×

Unsteady triple diffusive oscillatory flow in a Voigt fluid. (English) Zbl 07887313

Summary: Convective energy and mass transfer in a non-Newtonian fluid layers a wide-spread physical phenomenon in natural and technical systems. Triple diffusive convection plays a crucial role in chemical engineering by enabling the understanding and optimisation of mass transfer processes involving multiple components. It is essential for designing efficient separation systems, optimising catalysts, predicting reaction kinetics, and improving environmental processes. The motivation of this paper is to explore an Oscillatory flow of a triple diffusive convection in a Voigt fluid layer. The governing partial differential equations are transformed into coupled ordinary differential equations with the help of the oscillation technique. The study emphasises the effects of known physical parameters, such as the thermal Grashof number, solutal Grashof number, Prandtl number, Lewis numbers and Voigt fluid parameters on velocity, temperature, concentrations and rate of heat and mass transfers. In particularly, the study finds that skin friction increases on both channel plates with increasing injection on the heated plate.

MSC:

76A05 Non-Newtonian fluids
76R50 Diffusion
76R10 Free convection
80A19 Diffusive and convective heat and mass transfer, heat flow
Full Text: DOI

References:

[1] Chen, CF; Johnson, DH, Double-diffusive convection: a report on an Engineering Foundation conference, J. Fluid Mech., 138, 405-416, 1984 · doi:10.1017/S0022112084000173
[2] Hill, AA; Malashetty, MS, An operative method to obtain sharp nonlinear stability for systems with spatially dependent coefficients, Proc. R. Soc. Lond. A, 468, 323-336, 2012 · Zbl 1364.76213
[3] Shyy, W.; Chen, MH, Double-diffusive flow in enclosures, Phys. Fluids A, 3, 11, 2592-2607, 1991 · Zbl 0825.76793 · doi:10.1063/1.858200
[4] Kuznetsov, AV; Nield, DA, Double-diffusive natural convective boundary-layer flow of a nanofluid past a vertical plate, Int. J. Therm. Sci., 50, 5, 712-717, 2011 · doi:10.1016/j.ijthermalsci.2011.01.003
[5] Badruddin, IA; Khan, TM; Kamangar, S., Effect of variable heating on double diffusive flow in a square porous cavity, AIP Conf. Proc., 1728, 1, 2016 · doi:10.1063/1.4946740
[6] Turner, JS, Multicomponent convection, Annu. Rev. Fluid Mech., 17, 11-44, 1985 · doi:10.1146/annurev.fl.17.010185.000303
[7] Huppert, HE; Turner, JS, Double-diffusive convection, J. Fluid Mech., 106, 299-329, 1981 · Zbl 0461.76076 · doi:10.1017/S0022112081001614
[8] Nasir, M.; Waqas, M.; Kausar, MS; Bég, OA; Zamri, N., Cattaneo-Christov dual diffusive non-Newtonian nanoliquid flow featuring nonlinear convection, Chin. J. Phys., 2022 · doi:10.1016/j.cjph.2022.05.005
[9] Platten, JK; Legros, JC, Convection in Liquids, 2011, New York: Springer, New York
[10] Griffiths, RW, The influence of a third diffusing component upon the onset of convection, J. Fluid Mech., 92, 659-670, 1979 · Zbl 0445.76036 · doi:10.1017/S0022112079000811
[11] Terrones, G., Cross diffusion effects on the stability criteria in a triply diffusive system, Phys. Fluids, 5, 2172-2182, 1993 · Zbl 0782.76037 · doi:10.1063/1.858556
[12] Straughan, B.; Tracey, J., Multi-component convection-diffusion with internal heating or cooling, Acta Mech., 133, 219-239, 1999 · Zbl 0922.76170 · doi:10.1007/BF01179019
[13] Khan, ZH; Khan, WA; Sheremet, MA; Tang, J.; Sun, L., Irreversibilities in a triple diffusive flow in various porous cavities, Chin. J. Phys., 73, 239-255, 2021 · Zbl 07837785 · doi:10.1016/j.cjph.2021.06.017
