Skip to main content
SpringerLink
Log in

OHAM Analysis on Bio-convective Flow of Partial Differential Equations of Casson Nanofluid Under Thermal Radiation Impact Past over a Stretching Sheet

  • Research
  • Published:
BioNanoScience Aims and scope Submit manuscript

Abstract

The combined impacts of nonlinear thermal radiation and energy of activation in the Casson’s flow of the boundary layer nanofluid across a stretched surface are examined in the current article while taking Brownian motion into account. The transformation of similarity is used to first transform the fundamental equations, and after that, the following equations are processed numerically. The energy equation with nonlinear expressions also makes use of the additional properties of thermal radiation. Additionally, the present continuation additionally takes the effect of activation energy into account, making the study highly flexible. Analysis is done on the effect of many physical parameters on the velocity, concentration, and temperature fields, including the activation energy, Lewis number, thermal radiation, and others. In addition to this, the practical applications of physical parameters on the reduced Sherwood number and Nusselt number are discussed. It is determined from the computed results that the local Nusselt number is reduced when the results of the thermophoretic parameter, Brownian parameter, and radiation parameter are added. The temperature profile is boosted by an increment in radiation parameter, while a raise in thermophoresis shows a rise in the concentration profile. Making use of the required factors of similarity, the resulting nonlinear equations (PDEs) are converted into nonlinear ODEs. The BVPh2.0 in the Mathematica software was used to quantitatively evaluate the non-linear ODEs. According to the study, the existence of activation energy can improve reaction processes more than its absence. The stated results are said to be valuable for industrial processes and improvements in heat and energy resources based on the calculated scientific conclusions.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

Data Availability

No datasets were generated or analyzed during the current study.

Abbreviations

\((u, v)\) :

Velocity components along (x, y)-axis ms–1

μ:

Dynamic viscosity kg/m.s

\(\nu\) :

Kinematic viscosity m2s–1

ρ:

Fluid density  kg/m3

ρp :

Density of the particle kgm–3

α:

Thermal diffusivity  m2s–1

k :

Thermal conductivity Wm–1K–1

\(T\) :

Temperature K 

\(C\) :

Concentration fluid  kgm–3

\({(\rho c)}_{\uprho }\) :

Effective heat capacity Jm–3K–1

\({(\rho c)}_{{\text{f}}}\) :

Fluid’s heat capacity Jm–3K–1

\({h}_{{\text{f}}}\) :

Convective heat transmission coefficient

\({D}_{{\text{B}}}\) :

Brownian diffusion coefficient m2s–1

\({D}_{{\text{T}}}\) :

Thermophoresis diffusion coefficient m2s–1   

\(M\) :

Hartmann constant

\(S\) :

Suction parameter

\({{\varvec{N}}}_{\mathbf{t}}\) :

Thermophoretic parameter

\({\text{Nb}}\) :

Brownian motion factor

\({\text{Rd}}\) :

Heat radiation parameter

\({\text{Pr}}\) :

Prandtl number

\(\gamma\) :

Casson parameter

\(Le\) :

Lewis coefficients

\(Q\) :

Heat generation/absorption W/m3

\({\text{Lb}}\) :

Bioconvection Lewis number

\({\text{Pe}}\) :

Peclet factor

\({{F}_{{\text{r}}}}\) :

Forchheimer number

References

  1. Buongiorno, J. (2006). Convective transport in nanofluids.

  2. Khan, N., Ali, F., Arif, M., Ahmad, Z., Aamina, A., & Khan, I. (2021). Maxwell nanofluid flow over an infinite vertical plate with ramped and isothermal wall temperature and concentration. Mathematical Problems in Engineering, 2021, 1–19.

    Google Scholar 

  3. Chuong, C. J., & Fung, Y. C. (1986). Frontiers in biomechanics (pp. 117–139). Residual stress in arteries. Springer.

    Book  Google Scholar 

  4. Dash, R. K., Mehta, K. N., & Jayaraman, G. (1996). Casson fluid flow in a pipe filled with a homogeneous porous medium. International Journal of Engineering Science, 34(10), 1145–1156.

