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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 85, 2024 - Issue 7
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Articles

Numerical examination of the Darcy–Forchheimer Casson model with instigation energy and second-order momentum slip: Thermal features

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Pages 940-963 | Received 01 Jun 2023, Accepted 06 Sep 2023, Published online: 29 Sep 2023

References

  • P. S. Gupta and A. S. Gupta, “Heat and mass transfer on a stretching sheet with suction or blowing,” Can. J. Chem. Eng., vol. 55, no. 6, pp. 744–746, Dec. 1977. DOI: 10.1002/cjce.5450550619.
  • S. K. Khan, “Boundary layer viscoelastic fluid flow over an exponentially stretching sheet,” Int. J. Appl. Mech. Eng., vol. 11, no. 2, pp. 321–335, 2006.
  • E. Sanjayanand and S. K. Khan, “On heat and mass transfer in a viscoelastic boundary layer flow over an exponentially stretching sheet,” Int. J. Therm. Sci., vol. 45, no. 8, pp. 819–828, 2006. DOI: 10.1016/j.ijthermalsci.2005.11.002.
  • E. Magyari and B. Keller, “Heat and mass transfer in the boundary layers on an exponentially stretching continuous surface,” J. Phys. D: Appl. Phys., vol. 32, no. 5, pp. 577–585, 1999. DOI: 10.1088/0022-3727/32/5/012.
  • M. K. Partha, P. V. S. N. Murthy and G. P. Rajasekhar, “Effect of viscous dissipation on the mixed convection heat transfer from an exponentially stretching surface,” Heat Mass Transfer, vol. 41, no. 4, pp. 360–366, 2005. DOI: 10.1007/s00231-004-0552-2.
  • E. M. A. Elbashbeshy, “Heat transfer over an exponentially stretching continuous surface with suction,” Arch Mech., vol. 53, no. 6, pp. 643–651, 2001.
  • S. Mukhopadhyay, “MHD boundary layer flow and heat transfer over an exponentially stretching sheet embedded in a thermally stratified medium,” Alex. Eng. J., vol. 52, no. 3, pp. 259–265, 2013. DOI: 10.1016/j.aej.2013.02.003.
  • F. Mabood, W. A. Khan and A. M. Ismail, “MHD flow over exponential radiating stretching sheet using homotopy analysis method,” J. King Saud Uni.-Eng. Sci., vol. 29, no. 1, pp. 68–74, 2017. DOI: 10.1016/j.jksues.2014.06.001.
  • A. Ishak, “MHD boundary layer flow due to an exponentially stretching sheet with radiation effect,” Sains Malaysiana, vol. 40, no. 4, pp. 391–395, 2011.
  • S. Pramanik, “Casson fluid flow and heat transfer past an exponentially porous stretching surface in presence of thermal radiation,” Ain Shams Eng. J., vol. 5, no. 1, pp. 205–212, 2014. DOI: 10.1016/j.asej.2013.05.003.
  • S. Nadeem, R. Haq and C. Lee, “MHD flow of a Casson fluid over an exponentially shrinking sheet,” Sci. Iran., vol. 19, no. 6, pp. 1550–1553, 2012. DOI: 10.1016/j.scient.2012.10.021.
  • S. Mukhopadhyay, P. R. De, K. Bhattacharyya and G. C. Layek, “Casson fluid flow over an unsteady stretching surface,” Ain Shams Eng. J., vol. 4, no. 4, pp. 933–938, 2013. DOI: 10.1016/j.asej.2013.04.004.
  • M. Hussain, A. Ali, A. Ghaffar and M. Inc, “Flow and thermal study of MHD Casson fluid past a moving stretching porous wedge,” J Therm. Anal. Calorim., vol. 147, no. 12, pp. 6959–6969, 2022. DOI: 10.1007/s10973-021-10983-0.