[14] Umavathi, JC; Ali, HM; Patil, SL, Triple diffusive mixed convection flow in a duct using convective boundary conditions, Math. Methods Appl. Sci., 43, 15, 9223-9244, 2020 · Zbl 1454.35300 · doi:10.1002/mma.6617
[15] Raghunatha, KR; Shivakumara, IS, Triple diffusive convection in a viscoelastic Oldroyd-B fluid layer, Phys. Fluids, 33, 6, 2021 · doi:10.1063/5.0054938
[16] Raghunatha, KR; Shivakumara, IS; Swamy, MS, Effect of cross-diffusion on the stability of a triple-diffusive Oldroyd-B fluid layer, Z. Angew. Math. Phys., 70, 1-21, 2019 · Zbl 1437.76003 · doi:10.1007/s00033-019-1143-x
[17] Raghunatha, KR; Shivakumara, IS, Double-diffusive convection in a rotating viscoelastic fluid layer, ZAMM J. Appl. Math. Mech., 101, 4, 2021 · Zbl 07809799 · doi:10.1002/zamm.201900025
[18] Shivakumara, IS; Raghunatha, KR; Savitha, MN; Dhananjaya, M., Implication of cross-diffusion on the stability of double diffusive convection in an imposed magnetic field, Z. Angew. Math. Phys., 72, 3, 117, 2021 · Zbl 1471.76032 · doi:10.1007/s00033-021-01544-4
[19] Raghunatha, KR; Vinod, Y.; Manjunatha, BV, Application of Bernoulli wavelet method on triple-diffusive convection in Jeffery-Hamel flow, Heat Transf., 52, 8, 5269-5301, 2023 · doi:10.1002/htj.22928
[20] Padma, R.; Ponalagusamy, R.; Selvi, RT, Mathematical modeling of electro hydrodynamic non-Newtonian fluid flow through tapered arterial stenosis with periodic body acceleration and applied magnetic field, Appl. Math. Comput., 362, 2019 · Zbl 1433.76194
[21] Ponalagusamy, R., Particulate suspension Jeffrey fluid flow in a stenosed artery with a particle-free plasma layer near the wall, Korea-Aust. Rheol. J., 28, 217-227, 2016 · doi:10.1007/s13367-016-0022-7
[22] Ponalagusamy, R.; Tamil Selvi, R., Influence of magnetic field and heat transfer on two-phase fluid model for oscillatory blood flow in an arterial stenosis, Meccanica, 50, 927-943, 2015 · Zbl 1317.76105 · doi:10.1007/s11012-014-9990-1
[23] Ponalagusamy, R.; Murugan, D., Dispersion of a solute in blood flowing through narrow arteries with homogeneous first-order chemical reaction, Proc. Natl Acad. Sci. India A, 91, 1-6, 2021 · Zbl 1490.92022
[24] Ponalagusamy, R.; Murugan, D., Effect of electro-magneto-hemodynamic environs on dispersion of solute in the peristaltic motion through a channel with chemical reaction, wall properties and porous medium, Korea-Aust. Rheol. J., 34, 1, 69-90, 2022 · doi:10.1007/s13367-022-00024-z
[25] Ponalagusamy, R.; Murugan, D., Transport of a reactive solute in electroosmotic pulsatile flow of non-Newtonian fluid through a circular conduit, Chin. J. Phys., 81, 243-269, 2023 · Zbl 1542.76003 · doi:10.1016/j.cjph.2022.11.002
[26] Ponalagusamy, R.; Murugan, D., Impact of variable viscosity, chemical reaction and electro-osmotic mechanism on the dispersal of solute through a uniform channel with permeable walls, Int. J. Appl. Comput. Math., 8, 2, 55, 2022 · doi:10.1007/s40819-022-01259-8
[27] Voigt, W., Ueber die Beziehungzwischen den beiden Elasticitäts constant enisotroper Körper, Ann. Phys., 274, 12, 573-587, 1889 · JFM 21.1039.01 · doi:10.1002/andp.18892741206
[28] Peek, AA, Viscoelastic properties of human knee joint soft tissues under high strain rate deformations, J. Biomech. Eng., 139, 12, 2017
[29] Hurren, CJ, Viscoelastic characterization of polyethylene using oscillatory shear measurements, Polym. Test., 67, 156-167, 2018
[30] Lee, H., Viscoelastic properties of silicone rubber for low-frequency acoustic applications, Appl. Acoust., 144, 91-97, 2019