    Article  CAS  Google Scholar 

  5. Shaheen, N., Alshehri, H. M., Ramzan, M., Shah, Z., & Kumam, P. (2021). Soret and Dufour effects on a Casson nanofluid flow past a deformable cylinder with variable characteristics and Arrhenius activation energy. Scientific Reports, 11(1), 19282.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  6. Anwar, M. I., Khan, I., Sharidan, S., & Salleh, M. Z. (2012). Conjugate effects of heat and mass transfer of nanofluids over a nonlinear stretching sheet. International Journal of Physical Sciences, 7(26), 4081–4092.

    Article  CAS  Google Scholar 

  7. Aman, S., Khan, I., Ismail, Z., Salleh, M. Z., Alshomrani, A. S., & Alghamdi, M. S. (2017). Magnetic field effect on Poiseuille flow and heat transfer of carbon nanotubes along a vertical channel filled with Casson fluid. AIP Advances, 7(1).

  8. Sayed-Ahmed, M. E., Attia, H. A., & Ewis, K. M. (2011). Time dependent pressure gradient effect on unsteady MHD Couette flow and heat transfer of a Casson fluid. Engineering, 3(1), 38.

    Article  CAS  Google Scholar 

  9. Ibrahim, M. G., & Abou-Zeid, M. Y. (2022). Influence of variable velocity slip condition and activation energy on MHD peristaltic flow of Prandtl nanofluid through a non-uniform channel. Scientific Reports, 12(1), 18747.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  10. Bayareh, M. (2023). An overview of non-Newtonian nanofluid flow in macro-and micro-channels using two-phase schemes. Engineering Analysis with Boundary Elements, 148, 165–175.

    Article  MathSciNet  Google Scholar 

  11. Sreenivasulu, P., Poornima, T., & Reddy, N. B. (2019). Influence of joule heating and non-linear radiation on MHD 3D dissipating flow of Casson nanofluid past a non-linear stretching sheet. Nonlinear Engineering, 8(1), 661–672.

    Article  ADS  Google Scholar 

  12. Mustefa, M., Hayet, T., Pop, I., & Aziz, A. (2011). Unsteady boundary layer flow of a Casson fluid impulsively started moving flat plate. Heat Transfer-Asian Ras, 40(6), 563–576.

    Article  Google Scholar 

  13. Mukhopadhyay, S. (2013). Casson fluid flow and heat transfer over a nonlinearly stretching surface. Chinese Physics B, 22(7), 074701.

    Article  Google Scholar 

  14. Mukhopadhyay, S., Bhattacharyya, K., & Hayat, T. (2013). Exact solutions for the flow of Casson fluid over a stretching surface with transpiration and heat transfer effects. Chinese Physics B, 22(11), 114701.

    Article  Google Scholar 

  15. Nadeem, S., Haq, R. U., & Akbar, N. S. (2013). MHD three-dimensional boundary layer flow of Casson nanofluid past a linearly stretching sheet with convective boundary condition. IEEE Transactions on Nanotechnology, 13(1), 109–115.

    Article  ADS  Google Scholar 

  16. Nadeem, S., Mehmood, R., & Akbar, N. S. (2014). Optimized analytical solution for oblique flow of a Casson-nano fluid with convective boundary conditions. International Journal of Thermal Sciences, 78, 90–100.

    Article  Google Scholar 

  17. Hussanan, A., Zuki Salleh, M., Tahar, R. M., & Khan, I. (2014). Unsteady boundary layer flow and heat transfer of a Casson fluid past an oscillating vertical plate with Newtonian heating. PLoS ONE, 9(10), e108763.

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  18. Mukhopadhyay, S., & Mandal, I. C. (2014). Boundary layer flow and heat transfer of a Casson fluid past a symmetric porous wedge with surface heat flux. Chinese Physics B, 23(4), 044702.

