[1] |
Pearlstein, AJ; Harris, RM; Terrones, G., The onset of convective instability in a triply diffusive fluid layer, J. Fluid Mech., 202, 443-465 (1989) · Zbl 0666.76066 · doi:10.1017/S0022112089001242 |
[2] |
Griffiths, RW, The influence of a third diffusing component upon the onset of convection, J. Fluid Mech., 4, 659-670 (1979) · Zbl 0445.76036 · doi:10.1017/S0022112079000811 |
[3] |
Poulikakos, D., The effect of a third diffusing component on the onset of convection in a horizontal porous layer, Phys. Fluids., 10, 3172 (1985) · Zbl 0573.76045 · doi:10.1063/1.865359 |
[4] |
Sameena, T.; Pranesh, S., Triple diffusive convection in Oldroyd-B liquid, IOSR., 4, 7-13 (2016) · doi:10.9790/0990-0405010718 |
[5] |
Raghunatha, KR; Shivakumara, IS, Stability of triple diffusive convection in a viscoelastic fluid-saturated porous layer, Appl. Math. Mech., 10, 1385-1410 (2018) · Zbl 1402.76129 · doi:10.1007/s10483-018-2376-8 |
[6] |
Sameena, T.; Pranesh, S., Heat and mass transfer of triple diffusive convection in a rotating liquid using Ginzburg-Landau model, Int. J. Mech. Mechatron. Eng., 3, 545-550 (2017) |
[7] |
Raghunatha, KR; Shivakumara, IS; Shankar, BM, Weakly nonlinear stability analysis of triple diffusive convection in a Maxwell fluid saturated porous layer, Appl. Math. Mech., 2, 153-168 (2017) · Zbl 1382.76014 |
[8] |
Awasthi, MK; Kumar, V.; Patel, RK, Onset of triply diffusive convection in a Maxwell fluid saturated porous layer with internal heat source, Ain Shams Eng. J., 4, 1591-1600 (2018) · doi:10.1016/j.asej.2016.11.012 |
[9] |
Gayathri, M.; Pranesh, S.; Sameena, T., Effects of magnetic field and internal heat generation on triple diffusive convection in an Oldroyd-B liquid, Int. J. Res. Advent Technol., 6, 154-163 (2019) |
[10] |
Pranesh, S.; Siddheshwar, PG; Zhao, Y.; Ansa, M., Linear and nonlinear triple diffusive convection in the presence of sinusoidal/non-sinusoidal gravity modulation: A comparative study, Mech. Res. Commun., 113, 103694 (2021) · doi:10.1016/j.mechrescom.2021.103694 |
[11] |
Pranesh, S.; Siddheshwar, PG; Sameena, T.; Yekasi, V., Convection in a horizontal layer of water with three diffusing components, SN Appl. Sci. (2020) · doi:10.1007/s42452-020-2478-9 |
[12] |
Shivakumara, IS; Naveen Kumar, SB, Linear and weakly nonlinear triple diffusive convection in a couple stress fluid layer, Int. J. Heat Mass Transf., 68, 542-553 (2014) · doi:10.1016/j.ijheatmasstransfer.2013.09.051 |
[13] |
Bush, MB, Viscous Flow Applications, 134-160 (1989), Berlin, Heidelberg: Springer, Berlin, Heidelberg · Zbl 0696.76003 · doi:10.1007/978-3-642-83683-1_7 |
[14] |
Stokes, VK, Couple stresses in fluids, Phys. Fluids, 9, 1709-1715 (1966) · doi:10.1063/1.1761925 |
[15] |
Mohd Rusdi, ND; Mohd Mokhtar, NF; Senu, N.; Mohamed Isa, SSP, Stability convection in a fluid saturated in an anisotropic porous medium with internal heating effect, J. Adv. Res. Fluid Mech. Therm. Sci., 2, 75-84 (2020) · doi:10.37934/arfmts.76.2.7584 |
[16] |
Maiti, S.; Misra, JC, Peristaltic transport of a couple stress fluid: some applications to hemodynamics, J. Mech. Med. Biol., 3, 1250048 (2012) · doi:10.1142/S0219519411004733 |
[17] |
Chaturani, P., Viscosity of Poiseuille flow of a couple stress fluid with applications to blood flow, Biorheology, 2, 119-128 (1978) · doi:10.3233/BIR-1978-15206 |
