Skip to main content

Advertisement

SpringerLink
Log in

The flow of magnetised convective Casson liquid via a porous channel with shrinking and stationary walls

  • Published:
Pramana Aims and scope Submit manuscript

Abstract

Many engineers and scientists are working on various studies such as cosmetics, medicines, chemicals, oil, gas, food and many others due to the numerous applications of non-Newtonian fluids in technological development and improvement. It is difficult to deal with non-Newtonian fluids compared to Newtonian fluids. Due to the vast applications, a numerical investigation of mixed and convective Casson liquid flow through a duct within a permeable medium under the Lorentz force effect is carried out. The problem is modelled mathematically by employing the mass, momentum, heat energy and conservation laws. The partial differential equations (PDEs) are changed into nonlinear ordinary differential equations (ODEs). These ODEs are numerically computed using the shooting technique and then validated through the Runge–Kutta–Fehlberg method. The influence due to Reynolds, Prandtl and Schmidt numbers and Casson, magnetic, porosity, thermal buoyancy and reaction rate parameters are illustrated graphically and in tabular representation to make the analysis more interesting. This study revealed that the transfer rates of heat energy and mass at the lower wall enhanced with the augmenting values of the thermal buoyancy parameter. There is a linear relationship between the velocity of the Casson parameter and Reynolds numbers. Moreover, velocity enhances with the higher magnetic and porosity parameters and diminishes with higher values of thermal buoyancy, Reynolds number and porosity parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11

Similar content being viewed by others

References

  1. L A Lund, Z Omar, I Khan, J Raza, M Bakouri and I Tlili, Symmetry 11(3), 412 (2019)

    Article  ADS  Google Scholar 

  2. S Bailoor, J H Seo and R Mittal, Phys. Fluids 31, 011703 (2019)

    Article  ADS  Google Scholar 

  3. S Dero, A M Rohni, A Saaban and I Khan, Energies 12, 4529 (2019)

    Article  Google Scholar 

  4. S M Abo-Dahab, M A Abdelhafez, F Mebarek-Oudina and S M Bilal, Indian J. Phys. 95, 2703 (2021), https://doi.org/10.1007/s12648-020-01923-z

    Article  ADS  Google Scholar 

  5. A Morozov and W Van Saarloos, J. Stat. Phys. 175, 554 (2019)

    Article  MathSciNet  ADS  Google Scholar 

  6. B Sharma, S Kumar, C Cattani and D Baleanu, J. Comput. Nonlinear Dyn. 15, 011009 (2020)

    Article  Google Scholar 

  7. C Rajashekhar, F Mebarek-Oudina, H Vaidya, K V Prasad, G Manjunatha and H Balachandra, Heat Transf. 50(5), 5106 (2021), https://doi.org/10.1002/htj.22117

    Article  Google Scholar 

  8. K Swain, B Mahanthesh and F Mebarek-Oudina, Heat Transf. 50(1), 754 (2021), https://doi.org/10.1002/htj.21902

    Article  Google Scholar 

  9. R Djebali, F Mebarek-Oudina and C Rajashekhar, Phys. Scr. 96(8), 085206 (2021), https://doi.org/10.1088/1402-4896/abfe31

    Article  ADS  Google Scholar 

  10. M K Murthy, C S Raju, V Nagendramma, S A Shehzad and A J Chamkha, Defect Diffusion Forum 393, 73 (2019)

    Article  Google Scholar 

  11. R Sivaraj, A J Benazir, S Srinivas and A J Chamkha, Eur. Phys. J. Special Topics 228, 35 (2019)

    Article  ADS  Google Scholar 

  12. J Raza, Propulsion Power Res. 8(2), 138 (2019)

    Article  Google Scholar 

  13. R Alizadeh, S R Gomari, A Alizadeh, N Karimi and L K Li, Comp. Math. Appl. (2019), https://doi.org/10.1016/j.camwa.2019.10.021

