, temperature and concentration are presented in tabular form. The Hall parameter is observed to strengthen the secondary flow while diminishing the primary flow. Dufour number and heat source parameter enhance the fluid temperature and velocity profiles while the heat sink declines them. Enhancement of the acceleration parameter significantly amplifies the primary skin friction coefficient. Suction boosts the heat transport as well as the mass transport rates at the surface of the plate, whereas injection declines them. Further, the Dufour number causes a significant reduction in the Nusselt number and magnitude of the secondary skin friction coefficient. The practical applications of the current research are the design of aircraft, cooling of microchips, Hall accelerators, separation of isotopes and many more.
Open Research
DATA AVAILABILITY STATEMENT
The data that support the findings of this study are available in the supplementary material of this article.
REFERENCES
- 1Cowling TG. Magnetohydrodynamics. Interscience Publishers; 1957.
- 2Davidson PA. Introduction to Magnetohydrodynamics. Cambridge University Press; 2016. doi:10.1017/9781316672853
10.1017/9781316672853 Google Scholar
- 3Goedbloed JP, Poedts S. Principles of Magnetohydrodynamics: With Applications to Laboratory and Astrophysical Plasmas. Cambridge University Press; 2004. doi:10.1017/CBO9780511616945
10.1017/CBO9780511616945 Google Scholar
- 4 DB Ingham, A Bejan, E Mamut, I Pop, eds. Emerging Technologies and Techniques in Porous Media. Kluwer Academic Publishers; 2004. doi:10.1007/978-94-007-0971-3
10.1007/978-94-007-0971-3 Google Scholar
- 5Nield DA, Bejan A. Convection in Porous Media. Springer International Publishing; 2017. doi:10.1007/978-3-319-49562-0
10.1007/978-3-319-49562-0 Google Scholar
- 6Makinde OD, Mishra SR. Chemically reacting MHD mixed convection variable viscosity Blasius flow embedded in a porous medium. Defect Diffus Forum. 2017; 374: 83-91. doi:10.4028/www.scientific.net/DDF.374.83
10.4028/www.scientific.net/DDF.374.83 Google Scholar
- 7Krishna MV, Chamkha AJ. Hall effects on MHD squeezing flow of a water-based nanofluid between two parallel disks. J Porous Media. 2019; 22(2): 209-223. doi:10.1615/JPorMedia.2018028721
- 8Krishna MV, Vajravelu K. Rotating MHD flow of second grade fluid through porous medium between two vertical plates with chemical reaction, radiation absorption, Hall, and ion slip impacts. Biomass Conv Bioref. 2022. doi:10.1007/s13399-022-02802-9
- 9Pattnaik PK, Abbas MA, Mishra S, Khan SU, Bhatti MM. Free convective flow of Hamilton-crosser model gold-water nanofluid through a channel with permeable moving walls. Comb Chem High Throughput Screen. 2022; 25(7): 1103-1114. doi:10.2174/1386207324666210813112323
- 10Umamaheswar M, Raju MC, Varma SVK. Effects of time dependent variable temperature and concentration boundary layer on MHD free convection flow past a vertical porous plate in the presence of thermal radiation and chemical reaction. Int J Appl Comput Math. 2017; 3: 679-692. doi:10.1007/s40819-015-0124-9
10.1007/s40819-015-0124-9 Google Scholar
- 11Krishna MV, Chamkha AJ. MHD peristaltic rotating flow of a couple stress fluid through a porous medium with wall and slip effects. Spec Top Rev Porous Media: Int J. 2019; 10(3): 245-258. doi:10.1615/SpecialTopicsRevPorousMedia.2019028609
10.1615/SpecialTopicsRevPorousMedia.2019028609 Google Scholar
- 12Mathur P, Mishra SR, Pattnaik PK, Dash RK. Characteristics of Darcy–Forchheimer drag coefficients and velocity slip on the flow of micropolar nanofluid. Heat Transfer. 2021; 50(7): 6529-6547. doi:10.1002/htj.22191
10.1002/htj.22191 Google Scholar
- 13Razaq A, Hayat T, Khan SA, Momani S. ATSS model based upon applications of Cattaneo–Christov thermal analysis for entropy optimized ternary nanomaterial flow with homogeneous–heterogeneous chemical reactions. Alexandria Eng J. 2023; 79: 390-401. doi:10.1016/j.aej.2023.08.013
