Skip to main content
Log in

Cattaneo–Christov heat flux model for stagnation point flow of micropolar nanofluid toward a nonlinear stretching surface with slip effects

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

Cattaneo–Christov with variable thermal relaxation time and entropy generation is the main concern of this study. The micropolar fluid with absorption of heat in the existence of mixed convection and partial slip is scrutinized. Two distinct nanoparticles, i.e., single-wall carbon nanotube and multi-wall carbon nanotube, are immerged in micropolar fluid to interrogate the feature of heat and mass transfer. The non-dimensional similarity transformation is utilized to transform the partial differential equations into nonlinear ordinary differential equations, and resulting coupled equations are solved numerically using bvp4c from MATLAB. The present results show the fabulous agreement with previous published results. The temperature field diminishes with larger thermal relaxation time parameter. Entropy generation profile is an increasing function of Brinkmann number, while Bejan number is a diminishing function. Further the solid volume fraction diminishes the velocity profile and enhances the temperature distribution and entropy generation.

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

Access this article

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

References

  1. Farooq M, Ahmad S, Javed M, Anjum A. Chemically reactive species in squeezed flow through modified Fourier’s and Fick’s laws. Eur Phys J Plus. 2018;133:63.

    Google Scholar 

  2. Nadeem S, Ahmad S, Muhammad N. Cattaneo–Christov flux in the flow of a viscoelastic fluid in the presence of Newtonian heating. J Mol Liq. 2017;237:180–4.

    CAS  Google Scholar 

  3. Alamri SZ, Khan AA, Azeez M, Ellahi R. Effects of mass transfer on MHD second grade fluid towards stretching cylinder: a novel perspective of Cattaneo–Christov heat flux model. Phys Lett A. 2019;383(2–3):276–81.

    CAS  Google Scholar 

  4. Cattaneo C. Sulla conduzione del calore. Atti Sem Mat Fis Univ Modena. 1948;3:83–101.

    Google Scholar 

  5. Christov CI. On frame indifferent formulation of the Maxwell-Cattaneo model of finite-speed heat conduction. Mech Res Commun. 2009;36(4):481–6.

    Google Scholar 

  6. Shah Z, Tassaddiq A, Islam S, Alklaibi AM, Khan I. Cattaneo–Christov Heat Flux Model for Three-Dimensional Rotating Flow of SWCNT and MWCNT Nanofluid with Darcy-Forchheimer Porous Medium Induced by a Linearly Stretchable Surface. Symmetry. 2019;11(3):331.

    CAS  Google Scholar 

  7. Han S, Zheng L, Li C, Zhang X. Coupled flow and heat transfer in viscoelastic fluid with Cattaneo–Christov heat flux model. Appl Math Lett. 2014;38:87–93.

    Google Scholar 

  8. Lu D, Ramzan M, Ahmad S, Chung JD, Farooq U. Upshot of binary chemical reaction and activation energy on carbon nanotubes with Cattaneo–Christov heat flux and buoyancy effects. Phys Fluids. 2017;29:123103.

    Google Scholar 

  9. Nadeem S, Ahmad S, Muhammad N, Mustafa MT. Chemically reactive species in the flow of a Maxwell fluid. Results Phys. 2017;7:2607–13.

    Google Scholar 

  10. Khan U, Ahmad S, Ramzan M, Suleman M, Lu D, Inam S. Numerical Simulation of Darcy-Forchheimer 3D Unsteady Nanofluid Flow Comprising Carbon Nanotubes with Cattaneo–Christov Heat Flux and Velocity and Thermal Slip Conditions. Processes. 2019;7(10):687.

    Google Scholar 

  11. Kumari M, Nath G. Unsteady incompressible boundary layer flow of a micropolar fluid at a stagnation point. Int J Eng Sci. 1984;22(6):755–68.

    Google Scholar 

  12. Eringen AC. Microcontinuum field theories: II. Fluent media, vol. 2. Berlin: Springer; 2001.

    Google Scholar 

  13. Lukaszewicz G. Micropolar fluids: theory and applications. Basel: Brikhauser; 1999.

    Google Scholar 

  14. Nadeem S, Khan MN, Muhammad N, Ahmad S. Erratum to: Mathematical analysis of bio-convective micropolar nanofluid Erratum to: Journal of Computational Design and Engineering. J Comput Des Eng. 2019;6:233–42.