[18] |
Kumar, P., Thermosolutal magneto: rotatory convection in couple: stress fluid through porous medium, J. Appl. Fluid Mech., 5, 45 (2012) |
[19] |
Layek, GC; Pati, N., Chaotic thermal convection of couple-stress fluid layer, Nonlinear Dyn., 2, 837-852 (2017) · Zbl 1390.37141 |
[20] |
Keshri, OP; Kumar, A.; Gupta, VK, Effect of internal heat source on magneto-stationary convection of couple stress fluid under magnetic field modulation, Chin. J. Phys., 57, 105-115 (2019) · Zbl 1539.80013 · doi:10.1016/j.cjph.2018.12.006 |
[21] |
Nandal, R.; Mahajan, A., Penetrative convection in couple-stress fluid via internal heat source/sink with the boundary effects, J. Non-Newtonian Fluid Mech., 260, 133-141 (2018) · doi:10.1016/j.jnnfm.2018.07.004 |
[22] |
Valanis, KC; Sun, TC, Poiseuille flow of a couple stress fluid with applications to blood flow, Biorheology, 2, 85-97 (1969) · doi:10.3233/BIR-1969-6203 |
[23] |
Straughan, B.; Tracey, J., Multi-component convection-diffusion with internal heating or cooling, Acta Mech., 1, 219-238 (1999) · Zbl 0922.76170 · doi:10.1007/BF01179019 |
[24] |
Tasaka, Y.; Takeda, Y., Effects of heat source distribution on natural convection induced by internal heating, Int. J. Heat Mass Transf., 6, 1164-1174 (2005) · Zbl 1189.76564 · doi:10.1016/j.ijheatmasstransfer.2004.09.044 |
[25] |
Tritton, DJ; Zarraga, MN, Convection in horizontal layers with internal heat generation, Exp. J. Fluid Mech., 1, 21-31 (1967) · doi:10.1017/S0022112067001272 |
[26] |
Miquel, B.; Lepot, S.; Bouillaut, V.; Gallet, B., Convection driven by internal heat sources and sinks: heat transport beyond the mixing-length or “ultimate” scaling regime, Phys. Rev. Fluids. (2019) · doi:10.1103/PhysRevFluids.4.121501 |
[27] |
Nandal, R.; Mahajan, A., Linear and nonlinear stability analysis of a fluid-saturated Darcy-Brinkman porous media via internal heat source/sink with the effect of boundary heating/cooling, J. Porous Media., 5, 545-562 (2019) · doi:10.1615/JPorMedia.2019028958 |
[28] |
Ramachandramurthy, V.; Aruna, AS; Kavitha, N., Bénard-Taylor convection in temperature-dependent variable viscosity newtonian liquids with internal heat source, Int. J. Appl. Comput. Math. (2020) · Zbl 1461.76160 · doi:10.1007/s40819-020-0781-1 |
[29] |
Shivaraj, B.; Siddheshwar, PG; Uma, D., Effects of variable viscosity and internal heat generation on Rayleigh-Bénard convection in Newtonian dielectric liquid, Int. J. Appl. Comput. Math. (2021) · Zbl 1489.76020 · doi:10.1007/s40819-021-01060-z |
[30] |
Kanchana, C.; Zhao, Y., Effect of internal heat generation/absorption on Rayleigh-Bénard convection in water well-dispersed with nanoparticles or carbon nanotubes, Int. J. Heat Mass Transf., 127, 1031-1047 (2018) · doi:10.1016/j.ijheatmasstransfer.2018.06.122 |
[31] |
Itaya, Y.; Okouchi, K.; Uchiyama, S.; Mori, S.; Hasatani, M., Internal heating effect and application of microwaves with fluidization of electrically conductive particles in the ceramic drying Process, Dev. Chem. Eng. Miner. Process., 4, 381-400 (2008) · doi:10.1002/apj.5500100410 |
[32] |
Venezian, G., Effect of modulation on the onset of thermal convection, J. Fluid Mech., 2, 243-254 (1969) · Zbl 0164.28901 · doi:10.1017/S0022112069001091 |