- 14Mittal AS, Patel HR. Influence of thermophoresis and Brownian motion on mixed convection two dimensional MHD Casson fluid flow with non-linear radiation and heat generation. Phys A: Stat Mech Appl. 2020; 537:122710. doi:10.1016/j.physa.2019.122710
- 15Jena S, Mishra SR, Pattnaik PK. Development in the heat transfer properties of nanofluid due to the interaction of inclined magnetic field and non-uniform heat source. J Nanofluids. 2020; 9(3): 143-151. doi:10.1166/JON.2020.1749
10.1166/jon.2020.1749 Google Scholar
- 16Kumar MA, Reddy YD, Rao VS, Goud BS. Thermal radiation impact on MHD heat transfer natural convective nano fluid flow over an impulsively started vertical plate. Case Stud Therm Eng. 2021; 24:100826. doi:10.1016/j.csite.2020.100826
- 17Nisar KS, Mohapatra R, Mishra SR, Reddy MG. Semi-analytical solution of MHD free convective Jeffrey fluid flow in the presence of heat source and chemical reaction. Ain Shams Eng J. 2021; 12(1): 837-845. doi:10.1016/j.asej.2020.08.015
- 18Pattnaik PK, Moapatra DK, Mishra SR. Influence of velocity slip on the MHD flow of a micropolar fluid over a stretching surface. In: SR Mishra, TN Dhamala, OD Makinde, eds. Recent Trends in Applied Mathematics: Lecture Notes in Mechanical Engineering. Springer; 2021: 307-321. doi:10.1007/978-981-15-9817-3_21
10.1007/978-981-15-9817-3_21 Google Scholar
- 19Pattanaik PC, Mishra S, Jena S, Pattnaik P. Impact of radiative and dissipative heat on the Williamson nanofluid flow within a parallel channel due to thermal buoyancy. Proc Inst Mech Eng Part N: J Nanomater Nanoeng Nanosyst. 2022; 236: 3-18. doi:10.1177/23977914221080046
- 20Khan SA, Razaq A, Alsaedi A, Hayat T. Modified thermal and solutal fluxes through convective flow of Reiner–Rivlin material. Energy. 2023; 283:128516. doi:10.1016/j.energy.2023.128516
- 21Krishna MV, Jyothi K, Chamkha AJ. Heat and mass transfer on MHD flow of second-grade fluid through porous medium over a semi-infinite vertical stretching sheet. J Porous Media. 2020; 23(8): 751-765. doi:10.1615/JPorMedia.2020023817
- 22Mishra S, Mahanthesh B, Mackolil J, Pattnaik PK. Nonlinear radiation and cross-diffusion effects on the micropolar nanoliquid flow past a stretching sheet with an exponential heat source. Heat Transfer. 2021; 50(4): 3530-3546. doi:10.1002/htj.22039
10.1002/htj.22039 Google Scholar
- 23Shawky HM, Eldabe NTM, Kamel KA, Abd-Aziz EA. MHD flow with heat and mass transfer of Williamson nanofluid over stretching sheet through porous medium. Microsyst Technol. 2019; 25: 1155-1169. doi:10.1007/s00542-018-4081-1
- 24Gautam AK, Verma AK, Bhattacharyya K, Banerjee A. Soret and Dufour effects on MHD boundary layer flow of non-Newtonian Carreau fluid with mixed convective heat and mass transfer over a moving vertical plate. Pramana J Phys. 2020; 94: 108. doi:10.1007/s12043-020-01984-z
- 25Ahamad NA, Krishna MV, Chamkha AJ. Radiation–absorption and Dufour effects on magnetohydrodynamic rotating flow of a nanofluid over a semi-infinite vertical moving plate with a constant heat source. J Nanofluids. 2020; 9(3): 177-186. doi:10.1166/jon.2020.1743
- 26Bejawada SG, Yanala DR. Finite element Soret Dufour effects on an unsteady MHD heat and mass transfer flow past an accelerated inclined vertical plate. Heat Transfer. 2021; 50(8): 8553-8578. doi:10.1002/htj.22290
- 27Raghunath K, Mohanaramana R. Hall, Soret, and rotational effects on unsteady MHD rotating flow of a second-grade fluid through a porous medium in the presence of chemical reaction and aligned magnetic field. Int Commun Heat Mass Transfer. 2022; 137:106287. doi:10.1016/j.icheatmasstransfer.2022.106287
- 28Nayak A, Panda S, Phukan DK. Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species. Appl Math Mech. 2014; 35: 849-862. doi:10.1007/s10483-014-1830-9
10.1007/s10483-014-1830-9 Google Scholar
- 29Krishna MV, Chamkha AJ. Hall and ion slip effects on MHD rotating boundary layer flow of nanofluid past an infinite vertical plate embedded in a porous medium. Results Phys. 2019; 15:102652. doi:10.1016/j.rinp.2019.102652