    Google Scholar 

  15. Nadeem S, Rehman A, Vajravelu K, Lee J, Lee C. Axisymmetric stagnation flow of a micropolar nanofluid in a moving cylinder. Math Probl Eng. 2012. https://doi.org/10.1155/2012/378259.

    Article  Google Scholar 

  16. Balaram M, Sastri VUK. Micropolar free convection flow. Int J Heat Mass Transf. 1973;16(2):437–41.

    CAS  Google Scholar 

  17. Das K. Slip effects on MHD mixed convection stagnation point flow of a micropolar fluid towards a shrinking vertical sheet. Comput Math Appl. 2012;63(1):255–67.

    Google Scholar 

  18. Maleki H, Safaei MR, Alrashed AAAA, Kasaeian A. Flow and heat transfer in non-Newtonian nanofluids over porous surfaces. J Therm Anal Calorim. 2019;135(3):1655–66.

    CAS  Google Scholar 

  19. Nazari S, Ellahi R, Sarafraz MM, Safaei MR, Asgari A, Akbari OA. Numerical study on mixed convection of a non-Newtonian nanofluid with porous media in a two lid-driven square cavity. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08841-1.

    Article  Google Scholar 

  20. Heydari A, Akbari OA, Safaei MR, Derakhshani M, Alrashed AAAA, Mashayekhi R, Shabani GAS, Zarringhalam M, Nguyen TK. The effect of attack angle of triangular ribs on heat transfer of nanofluids in a microchannel. J Therm Anal Calorim. 2018;131(3):2893–912.

    CAS  Google Scholar 

  21. Seth GS, Bhattacharyya A, Mishra MK. Study of partial slip mechanism on free convection flow of viscoelastic fluid past a nonlinearly stretching surface. Comput Therm Sci Int J. 2019;11(1–2):105–17.

    Google Scholar 

  22. Ellahi R, Hussain F, Ishtiaq F, Hussain A. Peristaltic transport of Jeffrey fluid in a rectangular duct through a porous medium under the effect of partial slip: An application to upgrade industrial sieves/filters. Pramana. 2019;93(3):34.

    Google Scholar 

  23. Zaib A, Haq RU, Chamkha AJ, Rashidi MM. Impact of partial slip on mixed convective flow towards a Riga plate comprising micropolar TiO2-kerosene/water nanoparticles. Int J Numer Methods Heat Fluid Flow. 2019;29(5):1647–62.

    Google Scholar 

  24. Ariel PD. Axisymmetric flow due to a stretching sheet with partial slip. Comput Math Appl. 2007;54(7–8):1169–83.

    Google Scholar 

  25. Bejan A. A study of entropy generation in fundamental convective heat transfer. J Heat Transf. 1979;101(4):718–25.

    Google Scholar 

  26. Bejan A, Kestin J. Entropy generation through heat and fluid flow. J Appl Mech. 1983;50:475.

    Google Scholar 

  27. Bhatti MM, Sheikholeslami M, Shahid A, Hassan M, Abbas T. Entropy generation on the interaction of nanoparticles over a stretched surface with thermal radiation. Colloids Surf A. 2019;570:368–76.

    CAS  Google Scholar 

  28. Ellahi R, Sait SM, Shehzad N, Mobin N. Numerical simulation and mathematical modeling of electro-osmotic Couette-Poiseuille flow of MHD power-law nanofluid with entropy generation. Symmetry. 2019;11(8):1038.

    CAS  Google Scholar 

  29. Alkanhal TA, Sheikholeslami M, Arabkoohsar A, Haq R, Shafee A, Li Z, Tlili I. Simulation of convection heat transfer of magnetic nanoparticles including entropy generation using CVFEM. Int J Heat Mass Transf. 2019;136:146–56.

    CAS  Google Scholar 

  30. Choi SUS, Zhang ZG, Yu W, Lockwood FE, Grulke EA. Anomalous thermal conductivity enhancement in nanotube suspensions. Appl Phys Lett. 2001;79(14):2252–4.

    CAS  Google Scholar 

  31. Ahmed Z, Nadeem S, Saleem S, Ellahi R. Numerical study of unsteady flow and heat transfer CNT-based MHD nanofluid with variable viscosity over a permeable shrinking surface. Int J Numer Methods Heat Fluid Flow. 2019;29(12):4607–23.

