Poiseuille Flow with Couple Stresses Effect and No-slip Boundary Conditions

[1] Joseph, D.D., Stability of fluid motions I. Springer, New York 1976.

[2] Straughan, B., Explosive instabilities in mechanics, Springer, Heidelberg, 1998.

[3] Dongarra, J.J., Straughan, B., Walker, D.W., Chebyshev tau-QZ algorithm methods for calculating spectra of hydrodynamic stability problems, Applied Numerical Mathematics, 22(4), 1996, 399-434

[4] Yecko, P., Disturbance growth in two-fluid channel flow: The role of capillarity, International Journal of Multiphase Flow, 34(3), 2008, 272-282.

[5] Kaiser, R., Mulone, G., A note on nonlinear stability of plane parallel shear flows, Journal of Mathematical Analysis and Applications, 302(2), 2005, 543-556.

[6] Galdi, G.P., Robertson, A.M., The relation between flow rate and axial pressure gradient for time-periodic Poiseuille flow in a pipe, Journal of Mathematical Fluid Mechanics, 7(2), 2005, S215-S223.

[7] Galdi, G.P., Pileckas, K., Silvestre, A.L., On the unsteady Poiseuille flow in a pipe, Zeitschrift für angewandte Mathematik und Physik, 58(6), 2007, 994-1007.

[8] Webber, M., Straughan, B., Stability of pressure-driven flow in a microchannel, Rendiconti del Circolo Matematico di Palermo: serie II, 78(2), 2006, 343-357.

[9] Straughan, B., Harfash, A.J., Instability in Poiseuille flow in a porous medium with slip boundary conditions, Microfluidics and Nanofluidics, 15(1), 2013, 109-115.

[10] Chang, M.H., Chen, F., Straughan, B., Instability of Poiseuille flow in a fluid overlying a porous layer, Journal of Fluid Mechanics, 564, 2006, 287-303.

[11] Hill, A.A., Straughan, B., Poiseuille flow in a fluid overlying a porous medium, Journal of Fluid Mechanics, 603, 2008, 137-149.

[12] Chandrasekhar, S., Hydrodynamic and hydromagnetic stability, Dover, New York, 1981.

[13] Stokes, V.K., Couple stresses in fluids, The Physics of Fluids, 9(9), 1966, 1709-1715.

[14] Walicki, E., Walicka, A., Interia effect in the squeeze film of a couple-stress fluid in biological bearings, Applied Mechanics and Engineering, 4(2), 1999, 363-373.

[15] Gaikwad, S.N., Kouser, S., Double diffusive convection in a couple stress fluid-saturated porous layer with internal heat source, International Journal of Heat and Mass Transfer, 78, 2014, 1254-1264.

[16] Devi, R., Mahajan, A., Global stability for thermal convection in a couple-stress fluid, International Communications in Heat and Mass Transfer, 38(7), 2011, 938-942.

[17] Malashetty, M.S., Kollur, P., The onset of double-diffusive convection in a couple of stress fluid-saturated anisotropic porous layer, Transport in Porous Media, 86(2), 2011, 435-459.

[18] Harfash, A.J., Meftenb, G.A., Couple stresses effect on linear instability and nonlinear stability of convection in a reacting fluid, Chaos, Solitons, and Fractals, 107, 2018, 18-25

[19] Harfash, A.J., Meftenb, G.A., Couple stresses effect on instability and nonlinear stability in a double-diffusive convection, Applied Mathematics, and Computation, 341, 2019, 301–320.

[20] Takashima, M., The stability of the modified plane Poiseuille flow in the presence of a transverse magnetic field, Fluid Dynamics Research, 17(6), 1996, 293-310.

[21] Hill, A.A., Straughan, B., Stability of Poiseuille flow in a porous medium, In R. Rannacher and A. Sequeira, editors, Advances in Mathematical Fluid Mechanics, Springer, Heidelberg, 2010.

[22] Webber, M., Instability of fluid flows, including boundary slip, Ph.D. thesis, Durham University, 2007.

[23] Straughan, B., Triply resonant penetrative convection, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 468(2148), 2012, 3804-3823.

[24] Harfash, A.J., Three-dimensional simulation of radiation induced convection, Applied Mathematics and Computation, 227, 2014, 92-101.

[25] Harfash, A.J., Three-dimensional simulations for convection induced by the selective absorption of radiation for the Brinkman model, Meccanica, 51(3), 2016, 501-515.

[26] Harfash, A.J., Alshara, A.K., On the stationary and oscillatory modes of triply resonant penetrative convection, International Journal of Numerical Methods for Heat and Fluid Flow, 26(5), 2016, 1391 - 1415.

[27] Harfash, A.J., Resonant penetrative convection in porous media with an internal heat source/sink effect, Applied Mathematics and Computation, 281, 2016, 323-342.

[28] Harfash, A.J., Stability analysis for penetrative convection in a fluid layer with throughflow, International Journal of Modern Physics C, 27(9), 2016, 1650101.

[29] Harfash, A.J., Nonhomogeneous porosity and thermal diffusivity effects on a double-diffusive convection in anisotropic porous media, International Journal of Nonlinear Sciences and Numerical Simulation, 17(5), 2016, 205-220.

[30] Harfash, A.J., Nashmi, F. K., Triply resonant double-diffusive convection in a fluid layer, Mathematical Modelling and Analysis, 22, 2017, 809-826.

[31] Harfash, A.J., H. A. Challoob, Slip boundary conditions and through flow effects on double-diffusive convection in internally heated heterogeneous Brinkman porous media, Chinese Journal of Physics, 56, 2018, 10-22.

[32] Hameed, A.A., Harfash, A.J., Unconditional nonlinear stability for double-diffusive convection in a porous medium with temperature-dependent viscosity and density, Heat Transfer-Asian Research, 48, 2019, 2948-2973.

[33] Challoob, H.A., Mathkhor, A.J., Harfash, A.J., Slip boundary condition effect on double-diffusive convection in a porous medium: Brinkman Model, Heat Transfer-Asian Research, 49, 2020, 258-268.

[34] Harfash, A.J., Numerical methods for solving some hydrodynamic stability problems, International Journal of Applied and Computational Mathematics, 1, 2015, 293–326.

[35] Ghalambaz, M., Grosan, T., Pop, I., Mixed convection boundary layer flow and heat transfer over a vertical plate embedded in a porous medium filled with a suspension of nano-encapsulated phase change materials, Journal of Molecular Liquids, 293, 2019, 111432.

[36] Ghalambaz, M., Chamkha, A.J., Wen, D., Natural convective flow and heat transfer of Nano-Encapsulated Phase Change Materials (NEPCMs) in a cavity, International Journal of Heat and Mass Transfer, 138, 2019, 738-749

[37] Mehryan, S. A. M., Izadpanahi, E., Ghalambaz, M., Chamkha, A.J., Mixed convection flow caused by an oscillating cylinder in a square cavity filled with Cu–Al O/water hybrid nanofluid, Journal of Thermal Analysis and Calorimetry, 137, 2019, 965-982.

[38] Hajjar, A., Mehryan, S.A.M., Ghalambaz, M., Time periodic natural convection heat transfer in a nano-encapsulated phase-change suspension, International Journal of Mechanical Sciences, 166, 2020, 105243.

[39] Ghalambaz, M., Doostani, A., Izadpanahi, E., Chamkha, A.J., Conjugate natural convection flow of Ag–MgO/water hybrid nanofluid in a square cavity, Journal of Thermal Analysis and Calorimetry, 2019, doi:10.1007/s10973-019-08617-7.