- 30Khan SA, Hayat T, Alsaedi A. Bioconvection entropy optimized flow of Reiner–Rivlin nanoliquid with motile microorganisms. Alexandria Eng J. 2023; 79: 81-92. doi:10.1016/j.aej.2023.07.069
- 31Schlichting H, Gersten K. Boundary-Layer Theory. Springer; 2017. doi:10.1007/978-3-662-52919-5
10.1007/978-3-662-52919-5 Google Scholar
- 32Nandkeolyar R, Das M, Sibanda P. Unsteady hydromagnetic heat and mass transfer flow of a heat radiating and chemically reactive fluid past a flat porous plate with ramped wall temperature. Math Probl Eng. 2013; 2013:381806. doi:10.1155/2013/381806
- 33Mahato R, Das M. Effect of suction/blowing on heat-absorbing unsteady radiative Casson fluid past a semi-infinite flat plate with conjugate heating and inclined magnetic field. Pramana J Phys. 2020; 94: 127. doi:10.1007/s12043-020-01990-1
- 34Gambo D, Gambo JJ. Role of suction/injection and slip flow on hydromagnetic free convective flow in a vertical coaxial cylinder under the influence of radial magnetic field. Heat Transfer. 2021; 50(5): 4775-4787. doi:10.1002/htj.22101
10.1002/htj.22101 Google Scholar
- 35Jha BK, Altine MM, Hussaini AM. Role of suction/injection on free convective flow in a vertical channel in the presence of point/line heat source/sink. J Heat Transfer. 2022; 144(6):062602. doi:10.1115/1.4054120
- 36Reddy NN, Reddy YD, Rao VS, Goud BS, Nisar KS. Multiple slip effects on steady MHD flow past a non-isothermal stretching surface in presence of Soret, Dufour with suction/injection. Int Commun Heat Mass Transfer. 2022; 134:106024. doi:10.1016/j.icheatmasstransfer.2022.106024
- 37Kataria H, Mittal AS, Mistry M. Effect of nonlinear radiation on entropy optimised MHD fluid flow. Int J Ambient Energy. 2022; 43(1): 6909-6918. doi:10.1080/01430750.2022.2059000
10.1080/01430750.2022.2059000 Google Scholar
- 38Pattnaik PK, Parida SK, Mishra SR, Abbas MA, Bhatti MM. Analysis of metallic nanoparticles (Cu, Al2O3, and SWCNTs) on magnetohydrodynamics water-based nanofluid through a porous medium. J Math. 2022; 2022:3237815. doi:10.1155/2022/3237815
- 39Krishna MV, Swarnalathamma BV, Chamkha AJ. Investigations of Soret, Joule and Hall effects on MHD rotating mixed convective flow past an infinite vertical porous plate. J Ocean Eng Sci. 2019; 4(3): 263-275. doi:10.1016/j.joes.2019.05.002
- 40Krishna MV, Chamkha AJ. Hall and ion slip effects on MHD rotating flow of elastico-viscous fluid through porous medium. Int Commun Heat Mass Transfer. 2020; 113:104494. doi:10.1016/j.icheatmasstransfer.2020.104494
- 41Kumar MA, Reddy YD, Goud BS, Rao VS. Effects of Soret, Dufour, Hall current and rotation on MHD natural convective heat and mass transfer flow past an accelerated vertical plate through a porous medium. Int J Thermofluids. 2021; 9:100061. doi:10.1016/j.ijft.2020.100061
10.1016/j.ijft.2020.100061 Google Scholar
- 42Hamid A, Kumar RN, Gowda RJP, et al. Impact of Hall current and homogeneous–heterogeneous reactions on MHD flow of GO-MoS2/water (H2O)-ethylene glycol (C2H6O2) hybrid nanofluid past a vertical stretching surface. Waves Random Complex Media. 2021: 1-18. doi:10.1080/17455030.2021.1985746
- 43Krishna MV, Ahamad NA, Chamkha AJ. Hall effects on unsteady magnetohydrodynamic flow of a nanofluid past an oscillatory vertical rotating flat plate embedded in porous media. J Nanofluids. 2021; 10(2): 259-269. doi:10.1166/jon.2021.1776
- 44Pattnaik JR, Dash GC, Singh S. Diffusion-thermo effect with Hall current on unsteady hydromagnetic flow past an infinite vertical porous plate. Alexandria Eng J. 2017; 56(1): 13-25. doi:10.1016/j.aej.2016.08.027
- 45Sarma D, Pandit KK. Effects of Hall current, rotation and Soret effects on MHD free convection heat and mass transfer flow past an accelerated vertical plate through a porous medium. Ain Shams Eng J. 2018; 9(4): 631-646. doi:10.1016/j.asej.2016.03.005
- 46Krishna MV, Ahamad NA, Chamkha AJ. Hall and ion slip effects on unsteady MHD free convective rotating flow through a saturated porous medium over an exponential accelerated plate. Alexandria Eng J. 2020; 59(2): 565-577. doi:10.1016/j.aej.2020.01.043