    Article  Google Scholar 

  19. Hussanan, A., Salleh, M. Z., Khan, I., & Shafie, S. (2017). Convection heat transfer in micropolar nanofluids with oxide nanoparticles in water, kerosene and engine oil. Journal of Molecular Liquids, 229, 482–488.

    Article  CAS  Google Scholar 

  20. Hussanan, A., & Trung, N. T. (2019). Heat transfer analysis of sodium carboxymethyl cellulose based nanofluid with titania nanoparticles. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 56(2), 248–256.

    Google Scholar 

  21. Hussanan, A., Salleh, M. Z., Alkasasbeh, H. T., & Khan, I. (2018). MHD flow and heat transfer in a Casson fluid over a nonlinearly stretching sheet with Newtonian heating. Heat Transfer Research, 49(12), 1185.

    Article  Google Scholar 

  22. Kocić, M., Stamenković, Ž, Petrović, J., & Bogdanović-Jovanović, J. (2023). MHD micropolar fluid flow in porous media. Advances in Mechanical Engineering, 15(6), 16878132231178436.

    Article  Google Scholar 

  23. Lund, L. A., Asghar, A., Rasool, G., & Yashkun, U. (2023). Magnetized Casson SA-hybrid nanofluid flow over a permeable moving surface with thermal radiation and Joule heating effect. Case Studies in Thermal Engineering, 50, 103510.

    Article  Google Scholar 

  24. Aslani, K. E., Benos, L., Tzirtzilakis, E., & Sarris, I. E. (2020). Micromagnetorotation of MHD micropolar flows. Symmetry, 12(1), 148.

    Article  ADS  Google Scholar 

  25. Ibrahim, W., & Shanker, B. (2012). Unsteady MHD boundary-layer flow and heat transfer due to stretching sheet in the presence of heat source or sink. Computers & Fluids, 70, 21–28.

    Article  MathSciNet  Google Scholar 

  26. Souayeh, B., Reddy, M. G., Sreenivasulu, P., Poornima, T. M. I. M., Rahimi-Gorji, M., & Alarifi, I. M. (2019). Comparative analysis on non-linear radiative heat transfer on MHD Casson nanofluid past a thin needle. Journal of Molecular Liquids, 284, 163–174.

    Article  CAS  Google Scholar 

  27. Wang, C. Y. (1984). The three-dimensional flow due to a stretching flat surface. The physics of fluids, 27(8), 1915–1917.

    Article  ADS  MathSciNet  Google Scholar 

  28. Tawade, J. V., Guled, C. N., Noeiaghdam, S., Fernandez-Gamiz, U., Govindan, V., & Balamuralitharan, S. (2022). Effects of thermophoresis and Brownian motion for thermal and chemically reacting Casson nanofluid flow over a linearly stretching sheet. Results in Engineering, 15, 100448.

    Article  CAS  Google Scholar 

  29. Shankaralingappa, B. M., Madhukesh, J. K., Sarris, I. E., Gireesha, B. J., & Prasannakumara, B. C. (2021). Influence of thermophoretic particle deposition on the 3D flow of sodium alginate-based Casson nanofluid over a stretching sheet. Micromachines, 12(12), 1474.

    Article  PubMed  PubMed Central  Google Scholar 

  30. Jamshed, W., Akgül, E. K., & Nisar, K. S. (2021). Keller box study for inclined magnetically driven Casson nanofluid over a stretching sheet: Single phase model. Physica Scripta, 96(6), 065201.

    Article  ADS  Google Scholar 

  31. Aybar, H. Ş, Sharifpur, M., Azizian, M. R., Mehrabi, M., & Meyer, J. P. (2015). A review of thermal conductivity models for nanofluids. Heat Transfer Engineering, 36(13), 1085–1110.

    Article  ADS  CAS  Google Scholar 

  32. Mukhopadhyay, S., & Layek, G. C. (2012). Effects of variable fluid viscosity on flow past a heated stretching sheet embedded in a porous medium in presence of heat source/sink. Meccanica, 47, 863–876.

