Analysis of the second-grade fluid flow in a porous channel by Cattaneo-Christov and generalized Fick's theories

Document Type : Research Article

Authors

1 Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan

2 Department of Mathematics and Statistics, International Islamic University, Islamabad 44000, Pakistan.

3 Department of Mathematics, COMSATS University Islamabad, Sahiwal 57000, Pakistan.

Abstract

This attempt executes the combined heat mass transport features in steady MHD viscoelastic fluid flow through stretching walls of channel. The channel walls are considered to be porous. The analysis of heat transport is made by help Cattaneo-Christov heat diffusion formula while generalized Fick’s theory is developed for study of mass transport. The system of partial differential expressions is changed into set of ordinary differential by introducing suitable variables. The homotopic scheme is introduced for solving the resultant equations and then validity of results are verified by various graphs. An extensive analysis has been performed for the influence of involved constraints on liquid velocity, concentration and temperature profiles. It is noted that the normal component of velocity decreases by increasing Reynolds number while retards for increasing viscoelastic constraint. Both temperature and concentration profiles enhanced by increasing combined parameter and Reynolds number. The presence of thermal relaxation number and concentration relaxation number declines both temperature and concentration profiles, respectively.

Keywords

Main Subjects

References

References:
1. Fourier, J.B.J., Theorie Analytique De La Chaleur, Paris (1822).
2. Cattaneo, C. "Sulla conduzione del calore", Atti Semin. Mat. Fis. Univ., Modena Reggio, Emilia, 3, pp. 83-101 (1948).
3. Christov, C.I. "On frame in different formulation of the Maxwell-Cattaneo model of finite speed heat conduction", Mech. Res. Commun., 36, pp. 481-486 (2009).
4. Straughan, B. "Thermal convection with the Cattaneo-Christov model", Int. J. Heat Mass Transfer, 53, pp. 95-98 (2010).
5. Han, S., Zheng, L., Li, C., and Zhang, X. "Coupled flow and heat transfer in viscoelastic  fluid with Cattaneo-Christov heat flux model", Appl. Math. Lett., 38, pp. 87-93 (2014).
6. Khan, J.A., Mustafa, M., Hayat, T., and Alsaedi, A. "Numerical study of Cattaneo-Christov heat  flux model for viscoelastic  flow due to an exponentially stretching surface", Plos One, 10, e0137363 (2015).
7. Meraj, M.A., Shehzad, S.A., Hayat, T., Abbasi, F.M., and Alsaedi, A. "Darcy-Forchheimer  flow of variable conductivity Jeffrey liquid with Cattaneo-Christov heat flux theory", App. Math. Mech.-Engl, 38, pp. 557-566 (2017).
8. Tripathy, R.S., Dash, G.C., Mishra, S.R., and Baag, S. "Chemical reaction effect on MHD free convective surface over a moving vertical plane through porous medium", Alexandria Eng. J., 54, pp. 673-679 (2015).
9. Javed, T., Ghaffari, A., and Ahmad, H. "Numerical study of unsteady MHD oblique stagnation point  flow with heat transfer over an oscillating  at plate", Can. J. Physics, 93, pp. 1138-1143 (2015).
10. Ali, N., Khan, S.U., and Abbas, Z. "Hydromagnetic flow and heat transfer of a Jeffrey  fluid over an oscillatory stretching surface", Z. Naturforschung A, 70, pp. 567-576 (2015).
11. Niranjan, H., Sivasankaran, S., and Bhuvaneswari, M. "Chemical reaction, Soret and Dufour effects on MHD mixed convection stagnation point flow with radiation and slip condition", Sci. Iran, 24, pp. 698-706 (2017).
12. Ghaffarpasand, O. and Fazeli, D. "Numerical analysis of MHD mixed convection  flow in a parallelogramic porous enclosure filled with nano fluid and in presence of magnetic field induction", Sci. Iran, 25, pp. 1789- 1807 (2018).
13. Khan, A.A., Usman H., Vafai, K., and Ellahi, R. "Study of peristaltic  flow of magnetohydrodynamics Walter's B fluid with slip and heat transfe", Sci. Iran, 23(6), pp. 2650-2662 (2016).
14. Ramli, N., Ahmad, S., and Pop, I. "MHD forced convection flow and heat transfer of ferro fluids over a moving at plate with uniform heat flux and secondorder slip effects", Sci. Iran, 25(4), pp. 2186-2197 (2018).
15. Ullaha, H., Islama, S., Khanb, I., Sharidanc, S., and Fizaa, M. "MHD boundary layer flow of an incompressible upper convected Maxwell fluid by optimal homotopy asymptotic method", Sci. Iran, 24(1), pp. 202-210 (2017).
16. Sheikholeslami, M. "Influence of magnetic field on Al2O3-H2O nano fluid forced convection heat transfer in a porous lid driven cavity with hot sphere obstacle by means of LBM", J. Mol. Liq., 263, pp. 472-488 (2018).
17. Sheikholeslami, M. "Application of Darcy law for nano fluid  flow in a porous cavity under the impact of Lorentz forces", J. Mol. Liq, 266, pp. 495-503 (2018).
18. Sheikholeslami, M., Li, Z., and Shafee, A. "Lorentz forces effect on NEPCM heat transfer during solidification in a porous energy storage system", Int. J. Heat Mass Transfer, 127, pp. 665-674 (2018).
