Flow and heat transfer characteristics of non-Newtonian fluid over an oscillating flat plate

References

• A. Amiri, A. Eslami, R. Mollaabbasi, F. Larachi, and S. M. Taghavi, “Removal of a yield stress fluid by a heavier Newtonian fluid in a vertical pipe,” J. Non-Newton. Fluid, vol. 268, pp. 81–100, 2019. DOI: 10.1016/j.jnnfm.2019.05.004.
   Web of Science ®Google Scholar
• F. J. H. Gijsen, F. N. van de Vosse, and J. D. Janssen, “The influence of the non-Newtonian properties of blood on the flow in large arteries: Steady flow in a carotid bifurcation model,” J. Biomech, vol. 32, no. 6, pp. 601–608, 1999. DOI: 10.1016/S0021-9290(99)00015-9.
   PubMed Web of Science ®Google Scholar
• I. A. Frigaard, K. G. Paso, and P. R. de Souza Mendes, “Bingham’s model in the oil and gas industry,” Rheol. Acta, vol. 56, no. 3, pp. 259–282, 2017. DOI: 10.1007/s00397-017-0999-y.
   Web of Science ®Google Scholar
• W. Roland, C. Marschik, M. Krieger, B. Löw-Baselli, and J. Miethlinger, “Symbolic regression models for predicting viscous dissipation of three-dimensional non-Newtonian flows in single-screw extruders,” J. Non-Newton. Fluid, vol. 268, pp. 12–29, 2019. DOI: 10.1016/j.jnnfm.2019.04.006.
   Web of Science ®Google Scholar
• D. S. Sankar and L. Usik, “Influence of slip velocity in Herschel-Bulkley fluid flow between parallel plates-A mathematical study,” J. Mech. Sci. Technol., vol. 30, no. 7, pp. 3203–3218, 2016. DOI: 10.1007/s12206-016-0629-0.
   Web of Science ®Google Scholar
• P. K. Singeetham and V. K. Puttanna, “Viscoplastic fluids in 2D plane squeeze flow: A matched asymptotics analysis,” J. Non-Newton. Fluid, vol. 263, pp. 154–175, 2019. DOI: 10.1016/j.jnnfm.2018.12.003.
   Web of Science ®Google Scholar
• N. J. Balmforth, Y. Forterre, and O. Pouliquen, “The viscoplastic Stokes layer,” J. Non-Newton. Fluid, vol. 158, no. 1–3, pp. 46–53, 2009. DOI: 10.1016/j.jnnfm.2008.07.008.
   Web of Science ®Google Scholar
• B. R. Duffy, D. Pritchard, and S. K. Wilson, “The shear-driven Rayleigh problem for generalised Newtonian fluids,” J. Non-Newton. Fluid, vol. 206, pp. 11–17, 2014. DOI: 10.1016/j.jnnfm.2014.02.001.
   Web of Science ®Google Scholar
• M. Das, R. Mahato and R. Nandkeolyar, “Newtonian heating effect on unsteady hydromagnetic Casson fluid flow past a flat plate with heat and mass transfer,” Alex. Eng. J., vol. 54, no. 4, pp. 871–879, 2015. DOI: 10.1016/j.aej.2015.07.007.
   Web of Science ®Google Scholar
• D. Liepsch and S. Moravec, “Pulsatile flow of non-Newtonian fluid in distensible models of human arteries,” BIR, vol. 21, no. 4, pp. 571–586, 1984. DOI: 10.3233/BIR-1984-21416.
   Google Scholar
• H. Pascal, “Similarity solutions to some unsteady flows of non-Newtonian fluids of power law behavior,” Int. J. Nonlin. Mech, vol. 27, no. 5, pp. 759–771, 1992. DOI: 10.1016/0020-7462(92)90032-3.
   Web of Science ®Google Scholar
• O. Jambal, T. Shigechi, G. Davaa, and S. Momoki, “Effects of viscous dissipation and fluid axial heat conduction on heat transfer for non-Newtonian fluids in ducts with uniform wall temperature: Part I: Parallel plates and circular ducts,” Int. Commun. Heat Mass, vol. 32, no. 9, pp. 1165–1173, 2005. DOI: 10.1016/j.icheatmasstransfer.2005.07.002.
