References

PERMANENT SOLUTIONS FOR TWO MIXED INITIAL-BOUNDARY VALUE PROBLEMS WHICH DESCRIBE MOTIONS OF BURGERS FLUIDS BETWEEN PARALLEL PLATES: APPLICATIONS


[1] J. M. Burgers, Mechanical Considerations-Model System-Phenomenological Theories of Relaxation and Viscosity, First Report on Viscosity and Plasticity, Editor J. M. Burgers, Nordemann Publishing Company, New York, 1939.

[2] M. C. Wang and K. Y. Lee, Creep behavior of cement stabilized soils, Highway Research Record 442 (1973), 727-740.

[3] C. A. Tovar, C. A. Cerdeirina, L. Romani, B. Prieto and J. Carballo, Viscoelastic behavior of Arzua-Ulloa cheese, Journal of Texture Studies 34(2) (2003), 115-129.
DOI: https://doi.org/10.1111/j.1745-4603.2003.tb01370.x

[4] R. N. J. Saal and J. W. A. Labout, Rheological Properties of Asphalts, in: F. R. Eirich (Editor), Rheology Theory and Application, vol. II, Academic Press, New York, 1958.

[5] A. R. Lee and A. H. D. Markwick, The mechanical properties of bituminous surfacing materials under constant stress, Journal of the Society of Chemical Industry 56 (1937), 146-154.

[6] W. R. Peltier, P. Wu and D. A. Yuen, The Viscosities of the Earth Mantle, in: F. D. Stacey, M. S. Paterson and A. Nicholas (Editor), Anelasticity in the Earth, American Geophysical Union, Colorado, 1981.

[7] D. A. Yuen and W. R. Peltier, Normal modes of the viscoelastic earth, Geophysical Journal International 69(2) (1982), 495-526.
DOI: https://doi.org/10.1111/j.1365-246X.1982.tb04962.x

[8] P. N. Chopra, High-temperature transient creep in olivine rocks, Tectonophysics 279(1-4) (1997), 93-111.
DOI: https://doi.org/10.1016/S0040-1951(97)00134-0

[9] B. H. Tan, I. Jackson and J. D. F. Gerald, High-temperature viscoelasticity of fine-grained polycrystalline olivine, Physics and Chemistry of Minerals 28 (2001), 641-664.
DOI: https://doi.org/10.1007/s002690100189

[10] J. M. Krishnan and K. R. Rajagopal, Thermodynamic framework for the constitutive modelling of asphalt concrete: Theory and applications, Journal of Materials in Civil Engineering 16(2) (2004), 155-166.
DOI: https://doi.org/10.1061/(ASCE)0899-1561(2004)16:2(155)

[11] P. Ravindran, J. M. Krishnan and K. R. Rajagopal, A note on the flow of a Burgers’ fluid in an orthogonal rheometer, International Journal of Engineering Science 42(19-20) (2004), 1973-1985.
DOI: https://doi.org/10.1016/j.ijengsci.2004.07.007

[12] Safia Akram, Asia Anjum, M. Khan and A. Hussain, On Stokes’ second problem for Burgers’ fluid over a plane wall, Journal of Applied and Computational Mechanics 7(3) (2021), 1514-1526.
DOI: https://doi.org/10.22055/jacm.2020.35227.2603

[13] C. Fetecau, N. A. Ahammad, D. Vieru and N. A. Shah, Steady-state solutions for two mixed initial-boundary value problems which describe isothermal motions of Burgers fluids: Application, Mathematics 10(19) (2022); Article 3681.
DOI: https://doi.org/10.3390/math10193681

[14] M. Hussain, M. Qayyum and Sidra Afzal, Modelling and analysis of MHD oscillatory flows of generalized Burgers’ fluid in a porous medium using Fourier transform, Journal of Mathematics (2022); Article ID 2373084, 13 pages.
DOI: https://doi.org/10.1155/2022/2373084

[15] C. Fetecau, A. Rauf, T. M. Qureshi and D. Vieru, Steady-state solutions for MHD motions of Burgers’ fluids through porous media with differential expressions of shear on boundary and applications, Mathematics 10(22) (2022); Article 4228.
DOI: https://doi.org/10.3390/math10224228

[16] M. Renardy, Inflow boundary conditions for steady flow of viscoelastic fluids with differential constitutive laws, Rocky Mountain Journal of Mathematics 18(2) (1988), 445-454.
https://www.jstor.org/stable/44237133

[17] M. Renardy, Recent advances in the mathematical theory of steady flow of viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics 29 (1988), 11-24.
DOI: https://doi.org/10.1016/0377-0257(88)85047-X

[18] C. Fetecau, D. Vieru, A. Rauf and T. M. Qureshi, Steady-state solutions for some motions of Maxwell fluids with pressure-dependence of viscosity, Journal of Mathematical Sciences: Advances and Applications 68 (2021), 1-28.
DOI: http://dx.doi.org/10.18642/jmsaa_7100122224

[19] C. Fetecau and D. Vieru, Analytical solutions for a general mixed initial-boundary value problem corresponding to hydromagnetic flows of second grade fluids through porous medium, Journal of Applied Mathematics and Computations 5(3) (2021) 225-236.
DOI: http://dx.doi.org/10.26855/jamc.2021.09.009

[20] E. S. Baranovskii and M. A. Artemov, Steady flows of second grade fluids in a channel, Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya 13 (2017), 342-353 (in Russian).
DOI: https://doi.org/10.21638/11701/spbu10.2017.401

[21] E. S. Baranovskii and M. A. Artemov, Steady Flows of Second-Grade Fluids Subject to Stick-Slip Boundary Conditions, In Proceedings of the 23rd International Conference Engineering Mechanics, Svratka, Czech Republik 15-18 May, 2017, pp. 110-113.

[22] Maria Javaid, M. Imran, C. Fetecau and D. Vieru, General solutions for the mixed boundary value problem associated to hydromagnetic flows of a viscous fluid between symmetrically heated parallel plates, Thermal Science 24 (2020), 1389-1405.
DOI: https://doi.org/10.2298/TSCI190608384J