    Google Scholar 

  32. Akbar NS, Khan ZH, Nadeem S. The combined effects of slip and convective boundary conditions on stagnation-point flow of CNT suspended nanofluid over a stretching sheet. J Mol Liq. 2014;196:21–5.

    CAS  Google Scholar 

  33. Haq RU, Nadeem S, Khan ZH, Noor NFM. Convective heat transfer in MHD slip flow over a stretching surface in the presence of carbon nanotubes. Phys B. 2015;457:40–7.

    Google Scholar 

  34. Nasir S, Islam S, Gul T, Shah Z, Khan MA, Khan W, Khan AZ, Khan S. Three-dimensional rotating flow of MHD single wall carbon nanotubes over a stretching sheet in presence of thermal radiation. Appl Nanosci. 2018;8(6):1361–78.

    CAS  Google Scholar 

  35. Saba F, Ahmed N, Hussain S, Khan U, Mohyud-Din S, Darus M. Thermal analysis of nanofluid flow over a curved stretching surface suspended by carbon nanotubes with internal heat generation. Appl Sci. 2018;8(3):395.

    Google Scholar 

  36. Hayat T, Farooq M, Alsaedi A. Homogeneous-heterogeneous reactions in the stagnation point flow of carbon nanotubes with Newtonian heating. AIP Adv. 2015;5(2):027130.

    Google Scholar 

  37. Zeeshan A, Ellahi R, Mabood F, Hussain F. Numerical study on bi-phase coupled stress fluid in the presence of Hafnium and metallic nanoparticles over an inclined plane. Int J Numer Methods Heat Fluid Flow. 2019;29(8):2854–69.

    Google Scholar 

  38. Jain S, Gupta P. Flow and heat transfer of carbon nanotubes nanofluid flow over a 3-D inclined nonlinear stretching sheet with porous media. In: Srinivasacharya D., Reddy K, editors. Numerical heat transfer and fluid flow. Lecture notes in mechanical engineering. Singapore: Springer; 2019. p. 321–9.

    Google Scholar 

  39. Nadeem S, Ahmad S, Muhammad N. Computational study of Falkner-Skan problem for a static and moving wedge. Sens Actuators B Chem. 2018;263:69–76.

    CAS  Google Scholar 

  40. Prakash J, Tripathi D, Tiwari AK, Sait SM, Ellahi R. “Peristaltic pumping of nanofluids through a tapered channel in a porous environment: Applications in blood flow. Symmetry. 2019;11(7):868.

    CAS  Google Scholar 

  41. Suleman M, Ramzan M, Ahmad S, Lu D. Numerical simulation for homogeneous–heterogeneous reactions and Newtonian heating in the silver-water nanofluid flow past a nonlinear stretched cylinder. Phys Scr. 2019;94(8):085702.

    CAS  Google Scholar 

  42. Sarafraz MM, Pourmehran O, Yang B, Arjomandi M, Ellahi R. Pool boiling heat transfer characteristics of iron oxide nano-suspension under constant magnetic field. Int J Therm Sci. 2020;147:106131.

    CAS  Google Scholar 

  43. Khan LA, Raza M, Mir NA, Ellahi R. Effects of different shapes of nanoparticles on peristaltic flow of MHD nanofluids filled in an asymmetric channel. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08348-9.

    Article  Google Scholar 

  44. Nasiri H, Jamalabadi MYA, Sadeghi R, Safaei MR, Nguyen TK, Shadloo MS. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows. J Therm Anal Calorim. 2019;135(3):1733–41.

    CAS  Google Scholar 

  45. Zaib A, Haq RU. Magnetohydrodynamics mixed convective flow driven through a static wedge including TiO2 nanomaterial with micropolar liquid: Similarity dual solutions via finite difference method. Proc Inst Mech Eng C J Mech Eng Sci. 2019;233:5813–25.

    CAS  Google Scholar 

  46. Yih KA. MHD forced convection flow adjacent to a non-isothermal wedge. Int Commun Heat Mass Transf. 1999;26(6):819–27.

    CAS  Google Scholar 

  47. White FM. Fluid mechanics. McGraw Hill; 2015.

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sohail Nadeem.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ahmad, S., Nadeem, S., Muhammad, N. et al. Cattaneo–Christov heat flux model for stagnation point flow of micropolar nanofluid toward a nonlinear stretching surface with slip effects. J Therm Anal Calorim 143, 1187–1199 (2021). https://doi.org/10.1007/s10973-020-09504-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-09504-2

Keywords

Navigation