19. Darcy, H.R.P.G., Les Fontaines Publiques de la volle de Dijon, Vector Dalmont, Paris (1856).
20. Khaled, A.R.A. and Vafai, K. "The role of porous media in modeling  flow and heat transfer in biological tissues", Int. J. Heat Mass Transfer, 46, pp. 4989-5003 (2003).
21. Attia, H.A. "Asymptotic solution for rotating disk flow in porous medium", Mech. Mechanical Eng., 14, pp. 119-136 (2010).
22. Attia, H.A., Abdeen, M.A.M., and Elbarawy, M.M. "Time varying rotating disk flow with heat transfer of a non-Newtonian 
uid in porous medium", Kragujevac Journal of Science, 36, pp. 33-40 (2014).
23. Siddiq, M.K., Rauf, A., Shehzad, S.A., Hayat, T., and Alsaedi, A. "Interaction of convective and Nield- Kuzentsov's conditions in hydromagnetic  flow on nanofluid subject to Darcy-Forchheimer effects", J. Porous Med., 20, pp. 989-998 (2017).
24. Sheikholeslami, M., Shehzad, S.A., Li, Z., and Shafee, A."Numerical modeling for alumina nano fluid magnetohydrodynamic convective heat transfer in a permeable medium using Darcy law", Int. J. Heat Mass Transfer, 127, pp. 614-622 (2018).
25. Ashraf, M. and Batool, K. "MHD  flow and heat transfer of a micropolar  fluid over a stretchable disk", Journal of Theoretical and Applied Mechanics, 51, pp. 25-38 (2013).
26. Turkyilmazoglu, M. "MHD  fluid flow and heat transfer due to a stretching rotating disk", Int. J. Therm. Sci., 51, pp. 195-201 (2012).
27. Hayat, T., Qayyum, S., Imtiaz, M., and Alsaedi, A. "Radiative flow due to stretchable rotating disk with variable thickness", Results in Physics, 7, pp. 156-165 (2017).
28. Hayat, T., Nawaz, M., Sajid, M., and Asghar, S. "The effect of thermal radiation on the flow of a second grade fluid", Comput. Math. Appl., 58, pp. 369-379 (2009).
29. Misra, J.C., Pal, B., and Gupta, A.S. "Oscillatory entry flow in a channel with pulsating walls", Int. J. Non-Linear Mech., 36, pp. 731-741 (2001).
30. Misra, J.C., Pal, B., and Gupta, A.S. "Hydromagnetic flow of a second-grade fluid in a channel-some applications to physiological systems", Math. Models Methods Appl. Sci., 8, pp. 1323-1342 (1998).
31. Misra, J.C., Shit, G.C., and Rath, H.J. "Flow and heat transfer of a MHD viscoelastic  fluid in a channel with stretching walls: some applications to haemodynamics", Comput. Fluids, 37, pp. 1-11 (2008).
32. Raftari, B. and Vajravelu, K. "Homotopy analysis method for MHD viscoelastic  fluid flow and heat transfer in a channel with a stretching wall", Commun. Nonlinear Sci. Numer. Simulat., 17, pp. 4149-4162 (2012).
33. Abbasi, M., Khaki, M., Rahbari, A., Ganji, D.D., and Rahimipetroudi, I. "Analysis of MHD flow characteristics of an UCM viscoelastic  flow in a permeable channel under slip conditions", J. Braz. Soc. Mech. Sci. Eng., 38, pp. 977-988 (2016).
34. Liao, S.J. "On the analytic solution of magnetohydrodynamic flows of non-Newtonian  fluids over a stretching sheet", J. Fluid Mech., 488, pp. 189-212 (2003).
35. Hayat, T., Waqas, M., Shehzad, S.A., and Alsaedi, A. "Effects of Joule heating and thermophoresis on the stretched flow with convective boundary conditions", Sci. Iran, 21, pp. 682-692 (2014).
36. Dangui-Mbani, U.O., Sui, J., Ming, C., Zheng, L., and Chen, G. "Heat transfer analysis for a free boundary problem arising in n-diffusion equation", Propulsion and Power Research, 5, pp. 261-266 (2016).
37. Zhu, J., Yang, D., Zheng, L., and Zhang, X. "Effects of second order velocity slip and nanoparticles migration on flow of Buongiorno nano fluid", Applied Mathematics Letters, 52, pp. 183-191 (2016).
38. Khan, S.U., Shehzad, S.A., and Ali, N. "Interaction of magneto-nanoparticles in Williamson fluid  flow over convective oscillatory moving surface", J. Braz. Soc. Mech. Sci. Eng., 40, p. 195 (2018).
39. Waqas, M., Hayat, T., Shehzad, S.A., and Alseadi, A. "Transport of magnetohydrodynamic nanomaterial in a stratified medium considering gyrotactic microorganisms", Physica B, Condensed Matter, 529, pp. 33-40 (2018).
40. Turkyilmazoglu, M. "Convergence accelerating in the homotopy analysis method: A new approach", Adv. Appl. Math. Mech., 10(4), pp. 925-947 (2018).
41. Turkyilmazoglu, M. "Parametrized Adomian decomposition method with optimum convergence", Transactions on Modelling and Computer Simulation, 27, pp. 1-22 (2017). DOI: 10.1145/3106373.
42. Turkyilmazoglu, M. "Determination of the correct range of physical parameters in the approximate analytical solutions of nonlinear equations using the Adomian decomposition method", Mediterranean J. Math., 13, pp. 4019-4037 (2016).
Scientia Iranica
Volume 27, Issue 4
Transactions on Mechanical Engineering (B)
July and August 2020
Pages 1945-1954

Files

Cited by

History

  • Receive Date: 18 July 2018
  • Revise Date: 10 December 2018
  • Accept Date: 04 February 2019

Share

How to cite

Statistics