  • Z. Iqbal and M. Saleem, “Convective heat transport features of Darcy Casson fluid flow in a vertical channel: a Lie group approach,” Waves Random Complex Media, pp. 1–14, 2022. DOI: 10.1080/17455030.2022.2142694. (In press)
  • P. H. Forchheimer, “Wasserbewegung durch boden,” Zeit. Ver. Deut. Ing., vol. 45, no. 50, pp. 1781–1788, 1901.
  • M. Muskat, “The flow of homogeneous fluids through porous media,” Soil Sci., vol. 46, no. 2, pp. 169, 1938. DOI: 10.1097/00010694-193808000-00008.
  • D. Pal and H. Mondal, “Hydromagnetic convective diffusion of species in Darcy–Forchheimer porous medium with non-uniform heat source/sink and variable viscosity,” Int. Commun. Heat Mass Transf., vol. 39, no. 7, pp. 913–917, 2012. DOI: 10.1016/j.icheatmasstransfer.2012.05.012.
  • M. M. Bhatti, K. Al-Khaled, S. U. Khan, W. Chammam and M. Awais, “Darcy–Forchheimer higher-order slip flow of Eyring–Powell nanofluid with nonlinear thermal radiation and bioconvection phenomenon,” J. Disp. Sci. Tech., vol. 44, no. 2, pp. 225–235, 2023. DOI: 10.1080/01932691.2021.1942035.
  • J. L. D. Palencia and S. Rahman, “Geometric perturbation theory and travelling waves profiles analysis in a Darcy–Forchheimer fluid model,” J. Nonlinear Math Phys., vol. 29, no. 3, pp. 556–572, 2022. DOI: 10.1007/s44198-022-00041-0.
  • J. L. D. Palencia, “A mathematical analysis of an extended MHD Darcy–Forchheimer type fluid,” Sci. Rep., vol. 12, no. 1, pp. 5228, 2022. DOI: 10.1038/s41598-022-08623-0.
  • J. L. D. Palencia, S. Rahman and A. N. Redondo, “Regularity and reduction to a Hamilton-Jacobi equation for a MHD Eyring-Powell fluid,” Alex. Eng. J., vol. 61, no. 12, pp. 12283–12291, 2022. DOI: 10.1016/j.aej.2022.06.003.
  • S. Rahman, J. L. D. Palencia and J. R. González, “Analysis and profiles of travelling wave solutions to a Darcy-Forchheimer fluid formulated with a non-linear diffusion,” MATH, vol. 7, no. 4, pp. 6898–6914, 2022. DOI: 10.3934/math.2022383.
  • S. Rahman and J. L. D. Palencia, “Regularity and analysis of solutions for a MHD flow with a p-Laplacian operator and a generalized Darcy–Forchheimer term,” Eur. Phys. J. Plus, vol. 137, no. 12, pp. 1328, 2022. DOI: 10.1140/epjp/s13360-022-03555-0.
  • S. Arrhenius, “Über die Dissociationswärme und den Einfluss der Temperatur auf den Dissociationsgrad der Elektrolyte,” Z. fur Phys. Chem., vol. 4, no. 1, pp. 96–116, 1889. DOI: 10.1515/zpch-1889-0108.
  • A. R. Bestman, “Natural convection boundary layer with suction and mass transfer in a porous medium,” Int. J. Energy Res., vol. 14, no. 4, pp. 389–396, 1990. DOI: 10.1002/er.4440140403.
  • A. Majeed, F. M. Noori, A. Zeeshan, T. Mahmood, S. U. Rehman and I. Khan, “Analysis of instigation energy in magnetohydrodynamic flow with chemical reaction and second order momentum slip model,” Case Stud. Thermal Eng., vol. 12, pp. 765–773, 2018. DOI: 10.1016/j.csite.2018.10.007.
  • A. Majeed, A. Zeeshan and F. M. Noori, “Numerical study of Darcy-Forchheimer model with instigation energy subject to chemically reactive species and momentum slip of order two,” AIP Adv., vol. 9, no. 4, pp. 45035, 2019. DOI: 10.1063/1.5095546.
  • A. Shafiq, A. B. Çolak and T. N. Sindhu, “Analyzing activation energy and binary chemical reaction effects with artificial intelligence approach in axisymmetric flow of third grade nanofluid subject to Soret and Dufour effects,” Heat Trans Res., vol. 54, no. 3, pp. 75–94, 2023. DOI: 10.1615/HeatTransRes.2022045008.