    Article  MathSciNet  Google Scholar 

  33. Raptis, A. (1998). Flow of a micropolar fluid past a continuously moving plate by the presence of radiation. International Journal of Heat and Mass Transfer, 18(41), 2865–2866.

    Article  Google Scholar 

  34. Rasool, G., Shafiq, A., Alqarni, M. S., Wakif, A., Khan, I., & Bhutta, M. S. (2021). Numerical scrutinization of Darcy-Forchheimer relation in convective magnetohydrodynamic nanofluid flow bounded by nonlinear stretching surface in the perspective of heat and mass transfer. Micromachines, 12(4), 374.

    Article  PubMed  PubMed Central  Google Scholar 

  35. Alsaadi, F. E., Ullah, I., Hayat, T., & Alsaadi, F. E. (2020). Entropy generation in nonlinear mixed convective flow of nanofluid in porous space influenced by Arrhenius activation energy and thermal radiation. Journal of Thermal Analysis and Calorimetry, 140, 799–809.

    Article  CAS  Google Scholar 

  36. RamReddy, C., & Naveen, P. (2020). Analysis of activation energy in quadratic convective flow of a micropolar fluid with chemical reaction and suction/injection effects. Multidiscipline Modeling in Materials and Structures, 16(1), 169–190.

    Article  CAS  Google Scholar 

  37. Ijaz Khan, M., & Alzahrani, F. (2021). Numerical simulation for the mixed convective flow of non-Newtonian fluid with activation energy and entropy generation. Mathematical Methods in the Applied Sciences, 44(9), 7766–7777.

    Article  ADS  MathSciNet  Google Scholar 

  38. Ahmed, S. E., Hussein, A. K., Mohammed, H. A., & Sivasankaran, S. (2014). Boundary layer flow and heat transfer due to permeable stretching tube in the presence of heat source/sink utilizing nanofluids. Applied Mathematics and Computation, 238, 149–162.

    Article  Google Scholar 

  39. Roy, N., & Pal, D. (2022). Influence of activation energy and nonlinear thermal radiation with ohmic dissipation on heat and mass transfer of a Casson nanofluid over stretching sheet. Journal of Nanofluids, 11(6), 819–832.

    Google Scholar 

  40. Wang, X., Rasool, G., Shafiq, A., Thumma, T., & Al-Mdallal, Q. M. (2023). Numerical study of hydrothermal and mass aspects in MHD driven Sisko-nanofluid flow including optimization analysis using response surface method. Scientific Reports, 13(1), 7821.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  41. Bejawada, S. G., & Nandeppanavar, M. M. (2023). Effect of thermal radiation on magnetohydrodynamics heat transfer micropolar fluid flow over a vertical moving porous plate. Experimental and Computational Multiphase Flow, 5(2), 149–158.

    Article  Google Scholar 

  42. Aslani, ΚE., & Sarris, I. E. (2021). Effect of micromagnetorotation on magnetohydrodynamic Poiseuille micropolar flow: Analytical solutions and stability analysis. Journal of Fluid Mechanics, 920, A25.

    Article  MathSciNet  CAS  Google Scholar 

  43. Liao, S. (2010). An optimal homotopy-analysis approach for strongly nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 15(8), 2003–2016.

    Article  ADS  MathSciNet  Google Scholar 

  44. Wang, F., Zhang, J., Algarni, S., Naveed Khan, M., Alqahtani, T, Ahmad, S., 2022. Numerical simulation of hybrid Casson nanofluid flow by the influence of magnetic dipole and gyrotactic microorganism. Waves in Random and Complex Media, 1–16.

  45. Wang, F., Jamshed, W., Ibrahim, R. W., Abdalla, N. S. E., Abd-Elmonem, A., & Hussain, S. M. (2023). Solar radiative and chemical reactive influences on electromagnetic Maxwell nanofluid flow in Buongiorno model. Journal of Magnetism and Magnetic Materials, 576, 170748.

