Numerical appraisal of the unsteady Casson fluid flow through Finite Element Method (FEM)

Document Type : Article

Authors

1 - Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh: 11566, Saudi Arabia - Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt

2 - Department of Mathematics, Faculty of Science, Firat University, 23119 Elazig, Turkey - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan

3 Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey

Abstract

An efficient numerical method is offered to discuss the effects of variable heat
flux, viscous dissipation, and the slip velocity on the viscous Casson heat transfer
(CHT) because the unsteady stretching sheet taken into reckoning the effect of
heat generation or absorption. The finite element method (FEM) is applied to
solve the resulting the ODEs which describe the problem. The effect of the factors
governing the HT such as unsteadiness parameter, slip velocity parameter, Casson
parameter, local Eckert number, heat generation parameter and the Prandtl number
are explored and given. Also, the local skin-friction coefficient and the local Nusselt
number at the stretching sheet are computed and discussed. Finally, the obtained
solutions confirm that the given procedure is an easy and efficient tool for assaying
the solution of such fluid models.

Keywords

References

References:
1. Crane, L.J. "Flow past a stretching plate", Zeitschrift fur Angewandte Mathematik und Physik, 21, pp. 645- 647 (1970).
2. Gupta, P.S. and Gupta, A.S. "Heat and mass transfer on a stretching sheet with suction or blowing", Can. J. Chem. Eng., 55, pp. 744-746 (1977).
3. Grubka, L.J. and Bobba, K.M. "Heat transfer characteristics of a continuous stretching surface with variable temperature", ASME J. Heat Transfer, 107, pp. 248-250 (1985).
4. Ali, A., Hussain, M., Anwar, M.S., et al.  Mathematical modeling and parametric investigation of blood flow through a stenosis artery", Applied Mathematics and Mechanics, 42, pp. 1675-1684 (2021).
5. Hussain, Z., Hayat, T., Alsaedi, A., et al. "Mixed convective  flow of CNTs nanofluid subject to varying viscosity and reactions", Scientifc Reports, 11, pp. 1- 14 (2021).
6. Irfan, M., Rafiq, K., Anwar, M.S., et al. "Evaluating the performance of new mass flux theory on Carreau nanofluid using the thermal aspects of convective heat transport", Pramana, 95, pp. 1-15 (2021).
7. Ali, I., Rasheed, A., Anwar, M.S., et al. "Fractional calculus approach for the phase dynamics of Josephson junction", Chaos, Solitons & Fractals, 143, p. 110572 (2021).
8. Hussain, Z., Hussain, A., Anwar, M.S., et al. "Analysis of Cattaneo-Christov heat flux in Jeffery fluid flow with heat source over a stretching cylinder", Journal of Thermal Analysis and Calorimetry, 147, pp. 3391- 3402 (2022).
9. Hussain, Z., Muhammad, S., and Anwar, M.S. "Effects of first-order chemical reaction and melting heat on hybrid nanoliquid flow over a nonlinear stretched curved surface with shape factors", Advances in Mechanical Engineering, 13(4), pp. 1-12 (2021).
10. Irfan, M., Rafiq, M.K., Waqas, M., et al. "Theoretical analysis of new mass  flux theory and Arrhenius activation energy in Carreau nanofluid with magnetic influence", International Communications in Heat and Mass Transfer, 120, pp. 105051 (2021).
11. Khan, K.A., Butt, A.R., Raza, N., et al. "Unsteady magneto-hydrodynamics flow between two orthogonal moving porous plates", The European Physical Journal Plus, 134, pp. 1-16 (2019).
12. Bayones, F.S., Nisar, K.S., Khan, K.A., et al. "Magneto-hydrodynamics (MHD) flow analysis with mixed convection moves through a stretching surface", AIP Advances, 11, pp. 1-8 (2021).
13. Khan, K.A., Seadawy, A.R., and Jhangeer, A. "Numerical appraisal under the influence of the time dependent Maxwell fluid flow over a stretching sheet", Mathematical Methods in the Applied Sciences, 44(7), pp. 5265-5279 (2021).
14. Khan, K.A., Butt, A., and Raza, N. "Influence of porous medium on magneto hydrodynamics boundary layer flow through elastic sheet with heat and mass transfer", J. Nanofluids, 8(4), pp. 725-735 (2019).
15. Seadawy, A.R., Raza, N., Khalil, O.H., et al. "Computational approach and flow analysis of chemically reactive tangent hyperbolic nanofluid over a cone and plate", Waves in Random and Complex Media (2021). https://DOI.org/10.1080/17455030.2021.1959960.
16. Khan, K.A., Jamil, F., Ali, J., et al. "Analytical simulation of heat and mass transmission in Casson fluid flow across a stretching surface", Mathematical Problems in Engineering, 2022, p. 5576194 (2022).
17. Aly, K., Seadawy, A.R., and Raza, N. "The homotopy simulation of MHD time dependent three-dimensional shear thinning 
fluid flow over a stretching plate", Chaos Solitons & Fractals, 157, p. 111888 (2022).
18. Bhattacharyya, K., Hayat, T., and Alsaedi, A. "Exact solution for boundary layer flow of Casson fluid over a permeable stretching/shrinking sheet", ZAMM Z. Angew. Math. Mech., 94, pp. 522-528 (2014).
19. Mukhopadhyay, S., Ranjan De, P., Bhattacharyya, K., and Layek, G.C. "Casson fluid  flow over an unsteady stretching surface", Ain Shams Engineering Journal, 4, pp. 933-938 (2013).