   Web of Science ®Google Scholar
• J. H. Rao, D. R. Jeng, and K. J. D. Witt, “Momentum and heat transfer in a power-law fluid with arbitrary injection/suction at a moving wall,” Int. J. Heat Mass Trans., vol. 42, no. 15, pp. 2837–2847, 1999. DOI: 10.1016/S0017-9310(98)00360-3.
   Web of Science ®Google Scholar
• S. P. Anjalidevi and R. Kandasamy, “Effects of chemical reaction, heat and mass transfer on laminar flow along a semi infinite horizontal plate,” Heat Mass Transf., vol. 35, no. 6, pp. 465–467, 1999. DOI: 10.1007/s002310050349.
   Web of Science ®Google Scholar
• M. Jalil, S. Asghar, and M. Mushtaq, “Analytical solutions of the boundary layer flow of power-law fluid over a power-law stretching surface,” Commun. Nonlinear Sci., vol. 18, no. 5, pp. 1143–1150, 2013. DOI: 10.1016/j.cnsns.2012.09.030.
   Web of Science ®Google Scholar
• B. H. L. Raju, V. D. Rao, and B. B. Krishna, “Flow and Heat Transfer of Quiescent Non-Newtonian Power-Law Fluid Driven by a Moving Plate: An Integral Approach,” Procedia Eng, vol. 127, pp. 485–492, 2015. DOI: 10.1016/j.proeng.2015.11.402.
   Google Scholar
• R. Panton, “The transient for Stokes's oscillating plate: A solution in terms of tabulated functions,” J. Fluid Mech., vol. 31, no. 4, pp. 819–825, 1968. DOI: 10.1017/S0022112068000509.
   Google Scholar
• A. R. A. Khaled and K. Vafai, “The effect of the slip condition on Stokes and Couette flows due to an oscillating wall: Exact solutions,” Int. J. Nonlin. Mech., vol. 39, no. 5, pp. 795–809, 2004. DOI: 10.1016/S0020-7462(03)00043-X.
   Web of Science ®Google Scholar
• M. A. A. Mahmoud, “Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation,” Math. Comput. Model., vol. 54, no. 5-6, pp. 1228–1237, 2011. no DOI: 10.1016/j.mcm.2011.03.034.
   Google Scholar
• D. Pal and S. Chakraborty, “Fluid flow induced by periodic temperature oscillation over a flat plate: Comparisons with the classical Stokes problems,” Phys. Fluids, vol. 27, no. 5, pp. 053601, 2015. DOI: 10.1063/1.4919733.
   Web of Science ®Google Scholar
• M. E. Erdogan, “A note on an unsteady flow of a viscous fluid due to an oscillating plane wall,” Int. J. Nonlin. Mech., vol. 35, no. 1, pp. 1–6, 2000. DOI: 10.1016/S0020-7462(99)00019-0.
   Web of Science ®Google Scholar
• A. Aziz, “A similarity solution for laminar thermal boundary layer over a flat plate with a convective surface boundary condition,” Commun. Nonlin. Sci., vol. 14, no. 4, pp. 1064–1068, 2009. DOI: 10.1016/j.cnsns.2008.05.003.
   Web of Science ®Google Scholar
• M. Shakhawath Hossain and N. E. Daidzic, “The Shear-Driven Fluid Motion Using Oscillating Boundaries,” J. Fluids Eng., vol. 134, no. 5, pp. 051203, 2012.
   Web of Science ®Google Scholar
• S. Gabbanelli, G. Drazer, and J. Koplik, “Lattice Boltzmann method for non-Newtonian (power-law) fluids,” Phys. Rev. E, vol. 72, no. 4, pp. 046312, 2005. DOI: 10.1103/PhysRevE.72.046312.
   Web of Science ®Google Scholar
• M. R. Eid and K. L. Mahny, “Unsteady MHD heat and mass transfer of a non-Newtonian nanofluid flow of a two-phase model over a permeable stretching wall with heat generation/absorption,” Adv. Powder Technol., vol. 28, no. 11, pp. 3063–3073, 2017. DOI: 10.1016/j.apt.2017.09.021.
