Asymptotic analysis of the thermomicropolar fluid flow through a thin channel with cooling

References

• Eringen AC. Theory of micropolar fluids. J Math Mech. 1966;16:1–18.
   Web of Science ®Google Scholar
• Eringen AC. Theory of thermomicrofluids. J Math Anal Appl. 1972;38(2):480–496.
   Web of Science ®Google Scholar
• Abd Elmaboud Y. Thermomicropolar fluid flow in a porous channel with peristalsis. J Porous Media. 2011;14(11):1033–1045.
   Web of Science ®Google Scholar
• Cheng C-Y. Nonsimilar solutions for double-diffusion boundary layers on a sphere in micropolar fluids with constant wall heat and mass fluxes. Appl Math Model. 2010;34(7):1892–1900.
   Web of Science ®Google Scholar
• Hossain MdM, Mandal AC, Roy NC, et al. Fluctuating flow of thermomicropolar fluid past a vertical surface. Appl Appl Math: Int J. 2013;8(1):128–150.
   Google Scholar
• Hossain MdM, Mandal AC, Roy NC, et al. Transient natural convection flow of thermomicropolar fluid of micropolar thermal conductivity along a nonuniformly heated vertical surface. Adv Mech Eng. 2014;2014:1–13.
   Google Scholar
• Rahman MM, Eltayeb I. Thermo-micropolar fluid flow along a vertical permeable plate with uniform surface heat flux in the presence of heat generation. Therm Sci. 2009;13(1):23–36.
   Web of Science ®Google Scholar
• Łukaszewicz G. Micropolar fluids, theory and application. Boston (MA): Birkhäuser Boston, Inc.; 1999.
   Google Scholar
• Eringen AC. Microcontinuum field theories II: fluent media. New York (NY): Springer; 2001.
   Google Scholar
• Payne LE, Straughan B. Critical Rayleigh numbers for oscillatory and nonlinear convection in an isotropic thermomicropolar fluid. Int J Eng Sci. 1989;27(7):827–836.
   Web of Science ®Google Scholar
• Beneš M, Pažanin I, Radulović M. Rigorous derivation of the asymptotic model describing a nonsteady micropolar fluid flow through a thin pipe. Comput Math Appl. 2018;76(9):2035–2060.
   Web of Science ®Google Scholar
• Dupuy D, Panasenko G, Stavre R. Asymptotic methods for micropolar fluids in a tube structure. Math Model Methods Appl Sci. 2004;14:735–758.
   Web of Science ®Google Scholar
• Dupuy D, Panasenko G, Stavre R. Asymptotic solution for a micropolar flow in a curvilinear channel. Z Angew Math Mech. 2008;88(10):793–807.
   Web of Science ®Google Scholar
• Pažanin I. Effective flow of micropolar fluid through a thin or long pipe. Math Probl Eng. 2011;2011:127070.
   Web of Science ®Google Scholar
• Pažanin I. Asymptotic behavior of micropolar fluid flow through a curved pipe. Acta Appl Math. 2011;116(1):1–25.
   Web of Science ®Google Scholar
• Pažanin I, Radulović M. Asymptotic analysis of the nonsteady micropolar fluid flow through a curved pipe. Appl Anal. 2020;99(12):2045–2092.
   Web of Science ®Google Scholar
• Łukaszewicz G. Long-time behavior of 2D micropolar fluid flows. Math Comput Model. 2001;34:487–509.
   Google Scholar
• Tarasinska A. Global attractor for heat convection problem in a micropolar fluid. Math Methods Appl Sci. 2006;29:1215–1236.
   Web of Science ®Google Scholar
• Beneš M, Pažanin I. Rigorous derivation of the effective model describing a nonisothermal fluid flow in a vertical pipe filled with porous medium. Contin Mech Thermodyn. 2018;30:301–317.
   Web of Science ®Google Scholar
• Marušić–Paloka E, Pažanin I. Non-isothermal fluid flow through a thin pipe with cooling. Appl Anal. 2009;88:495–515.
   Web of Science ®Google Scholar
• Marušić–Paloka E, Pažanin I. On the effects of curved geometry on heat conduction through a distorted pipe. Nonlinear Anal: Real World Appl. 2010;11:4554–4564.
   Web of Science ®Google Scholar
• Marušić–Paloka E, Pažanin I, Radulović M. On the Darcy–Brinkman–Boussinesq flow in a thin channel with irregularities. Transp Porous Media. 2020;131(2):633–660.
   Web of Science ®Google Scholar
• Kalita P, Łukaszewicz G, Siemianowski J. Rayleigh–Bénard problem for thermomicropolar fluids. Topol Methods Nonlinear Anal. 2018;52(2):477–514.
   Web of Science ®Google Scholar
• Keller HB. Numerical methods for two–point boundary value problems. Waltham (MA): Ginn–Blaisdell; 1978.
   Google Scholar
• Galdi GP. An introduction to the mathematical theory of the Navier–Stokes equations. Vol. II. New York (NY), USA: Springer; 1994. (Springer Tracts in Natural Philosophy; vol. 39).
   Google Scholar
• Pažanin I, Siddheshwar PG. Analysis of the Laminar Newtonian fluid flow through a thin fracture modelled as fluid-saturated sparsely packed porous medium. Z Naturforsch A. 2017;72:253–259.
   Google Scholar
• Marušić S, Marušić-Paloka E. Two-scale convergence for thin domains and its applications to some lower–dimensional models in fluid mechanics. Asymptot Anal. 2000;23:23–58.
   Web of Science ®Google Scholar