  • T. Hayat, A. Shafiq and A. Alsaedi, “MHD axisymmetric flow of third grade fluid by a stretching cylinder,” Alex. Eng. J., vol. 54, no. 2, pp. 205–212, 2015. DOI: 10.1016/j.aej.2015.03.013.
  • G. Rasool, T. Zhang, A. J. Chamkha, A. Shafiq, I. Tlili and G. Shahzadi, “Entropy generation and consequences of binary chemical reaction on MHD Darcy–Forchheimer Williamson nanofluid flow over non-linearly stretching surface,” Entropy, vol. 22, no. 1, pp. 18, 2020. DOI: 10.3390/e22010018.
  • A. B. Çolak, A. Shafiq and T. N. Sindhu, “Modeling of Darcy–Forchheimer bioconvective Powell Eyring nanofluid with artificial neural network,” Chin. J. Phys., vol. 77, pp. 2435–2453, 2022. DOI: 10.1016/j.cjph.2022.04.004.
  • A. Shafiq, A. B. Çolak, T. N. Sindhu and T. Muhammad, “Optimization of Darcy-Forchheimer squeezing flow in nonlinear stratified fluid under convective conditions with artificial neural network,” Heat Trans Res., vol. 53, no. 3, pp. 67–89, 2022. DOI: 10.1615/HeatTransRes.2021041018.
  • L. Wu, “A slip model for rarefied gas flows at arbitrary Knudsen number,” Appl. Phy. Lett., vol. 93, no. 25, pp. 253103, 2008. DOI: 10.1063/1.3052923.
  • T. Fang, J. Zhang and S. Yao, “Slip MHD viscous flow over a stretching sheet–an exact solution,” Commun. Nonlinear Sci. Num. Simulat., vol. 14, no. 11, pp. 3731–3737, 2009. DOI: 10.1016/j.cnsns.2009.02.012.
  • A. V. Roşca and I. Pop, “Flow and heat transfer over a vertical permeable stretching/shrinking sheet with a second order slip,” Int. J. Heat Mass Trans., vol. 60, pp. 355–364, 2013. DOI: 10.1016/j.ijheatmasstransfer.2012.12.028.
  • S. U. Khan, K. Al-Khaled and M. M. Bhatti, “Bioconvection analysis for flow of Oldroyd-B nanofluid configured by a convectively heated surface with partial slip effects,” Surf. Inter., vol. 23, pp. 100982, 2021. DOI: 10.1016/j.surfin.2021.100982.
  • I. Ullah, K. Bhattacharyya, S. Shafie and I. Khan, “Unsteady MHD mixed convection slip flow of Casson fluid over nonlinearly stretching sheet embedded in a porous medium with chemical reaction, thermal radiation, heat generation/absorption and convective boundary conditions,” PloS One, vol. 11, no. 10, pp. e0165348, 2016. DOI: 10.1371/journal.pone.0165348.
  • A. Shafiq, A. B. Çolak and T. N. Sindhu, “Significance of bioconvective flow of MHD thixotropic nanofluid passing through a vertical surface by machine learning algorithm,” Chin. J. Phys., vol. 80, pp. 427–444, 2022. DOI: 10.1016/j.cjph.2022.08.008.
  • T. Hayat, A. Shafiq, A. Alsaedi and M. Awais, “MHD axisymmetric flow of third grade fluid between stretching sheets with heat transfer,” Comput. Fluids, vol. 86, pp. 103–108, 2013. DOI: 10.1016/j.compfluid.2013.07.003.
  • A. Shafiq, A. B. Çolak and T. N. Sindhu, “Modeling of Soret and Dufour’s convective heat transfer in nanofluid flow through a moving needle with artificial neural network,” Arab J. Sci. Eng., vol. 48, no. 3, pp. 2807–2820, 2023. DOI: 10.1007/s13369-022-06945-9.
  • L. F. Shampine, I. Gladwell and S. Thompson, Solving ODEs with Matlab. Cambridge university Press, 2003. Doi:10.1017/CBO9780511615542.

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