   Web of Science ®Google Scholar
• D. Pritchard, C. R. McArdle, and S. K. Wilson, “The Stokes boundary layer for a power-law fluid,” J. Non-Newton. Fluid, vol. 166, no. 12-13, pp. 745–753, 2011. DOI: 10.1016/j.jnnfm.2011.04.011.
   Web of Science ®Google Scholar
• R. Zamolo and E. Nobile, “Solution of incompressible fluid flow problems with heat transfer by means of an efficient RBF-FD meshless approach,” Numer. Heat Tr. B–Fund, vol. 75, no. 1, pp. 19–42, 2019. DOI: 10.1080/10407790.2019.1580048.
   Web of Science ®Google Scholar
• S. Y. Deng, et al., “Unsteady electroosmotic flow of power-law fluid in a rectangular microchannel,” Mech. Res. Commun, vol. 39, no. 1, pp. 9–14, 2012. DOI: 10.1016/j.mechrescom.2011.09.003.
   Web of Science ®Google Scholar
• H. Ragueb and K. Mansouri, “A numerical study of viscous dissipation effect on non-Newtonian fluid flow inside elliptical duct,” Energ. Convers. Manage, vol. 68, pp. 124–132, 2013. DOI: 10.1016/j.enconman.2012.12.031.
   Web of Science ®Google Scholar
• H. Maleki, M. R. Safaei, H. Togun, and M. Dahari, “Heat transfer and fluid flow of pseudo-plastic nanofluid over a moving permeable plate with viscous dissipation and heat absorption/generation,” J. Therm. Anal. Calorim., vol. 135, no. 3, pp. 1643–1654, 2019. DOI: 10.1007/s10973-018-7559-2.
   Web of Science ®Google Scholar
• E. J. Kansa, “Multiquadrics—A scattered data approximation scheme with applications to computational fluid-dynamics—I surface approximations and partial derivative estimates,” Comput. Math. Appl, vol. 19, no. 8/9, pp. 127–145, 1990. no DOI: 10.1016/0898-1221(90)90270-T.
   Web of Science ®Google Scholar
• H. Zheng, C. Zhang, Y. Wang, J. Sladek, and V. Sladek, “A meshfree local RBF collocation method for anti-plane transverse elastic wave propagation analysis in 2D phononic crystals,” J. Comput. Phys, vol. 305, pp. 997–1014, 2016. DOI: 10.1016/j.jcp.2015.10.020.
   Web of Science ®Google Scholar
• L. Su, “A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem,” Appl. Math. Comput., vol. 354, pp. 232–247, 2019. DOI: 10.1016/j.amc.2019.02.035.
   Web of Science ®Google Scholar
• I. Siraj Ul, S. Haq, and M. Uddin, “A meshfree interpolation method for the numerical solution of the coupled nonlinear partial differential equations,” Eng. Anal. Bound. Elem,, vol. 33, no. 3, pp. 399–409, 2009. DOI: 10.1016/j.enganabound.2008.06.005.
   Web of Science ®Google Scholar
• S. Zhang, “A symplectic procedure for two-dimensional coupled elastic wave equations using radial basis functions interpolation,” Comput. Math. Appl, vol. 76, no. 9, pp. 2167–2178, 2018. DOI: 10.1016/j.camwa.2018.08.014.
   Web of Science ®Google Scholar
• A. Jafarabadi and E. Shivanian, “Numerical simulation of nonlinear coupled Burgers’ equation through meshless radial point interpolation method,” Eng. Anal. Bound. Elem,, vol. 95, pp. 187–199, 2018. DOI: 10.1016/j.enganabound.2018.07.014.
   Web of Science ®Google Scholar
• E. J. Kansa and P. Holoborodko, “On the ill-conditioned nature of C∞ RBF strong collocation,” Eng. Anal. Bound. Elem., vol. 78, pp. 26–30, 2017. DOI: 10.1016/j.enganabound.2017.02.006.
   Web of Science ®Google Scholar
• F. Afiatdoust and M. Esmaeilbeigi, “Optimal variable shape parameters using genetic algorithm for radial basis function approximation,” Ain Shams Eng. J., vol. 6, no. 2, pp. 639–647, 2015. DOI: 10.1016/j.asej.2014.10.019.