[33] |
Bhadauria, BS; Kiran, P., Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source, Ain Shams Eng. J., 4, 1287-1297 (2014) · doi:10.1016/j.asej.2014.05.005 |
[34] |
Bhadauria, BS; Singh, MK; Singh, A.; Singh, BK; Kiran, P., Stability analysis and internal heating effect on oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation, Int. J. Appl. Mech. Eng., 4, 785-803 (2016) · doi:10.1515/ijame-2016-0046 |
[35] |
Sameena, T.; Pranesh, S., Synchronous and asynchronous boundary temperature modulations on triple-diffusive convection in couple stress liquid using Ginzburg-Landau model, Int. J. Eng. Technol., 410, 645 (2018) · doi:10.14419/ijet.v7i4.10.21304 |
[36] |
Siddheshwar, PG; Uma, D.; Bhavya, S., Effects of variable viscosity and temperature modulation on linear Rayleigh-Bénard convection in Newtonian dielectric liquid, Appl. Math. Mech., 11, 1601-1614 (2019) · Zbl 1430.76175 · doi:10.1007/s10483-019-2537-9 |
[37] |
Kiran, P., Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity modulation, Ain Shams Eng. J., 2, 639-651 (2016) · doi:10.1016/j.asej.2015.06.005 |
[38] |
Sun, Q.; Wang, S.; Zhao, M.; Yin, C.; Zhang, Q., Weak nonlinear analysis of Darcy-Brinkman convection in Oldroyd-B fluid saturated porous media under temperature modulation, Int. J. Heat Mass Transf., 138, 244-256 (2019) · doi:10.1016/j.ijheatmasstransfer.2019.04.058 |
[39] |
Kanchana, C.; Siddheshwar, PG; Zhao, Y., Regulation of heat transfer in Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids using gravity, boundary temperature and rotational modulations, J. Therm. Anal. Calorim., 142, 1579 (2020) · doi:10.1007/s10973-020-09325-3 |
[40] |
Kumar, A.; Gupta, VK; Meena, N.; Hashim, I., Effect of rotational speed modulation on the weakly nonlinear heat transfer in Walter-B viscoelastic fluid in the highly permeable porous medium, Mathematics, 9, 1448 (2020) · doi:10.3390/math8091448 |
[41] |
Neha, A.; Siddheshwar, PG; Nagouda, S.; Pranesh, S., Thermoconvective instability in a vertically oscillating horizontal ferrofluid layer with variable viscosity, Heat Transf., 49, 4543 (2020) · doi:10.1002/htj.21840 |
[42] |
Siddheshwar, PG; Kanchana, C., Effect of trigonometric sine, square and triangular wave-type time-periodic gravity-aligned oscillations on Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids, Meccanica, 3, 451-469 (2019) · doi:10.1007/s11012-019-00957-w |
[43] |
Meghana, J.; Pranesh, S., Individual effects of four types of rotation modulation on Rayleigh-Bénard convection in a ferromagnetic fluid with couple stress, Heat Transf., 50, 6795-6815 (2021) · doi:10.1002/htj.22204 |
[44] |
Rudziva, M.; Sibanda, P.; Noreldin, OAI; Goqo, S., On trigonometric cosine, square, sawtooth, and triangular wave-type rotational modulations on triple-diffusive convection in salted water, Heat Transf., 50, 6886-6914 (2021) · doi:10.1002/htj.22208 |
[45] |
Roslan, R.; Abdulhameed, M.; Hashim, I.; Chamkha, AJ, Non-sinusoidal waveform effects on heat transfer performance in pulsating pipe flow, Alexandria Eng. J., 55, 3309-3319 (2016) · doi:10.1016/j.aej.2016.08.012 |
[46] |
Meenakshi, N.; Siddheshwar, PG, Controlling Rayleigh-Bénard Magneto convection in Newtonian Nanoliquids by Rotational, gravitational and temperature modulations: a comparative study, Arab. J. Sci. Eng. (2022) · doi:10.1007/s13369-022-06695-8 |