20. Boyd, J., Buick, J.M., and Green, S. "Analysis of the Casson and Carreau-Yasuda non-Newtonian blood models in steady and oscillatory  flow using the lattice Boltzmann method", Phys Fluids, 19, pp. 93-103 (2007).
21. Thompson, P.A. and Troian, S.M. "A general boundary condition for liquid  flow at solid surfaces", Nature, 389, pp. 360-362 (1997).
22. Megahed, A.M. "HPM for slip velocity effect on a liquid film over an unsteady stretching surface with variable heat  flux", The European Physical Journal Plus, 126, pp. 1-8 (2011).
23. Turkyilmazoglu, M. "Multiple solutions of heat and mass transfer of MHD slip flow for the viscoelastic fluid over a stretching sheet", Inter. J. Thermal Sciences, 50, pp. 2264-2276 (2011).
24. Megahed, A.M. "Variable viscosity and slip velocity effects on the flow and heat transfer of a power-law fluid over a non-linearly stretching surface with heat flux and thermal radiation", Rheologica Acta, 51, pp. 841-847 (2012).
25. Khader, M.M. and Saad, K.M. "A numerical study using Chebyshev collocation method for a problem of biological invasion: fractional Fisher equation", Int. J. Biomathematics, 11(8), pp. 1-15 (2018).
26. Khader, M.M. and Saad, K.M. "On the numerical evaluation for studying the fractional KdV, KdVBurger's, and Burger's equations", European Physical Journal Plus, 133, pp. 1-13 (2018).
27. Khader, M.M. and Saad, K.M. "A numerical approach for solving the problem of biological invasion (fractional Fisher equation) using Chebyshev spectral collocation method", Chaos, Solitons & Fractals, 110, pp. 169-177 (2018).
28. Saad, K.M., Khader, M.M., Gomez-Aguilar, J.F., and Baleanu, D., "Numerical solutions of the fractional Fisher's type equations with Atangana-Baleanu fractional derivative by using spectral collocation methods", Chaos, 29, pp. 1-5 (2019).
29. Khader, M.M. "The numerical solution for BVP of the liquid film flow over an unsteady stretching sheet with thermal radiation and magnetic field using the finite element method", Int. J. Modern Physics C., 30(11), pp. 1-8 (2019).
30. Khader, M.M. and Khadijah, M.A. "Galerkin-FEM for obtaining the numerical solution of the linear fractional Klein-Gordon equation", J. Applied Analysis and Computation, 9(1), pp. 261-270 (2019).
31. Kochnev, V.K. "Finite element method for atoms", Chemical Physics, 548(1), pp. 111197 (2021).
32. Zhang, Q. and Cu, C. "Condensed generalized finite element method", Numerical Methods in Partial Differential Equations, 37, pp. 1847-1868 (2021).
33. Tolle, K. and Marheineke, N. "Extended group finite element method", Applied Numerical Mathematics, 162, pp. 1-19 (2021).
34. Bertrand, F., Ern, A., and Radu, F.A. "Robust and reliable finite element methods in poromechanics", Computers and Mathematics with Applications, 91(1), pp. 1-2 (2021) .
35. Megahed A.M. "Variable heat flux effect on MHD flow and heat transfer over an unsteady stretching sheet in the presence of thermal radiation", Canadian J. of Physics, 92, pp. 86-91 (2014).
36. Shahmohamadi, H. "Analytic study on non-Newtonian natural convection boundary layer flow with variable wall temperature on a horizontal plate", Meccanica, 47, pp. 1313-1323 (2012).
37. Mustafa, M., Hayat, T., Pop, I., et al. "Stagnationpoint flow and heat transfer of a Casson fluid towards a stretching sheet", Zeitschrift fur Naturforschung A, 67, pp. 70-76 (2012).
38. Mostafa, A.A.M. "The effects of variable fluid properties on MHD Maxwell fluids over a stretching surface in the presence of heat generation/absorption", Chemical Engineering Communications, 198, pp. 131-146 (2011).
39. Megahed, A.M. "Effect of slip velocity on Casson thin film flow and heat transfer due to an unsteady stretching sheet in the presence of variable heat flux and viscous dissipation", Applied Mathematics and Mechanics, 36, pp. 1273-1284 (2015).
40. Megahed, A.M. "Improvement of heat transfer mechanism through a Maxwell  fluid flow over a stretching sheet embedded in a porous medium and convectively heated", Mathematics and Computers in Simulation, 187, pp. 97-109 (2021).
41. Megahed, A.M. "Carreau fluid flow due to nonlinearly stretching sheet with thermal radiation, heat flux, and variable conductivity", Applied Mathematics and Mechanics, 40, pp. 1615-1624 (2019).
42. Bhargava, R., Sharma, S., Takhar, H.S., et al. "Numerical solutions for micropolar transport phenomena over a nonlinear stretching sheet", Nonlinear Anal: Model. Cont., 12, pp. 45-63 (2007).
43. Reddy J.N., An Introduction to the Finite Element Method, New York: McGraw-Hill Book Co (1985).
44. Rana, P. and Bhargava, R. "Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study", Commun. Nonlinear Sci. Numer. Simulat., 17, pp. 212-226 (2012).
45. Prasad, K.V., Pal, D., and Datti, P.S. "MHD powerlaw fluid flow and heat transfer over a non-isothermal stretching sheet", Commun. Nonlinear Sci. Numer. Simulat., 14, pp. 2178-2189 (2009).
Scientia Iranica
Volume 30, Issue 2
Transactions on Mechanical Engineering (B)
March and April 2023
Pages 454-463

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History

  • Receive Date: 24 March 2022
  • Revise Date: 30 May 2022
  • Accept Date: 18 October 2022

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