    Article  CAS  Google Scholar 

  46. Wang, F., Ahmed, A., Khan, M. N., Ahammad, N. A., Alqahtani, A. M., Eldin, S. M., & Abdelmohimen, M. A. (2023). Natural convection in nanofluid flow with chemotaxis process over a vertically inclined heated surface. Arabian Journal of Chemistry, 16(4), 104599.

    Article  CAS  Google Scholar 

  47. Wang, F., Fatunmbi, E. O., Adeosun, A. T., Salawu, S. O., Animasaun, I. L., & Sarris, I. E. (2023). Comparative analysis between copper ethylene-glycol and copper-iron oxide ethylene-glycol nanoparticles both experiencing Coriolis force, velocity and temperature jump. Case Studies in Thermal Engineering, 47, 103028.

    Article  Google Scholar 

  48. Sohail, M., Nazir, U., Singh, A., Tulu, A., & Khan, M. J. (2024). Finite element analysis of cross fluid model over a vertical disk suspended to a tetra hybrid nanoparticles mixture. Scientific Reports, 14(1), 1–17.

    Article  Google Scholar 

  49. Waseem, F., Sohail, M., Ilyas, N., Awwad, E. M., Sharaf, M., Khan, M. J., & Tulu, A. (2024). Entropy analysis of MHD hybrid nanoparticles with OHAM considering viscous dissipation and thermal radiation. Scientific Reports, 14(1), 1096.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  50. Nazir, U., Mukdasai, K., Sohail, M., Singh, A., Alosaimi, M. T., Alanazi, M., & Tulu, A. (2023). Investigation of composed charged particles with suspension of ternary hybrid nanoparticles in 3D-power law model computed by Galerkin algorithm. Scientific Reports, 13(1), 15040.

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  51. Pal, D., & Roy, N. (2017). Influence of Brownian motion and thermal radiation on heat transfer of a nanofluid over stretching sheet with slip velocity. International Journal of Applied and Computational Mathematics, 3, 3355–3377.

    Article  MathSciNet  Google Scholar 

  52. Rasool, G., Shafiq, A., Hussain, S., Zaydan, M., Wakif, A., Chamkha, A. J., & Bhutta, M. S. (2022). Significance of Rosseland’s radiative process on reactive Maxwell nanofluid flows over an isothermally heated stretching sheet in the presence of Darcy-Forchheimer and Lorentz forces: Towards a new perspective on Buongiorno’s model. Micromachines, 13(3), 368.

    Article  PubMed  PubMed Central  Google Scholar 

  53. Kotha, G., Kolipaula, V. R., Venkata Sub Barao, M., Penki, S., & Chamkha, A. J. (2020). Internal heat generation on bioconvection of an MHD nanofluid flow due to gyrotactic microorganisms. The European Physical Journal Plus, 135, 1–19.

    Article  Google Scholar 

Download references

Funding

There is no external funding received for this research.

Author information

Authors and Affiliations

  1. Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, 64200, Pakistan

    Muhammad Sohail, Komal Ilyas, Esha Rafique & Shah Jahan

  2. Department of Basic Sciences, College of Sciences and Theoretical Studies, Dammam-Branch, Saudi Electronic University, Riyadh, Saudi Arabia

    Abha Singh

Authors
  1. Muhammad Sohail
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Komal Ilyas
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Esha Rafique
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Abha Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shah Jahan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

All the authors reviewed the manuscript and approved the submission.

Corresponding author

Correspondence to Muhammad Sohail.

Ethics declarations

Ethical Approval

Not applicable.

Research Involving Humans and Animals Statement

None.

Informed Consent

Not applicable.

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sohail, M., Ilyas, K., Rafique, E. et al. OHAM Analysis on Bio-convective Flow of Partial Differential Equations of Casson Nanofluid Under Thermal Radiation Impact Past over a Stretching Sheet. BioNanoSci. (2024). https://doi.org/10.1007/s12668-024-01329-9

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12668-024-01329-9

Keywords

Search

Navigation