[47] |
Kiran, P.; Bhadauria, BS, Chaotic convection in a porous medium under temperature modulation, Transp. Porous Med., 107, 745-763 (2015) · doi:10.1007/s11242-015-0465-1 |
[48] |
Bhadauria, BS; Kiran, P., Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under G-jitter, Int. J. Heat Mass Transf., 84, 610-624 (2015) · doi:10.1016/j.ijheatmasstransfer.2014.12.032 |
[49] |
Rudziva, M.; Sibanda, P.; Noreldin, OA; Goqo, SP, A numerical study of heat and mass transfer in a Darcy porous medium saturated with a couple stress fluid under rotational modulation, Appl. Math. Modell., 104, 455-473 (2022) · Zbl 1505.76087 · doi:10.1016/j.apm.2021.12.004 |
[50] |
Bazylak, A.; Djilali, N.; Sinton, D., Natural convection with distributed heat source modulation, Int. J. Heat Mass Transf., 9, 1649-1655 (2007) · Zbl 1124.80306 · doi:10.1016/j.ijheatmasstransfer.2006.10.033 |
[51] |
Noor, AS; Sameena, T.; Pranesh, S., Heat and mass transfer of triple diffusive convection in viscoelastic liquids under internal heat source modulations, Heat Transf., 51, 239 (2021) · doi:10.1002/htj.22305 |
[52] |
Noor, AS; Sameena, T.; Pranesh, S., Effect of internal heat source modulations on the onset of triple diffusive convection in viscoelastic liquids, Indian J. Eng. Mater. Sci., 28, 509-519 (2021) |
[53] |
Ansa, M.; Pranesh, S., Comparative study of sinusoidal and non-sinusoidal two-frequency internal heat modulation in a Rayleigh-Bénard system, Heat Transf., 51, 2780 (2021) |
[54] |
Meghana, J.; Pranesh, S., Rayleigh-Bénard convection in a Boussinesq-Stokes ferromagnetic fluid under sinusoidal and non-sinusoidal internal heat modulation, Heat Transf. (2022) · doi:10.1002/htj.22535 |
[55] |
Lyubimova, T.; Zubova, N., Onset of convection in a ternary mixture in a square cavity heated from above at various gravity levels, Microgravity Sci. Technol., 26, 241-247 (2014) · doi:10.1007/s12217-014-9383-z |
[56] |
Lyubimova, T.; Zubova, N.; Shevtsova, V., Effects of non-uniform temperature of the walls on the Soret experiment, Microgravity Sci. Technol., 31, 1-11 (2018) · doi:10.1007/s12217-018-9666-x |
[57] |
Pranesh, S.; Richa, S., Three-component convection in a vertically oscillating oldroyd-b fluid with cross effects, Microgravity Sci. Technol., 34, 1-20 (2022) · doi:10.1007/s12217-022-09935-6 |
[58] |
Raghunatha, KR; Shivakumara, IS, Triple diffusive convection in a viscoelastic Oldroyd-B fluid layer, Phys. Fluids., 33, 063108 (2021) · doi:10.1063/5.0054938 |
[59] |
Bhadauria, BS; Kiran, P., Study of heat and mass transport in temperature-dependent-viscous fluid under gravity modulation, Malaya J. Matematik., 1, 33-48 (2013) · Zbl 1369.34038 |
[60] |
Huppert, HE; Turner, JS, Double-diffusive convection, J. Fluid Mech., 106, 299-329 (1981) · Zbl 0461.76076 · doi:10.1017/S0022112081001614 |
[61] |
Siddheshwar, PG; Pranesh, S., An analytical study of linear and non-linear convection in Boussinesq-Stokes suspensions, Int. J. Non-Linear Mech., 39, 165-172 (2004) · Zbl 1348.76176 · doi:10.1016/S0020-7462(02)00169-5 |
[62] |
Chandrasekhar, S., Hydrodynamic and Hydromagnetic Stability (1961), New York: Oxford University Press, New York · Zbl 0142.44103 |