[31] Straughan, B., Stability in Kelvin-Voigt poroelasticity, Boll. Unione Mat. Ital., 14, 2, 357-366, 2021 · Zbl 1469.74059 · doi:10.1007/s40574-020-00268-z
[32] Straughan, B., Continuous dependence and convergence for a Kelvin-Voigt fluid of order one, Ann. Univ. Diferrara, 68, 1, 49-61, 2022 · Zbl 1506.35173 · doi:10.1007/s11565-021-00381-7
[33] Zvyagin, VG; Turbin, MV, The study of initial-boundary value problems for mathematical models of the motion of Kelvin-Voigt fluids, J. Math. Sci., 168, 157-308, 2010 · Zbl 1288.35005 · doi:10.1007/s10958-010-9981-2
[34] Kaya, M.; Çelebi, AO, Existence of weak solutions of the g-Kelvin-Voigt equation, Math. Comput. Model., 49, 3-4, 497-504, 2009 · Zbl 1171.35451 · doi:10.1016/j.mcm.2008.03.005
[35] Baranovskii, ES, Strong solutions of the incompressible Navier-Stokes-Voigt model, Mathematics, 8, 2, 181, 2020 · doi:10.3390/math8020181
[36] Kadchenko, SI; Kondyukov, AO, Numerical study of a flow of viscoelastic fluid of Kelvin-Voigt having zero order in a magnetic field, J. Comput. Eng. Math., 3, 2, 40-47, 2016 · Zbl 1455.76208 · doi:10.14529/jcem1602005
[37] Straughan, B., Competitive double diffusive convection in a Kelvin-Voigt fluid of order one, Appl. Math. Optim., 84, Suppl 1, 631-650, 2021 · Zbl 1480.76051 · doi:10.1007/s00245-021-09781-9
[38] Straughan, B., Thermosolutal convection with a Navier-Stokes-Voigt fluid, Appl. Math. Optim., 84, 3, 2587-2599, 2021 · Zbl 1475.76042 · doi:10.1007/s00245-020-09719-7
[39] Stone, HA; Stroock, AD, Engineering flows in small devices: microfluidics toward a lab-on-a-chip, Annu. Rev. Fluid Mech., 36, 381-411, 2005 · Zbl 1076.76076 · doi:10.1146/annurev.fluid.36.050802.122124
[40] Liu, Y.; Karniadakis, GE, Microfluidics Modeling Mechanics and Mathematics, 2013, Cambridge: Cambridge University Press, Cambridge
[41] Shapira, Y.; Rappaport, H., Oscillatory flows and enhanced heat transfer, Heat Mass Transf., 48, 777-1784, 2012
[42] Bouchoucha, M.; Ravelet, F., Energy harvesting from oscillatory flows: a review, Renew. Sustain. Energy Rev., 81, 2023-2036, 2016
[43] Sudo, K.; Sumida, M.; Yamane, R., Secondary motion of fully developed oscillatory flow in a curved pipe, J. Fluid Mech., 237, 189-208, 1992 · doi:10.1017/S0022112092003380
[44] Bianchi, P.; Williams, JD; Kappe, CO, Oscillatory flow reactors for synthetic chemistry applications, J. Flow Chem., 10, 475-490, 2020 · doi:10.1007/s41981-020-00105-6
[45] V.L. Kopparthy, N.D. Crews, Oscillating-flow thermal gradient PCR. bioRxiv 544908 (2019)
[46] Raghunatha, KR; Inc, M.; Vinod, Y., Viscoelastic effects on the oscillatory flow in a fluid-saturated porous layer, Heat Transf., 53, 1, 244-258, 2024 · doi:10.1002/htj.22952
[47] Raghunatha, KR; Vinod, Y.; Inc, M.; Yildirim, EN, Viscoelastic effects on the double-diffusive oscillatory flow in a fluid-saturated porous layer, Mod. Phys. Lett. B, 7, 2350167, 2023 · doi:10.1142/S0217984923501671
[48] Raghunatha, KR; Vinod, Y., Couple stress effects on the MHD oscillatory flow in a fluid-saturated porous layer, Heat Transf., 52, 5214-5230, 2023 · doi:10.1002/htj.22924
[49] Alhefthi, RK; Vinod, Y.; Raghunatha, KR; Inc, M., Couple stress effects on the MHD triple-diffusive oscillatory flow in a fluid-saturated porous layer, Mod. Phys. Lett. B, 2023 · doi:10.1142/S0217984924501161
[50] Falade, JA; Ukaegbu, JC; Egere, AC; Adesanya, SO, MHD oscillatory flow through a porous channel saturated with porous medium, Alex. Eng. J., 56, 1, 147-152, 2017 · doi:10.1016/j.aej.2016.09.016
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.