    Article  Google Scholar 

  14. M Casson, in: C C Mills (ed.), Rheology of disperse systems (Oxford, New York, 1959) pp. 84–194

  15. N T El-Dabe, M Y Abou-Zeid, O H El-Kalaawy, S M Moawad and O S Ahmed, Therm. Sci. 25, 257 (2021)

    Article  Google Scholar 

  16. M K Murthy, Defect Diffusion Forum 392, 29 (2019)

    Article  Google Scholar 

  17. K A Kumar, V Sugunamma, N Sandeep and J R Reddy, SN Appl. Sci. 1(7), 705 (2019)

    Google Scholar 

  18. S Haldar, S Mukhopadhyay and G C Layek, Mech. Adv. Mater. Struct. 26(17), 1498 (2019)

    Article  Google Scholar 

  19. K Ramesh, O Ojjela and N Nareshkumar, Heat Transf. Asian Res. 48(4), 1483 (2019)

    Article  Google Scholar 

  20. M Das, G Mahanta, S Shaw and S B Parida, Heat Transf. Asian Res. 48(5), 1761 (2019)

    Article  Google Scholar 

  21. B J Gireesha, C T Srinivasa, N S Shashikumar, M Macha, J K Singh and B Mahanthesh, Proceedings of the Institution of Mechanical Engineers, Part E: J. Process Mech. Eng. 233(5), 1173 (2019)

    Article  Google Scholar 

  22. B Mahanthesh, Mapana J. Sci. 16(3),13 (2017)

    Article  Google Scholar 

  23. J Mackolil and B Mahanthesh, J. Comput. Design Eng. 6(4), 593 (2019)

    Article  Google Scholar 

  24. K Swain, F Mebarek-Oudina and S M. Abo-Dahab, J. Therm. Anal. Calorim. 147, 1561 (2022), https://doi.org/10.1007/s10973-020-10432-4

    Article  Google Scholar 

  25. B J Gireesha, M. Archana, B Mahanthesh and B C Prasannakumara, Multidisc. Model. Mater. Struct. 15, 227 (2019)

    Article  Google Scholar 

  26. T Kunnegowda, B Mahanthesh, G Lorenzini and I L Animasaun, Math. Model. Eng. Probl. 6(3),369 (2019)

    Article  Google Scholar 

  27. J Raza, M Farooq, F Mebarek-Oudina and B Mahanthesh, Multidisc. Model. Mater. Struct. 15(5), 913 (2019)

    Article  Google Scholar 

  28. A I Alsabery, M A Ismael, A J Chamkha and I Hashim, Int. Commun. Heat Mass Transf. 110, 104442 (2020)

    Article  Google Scholar 

  29. F Mebarek-Oudina, Heat Transf. Asian Res. 48, 135 (2019)

    Article  Google Scholar 

  30. A Zaim, A Aissa, F Mebarek-Oudina, B Mahanthesh, G Lorenzini and M Sahnoun, Propulsion Power Res. 9(4), 383 (2020), https://doi.org/10.1016/j.jppr.2020.10.002

    Article  Google Scholar 

  31. L A Lund, Z Omar and I Khan, Comput. Meth. Prog. Biomed. 182, 105044 (2019)

    Article  Google Scholar 

  32. S Marzougui, M Bouabid, F Mebarek-Oudina, N Abu-Hamdeh, M Magherbi and K Ramesh, Int. J. Numer. Meth. Heat Fluid Flow 31(7), 2197 (2021), https://doi.org/10.1108/HFF-07-2020-0418

    Article  Google Scholar 

  33. F Mebarek-Oudina, R Bessaih, B Mahanthesh, A J Chamkha and J Raza, Int. J. Numer. Meth. Heat Fluid Flow 31(4), 1172 (2021), https://doi.org/10.1108/HFF-05-2020-0321

    Article  Google Scholar 

  34. K Asogwa, F Mebarek-Oudina and I Animasaun, Arab. J. Sci. Eng. 47(7), 8721 (2022), https://doi.org/10.1007/s13369-021-06355-3

    Article  Google Scholar 

  35. S Marzougui, F Mebarek-Oudina, A Mchirgui and M Magherbi, Int. J. Numer. Meth. Heat Fluid Flow 36(2), 2047 (2022), https://doi.org/10.1108/HFF-04-2021-0288

    Article  Google Scholar 

  36. P K Dadheech, P Agrawal, F Mebarek-Oudina, N Abu-Hamdeh and A Sharma, J. Nanofluids 9(3), 161 (2020), https://doi.org/10.1166/jon.2020.1741