- 47Krishna MV, Chamkha AJ. Hall and ion slip effects on magnetohydrodynamic convective rotating flow of Jeffreys fluid over an impulsively moving vertical plate embedded in a saturated porous medium with ramped wall temperature. Numer Methods Partial Differ Equ. 2021; 37(3): 2150-2177. doi:10.1002/num.22670
- 48Paul A. Transient free convective MHD flow past an exponentially accelerated vertical porous plate with variable temperature through a porous medium. Int J Eng Math. 2017; 2017:2981071. doi:10.1155/2017/2981071
10.1155/2017/2981071 Google Scholar
- 49Makinde OD, Venkateswarlu M, Monaledi RL. Unsteady MHD flow of radiating and rotating fluid with Hall current and thermal diffusion past a moving plate in a porous medium. Defect Diffus Forum. 2018; 389: 71-85. doi:10.4028/www.scientific.net/DDF.389.71
10.4028/www.scientific.net/DDF.389.71 Google Scholar
- 50Rath C, Nayak A, Panda S. Impact of viscous dissipation and Dufour on MHD natural convective flow past an accelerated vertical plate with Hall current. Heat Transfer. 2022; 51(6): 5971-5995. doi:10.1002/htj.22577
- 51Rath C, Nayak A. Transient natural convective flow of a radiative viscous incompressible fluid past an exponentially accelerated porous plate with chemical reaction species. Heat Transfer. 2023; 52(1): 467-494. doi:10.1002/htj.22703
- 52Cramer KR, Pai SI. Magnetofluid Dynamics for Engineers and Applied Physicists. McGraw-Hill Book Company; 1973.
- 53Ahmed N. MHD mass transfer flow past an impulsively started semi-infinite vertical plate with Soret effect and ramped wall temperature. In: FT Smith, H Dutta, JN Mordeson, eds. Mathematics Applied to Engineering, Modelling, and Social Issues. Springer; 2019: 245-279. doi:10.1007/978-3-030-12232-4_8
10.1007/978-3-030-12232-4_8 Google Scholar
- 54Khan SA, Hayat T, Alsaedi A. Irreversibility analysis in hydromagnetic Reiner–Rivlin nanofluid with quartic autocatalytic chemical reactions. Int Commun Heat Mass Transfer. 2022; 130:105797. doi:10.1016/j.icheatmasstransfer.2021.105797
- 55Hayat T, Ajaz U, Khan SA, Ahmad B. Entropy optimized radiative flow of viscous nanomaterial subject to induced magnetic field. Int Commun Heat Mass Transfer. 2022; 136:106159. doi:10.1016/j.icheatmasstransfer.2022.106159
- 56McLachlan NW. Complex Variable Theory and Transform Calculus: With Technical Applications. Cambridge University Press; 1955.
- 57Valsa J, Brančik L. Approximate formulae for numerical inversion of Laplace transforms. Int J Numer Model: Electron Netw Devices Fields. 1998; 11(3): 153-166.
- 58Bejawada SG, Reddy YD, Jamshed W, et al. Comprehensive examination of radiative electromagnetic flowing of nanofluids with viscous dissipation effect over a vertical accelerated plate. Sci Rep. 2022; 12:20548. doi:10.1038/s41598-022-25097-2
- 59Zangooee MR, Hosseinzadeh K, Ganji DD. Hydrothermal analysis of hybrid nanofluid flow on a vertical plate by considering slip condition. Theor Appl Mech Lett. 2022; 12(5):100357. doi:10.1016/j.taml.2022.100357
- 60Sridevi C, Sailakumari A. Unsteady magnetohydrodynamic (MHD) Cu–Al2O3/water hybrid nanofluid flow and heat transfer from an exponentially accelerated plate. J Nanofluids. 2023; 12(3): 832-841. doi:10.1166/jon.2023.1955
- 61Rawat SK, Upreti H, Kumar M. Numerical study of activation energy and thermal radiation effects on Oldroyd-B nanofluid flow using the Cattaneo–Christov double diffusion model over a convectively heated stretching sheet. Heat Transfer. 2021; 50(6): 5304-5331. doi:10.1002/htj.22125
10.1002/htj.22125 Google Scholar
- 62Khan SA, Hayat T, Alsaedi A. Simultaneous features of Soret and Dufour in entropy optimized flow of Reiner–Rivlin fluid considering thermal radiation. Int Commun Heat Mass Transfer. 2022; 137:106297. doi:10.1016/j.icheatmasstransfer.2022.106297
- 63Siddique I, Nadeem M, Awrejcewicz J, Pawłowski W. Soret and Dufour effects on unsteady MHD second-grade nanofluid flow across an exponentially stretching surface. Sci Rep. 2022; 12:11811. doi:10.1038/s41598-022-16173-8