   Web of Science ®Google Scholar
• W. Chen, Y. Hong, and J. Lin, “The sample solution approach for determination of the optimal shape parameter in the Multiquadric function of the Kansa method,” Comput. Math. Appl., vol. 75, no. 8, pp. 2942–2954, 2018. DOI: 10.1016/j.camwa.2018.01.023.
   Web of Science ®Google Scholar
• S. Rippa, “An algorithm for selecting a good value for the parameter c in radial basis function interpolation,” Adv. Comput. Math., vol. 11, no. 2/3, pp. 193–210, 1999. DOI: 10.1023/A:1018975909870.
   Web of Science ®Google Scholar
• S. A. Sarra, “Adaptive radial basis function methods for time dependent partial differential equations,” Appl. Numer. Math,, vol. 54, no. 1, pp. 79–94, 2005. DOI: 10.1016/j.apnum.2004.07.004.
   Web of Science ®Google Scholar
• S. Kaennakham and N. Chuathong, “An automatic node-adaptive scheme applied with a RBF-collocation meshless method,” Appl. Math. Comput, vol. 348, pp. 102–125, 2019. DOI: 10.1016/j.amc.2018.11.066.
   Web of Science ®Google Scholar
• F. Saberi Zafarghandi, M. Mohammadi, E. Babolian, and S. Javadi, “Radial basis functions method for solving the fractional diffusion equations,” Appl. Math. Comput, vol. 342, pp. 224–246, 2019. DOI: 10.1016/j.amc.2018.08.043.
   Web of Science ®Google Scholar
• Y. Hong, J. Lin, and W. Chen, “Simulation of thermal field in mass concrete structures with cooling pipes by the localized radial basis function collocation method,” Int. J. Heat Mass Tran, vol. 129, pp. 449–459, 2019. DOI: 10.1016/j.ijheatmasstransfer.2018.09.037.
   Web of Science ®Google Scholar
• G. C. Bourantas, V. C. Loukopoulos, G. R. Joldes, A. Wittek, and K. Miller, “An explicit meshless point collocation method for electrically driven magnetohydrodynamics (MHD) flow,” Appl. Math. Comput, vol. 348, pp. 215–233, 2019. DOI: 10.1016/j.amc.2018.11.054.
   Web of Science ®Google Scholar
• S. Srinivasan and K. R. Rajagopal, “Study of a variant of Stokes’ first and second problems for fluids with pressure dependent viscosities,” Int. J. Eng. Sci, vol. 47, no. 11-12, pp. 1357–1366, 2009. no DOI: 10.1016/j.ijengsci.2008.11.002.
   Web of Science ®Google Scholar
• L. Ai and K. Vafai, “An Investigation of Stokes' Second Problem for Non-Newtonian Fluids,” Numer. Heat Tr. A–Appl., vol. 47, no. 10, pp. 955–980, 2005. DOI: 10.1080/10407780590926390.
   Web of Science ®Google Scholar
• A. Sinha, J. C. Misra, and G. C. Shit, “Effect of heat transfer on unsteady MHD flow of blood in a permeable vessel in the presence of non-uniform heat source,” Alex. Eng. J., vol. 55, no. 3, pp. 2023–2033, 2016. DOI: 10.1016/j.aej.2016.07.010.
   Web of Science ®Google Scholar
• G. Sheng, Y. Su, and W. Wang, “A new fractal approach for describing induced-fracture porosity/permeability/compressibility in stimulated unconventional reservoirs,” J. Petrol. Sci. Eng, vol. 179, pp. 855–866, 2019. DOI: 10.1016/j.petrol.2019.04.104.
   Web of Science ®Google Scholar
• A. Chang, et al., “A time fractional convection-diffusion equation to model gas transport through heterogeneous soil and gas reservoirs,” Physica A, vol. 502, pp. 356–369, 2018. DOI: 10.1016/j.physa.2018.02.080.
   Web of Science ®Google Scholar
• H. Pouraria, J. K. Seo, and J. K. Paik, “Numerical modelling of two-phase oil-water flow patterns in a subsea pipeline,” Ocean Eng., vol. 115, pp. 135–148, 2016. DOI: 10.1016/j.oceaneng.2016.02.007.
   Web of Science ®Google Scholar