    Article  Google Scholar 

  37. I Chabani, F Mebarek-Oudina and A I Ismail, Micromachines 13(2), 224 (2022), https://doi.org/10.3390/mi13020224

    Article  Google Scholar 

  38. C R Bedick, L Kolczynski and C R Woodside, Combustion Flame 181, 225 (2017)

    Article  Google Scholar 

  39. L N Tao, ASME J. Heat Transf. 82, 233 (1960)

    Article  Google Scholar 

  40. T T Hamadah and R A Wirtz, ASME J. Heat Transf. 113, 507 (1991)

    Article  Google Scholar 

  41. S H Tasnim, M Shohel and M A H Mamun, Exerg. 2, 300 (2020)

    Article  Google Scholar 

  42. I Fersadou, H Kahalerras and M El Ganaoui, Comput. Fluids 121, 164 (2015), https://doi.org/10.1016/j.compfluid.2015.08.014

    Article  MathSciNet  Google Scholar 

  43. B S Chen and C C Liu, Int. J. Heat Mass Transf. 91, 1026 (2015)

    Article  MathSciNet  Google Scholar 

  44. M B Ashraf, T Hayat, S A Shehzad and B Ahmed, Neural Comp. Appl. 31, 249 (2019)

    Article  Google Scholar 

  45. F Mebarek-Oudina, N Keerthi Reddy and M Sankar, Adv. Fluid Dyn. Lecture Notes Mech. Eng. 923–937 (2021), https://doi.org/10.1007/978-981-15-4308-1_70

  46. B Mahanthesh, B J Gireesha, M Sheikholeslami, S A Shehzad and P B S Kumar, J. Nanofluids 7(6), 1089 (2018)

    Article  Google Scholar 

  47. J Raza, F Mebarek-Oudina and O D Makinde, Defect Diffusion Forum 387, 51 (2019)

    Article  Google Scholar 

  48. M Alkasassbeh, Z Omar, F Mebarek-Oudina, J Raza and A J Chamkha, Heat Transf. Asian Res. 48(4), 1224 (2019)

    Article  Google Scholar 

  49. K Ali and M Ashraf, J. Theor. Appl. Mech. 52, 557 (2014)

    Google Scholar 

  50. J Raza, F Mebarek-Oudina, P Ram and S Sharma, Defect Diffusion Forum 401, 92 (2020), https://doi.org/10.4028/www.scientific.net/DDF.401.92

    Article  Google Scholar 

  51. B V Pushpa, M Sankar and F Mebarek-Oudina, J Nanofluids 10(2), 292 (2021), https://doi.org/10.1166/jon.2021.1782

    Article  Google Scholar 

  52. A S Warke, K Ramesh, F Mebarek-Oudina and A Abidi, J. Therm. Anal. Calorim. 147 (12), 6901 (2022), https://doi.org/10.1007/s10973-021-10976-z

    Article  Google Scholar 

  53. F Mebarek-Oudina and I Chabani, J. Nanofluids 11(2), 155 (2022), https://doi.org/10.1166/jon.2022.1834

    Article  Google Scholar 

  54. Preeti, O Ojjela, P K Kambhatla and F Mebarek-Oudina, Pramana – J. Phys. 95, 182 (2021), https://doi.org/10.1007/s12043-021-02195-w

  55. S Aziz, I Ahmad, N Ali and S U Khan, J. Therm. Anal. Calorim. 146, 435 (2021), https://doi.org/10.1007/s10973-020-09962-8

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad (CUI), Vehari Campus, Pakistan

    J Raza

  2. Department of Physics, Faculty of Sciences, University of 20 Août 1955-Skikda, Skikda, Algeria

    F Mebarek-Oudina

  3. School of Quantitative Sciences, Universiti Utara Malaysia, Sintok, Malaysia

    L Ali Lund

Authors
  1. J Raza
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F Mebarek-Oudina
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. L Ali Lund
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F Mebarek-Oudina.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Raza, J., Mebarek-Oudina, F. & Ali Lund, L. The flow of magnetised convective Casson liquid via a porous channel with shrinking and stationary walls. Pramana - J Phys 96, 229 (2022). https://doi.org/10.1007/s12043-022-02465-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12043-022-02465-1

Keywords

PACS Nos

Search

Navigation