Startseite Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
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Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force

  • Mubbashar Nazeer ORCID logo EMAIL logo , Salman Saleem ORCID logo und M. Waqas Nazir ORCID logo
Veröffentlicht/Copyright: 6. Mai 2025
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 80 Heft 6

Abstract

The heat transfer analysis from the mixture flow of Carreau fluid in infinite horizontal parallel plates under the impact of the magnetic field is proposed in this theoretical analysis. The flow and heat transfer analysis through parallel plates offers various applications in nuclear reactors, microfluidic devices, lubrication systems, chemical, industrial and biological systems, etc. With motivation of current non-Newtonian fluids (Carrreau fluid) used in industries and chemical engineering, the goal of this research is to develop a mathematical model based on fluid phase and particulate phase to control the temperature of fluid and increase the convective heat transfer in considered non-Newtonian fluids under the suitable range of the physical parameters including magnetic field parameter, Darcy number, Power-law index, slip boundary conditions, volume fraction density and Weissenberg number. The nonlinear mathematical model is established with the contribution of the stress tensor and solved through the perturbation series technique. The computational results are discussed through plots and tables. From the calculated data it is perceived that volume fraction density improved the velocity and temperature distributions. It is also noted that the contribution of the magnetic field declines the flow and thermal field. The slip parameters and Darcy number upsurge the velocity and temperature fields. The comparative analysis between mixture phase flow and simple phase flow is also discussed and observed that the mixture phase flow gives more heat transfer in Carreau fluid as compared to simple phase fluid. The present research will help to understand the basic research of the mixture-phase flow of highly viscous fluid through the porous medium when the uniform magnetic field is applied transversely. Further, applications of the present study are found in medical treatment with wound healing and hyperthermia, heat exchangers, nuclear reactors, etc. This research can also be useful in petroleum industries for cleaning and purifying immiscible oils.

Keywords: magnetohydrodynamic flow; porous medium; convective heat transfer; perturbation series method; Carreau fluid model
Corresponding author: Mubbashar Nazeer, Department of Mathematics, Institute of Arts and Sciences, Government College University Faisalabad, Chiniot Campus, 35400, Pakistan, E-mail:

  1. Research ethics: Accepted.

  2. Informed consent: Not applicable.

  3. Author contributions: Dr. Mubbashar Nazeer: Validation, Writing and preparing origional draft, numerical algorithm. Dr. Salman Saleem: Writing – Review and Editing. Dr. M. Waqas Nazir: Ideas, Software development, Supervision.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors have no conflict of interest related to this manuscript.

  6. Research funding: The authors extend their appreciation to the Deanship of Scientific Research at King Khalid University for funding this work through a large group Research Project under grant number RGP.2/327/45.

  7. Data availability: This article does not contain any studies with human participants performed by any of the authors.

Appendix

γ = 1 1 − ϵ i ⁢ dP dX , A = n − 1 2 , B = α + 1 Dr 1 − ϵ i , S 1 = − γ B 2 , S 2 = γ B 2 Cos h B + B η Sin h B ,

S 3 = A B 3 η S 2 3 Sin h B 32 Cos h B + B η Sin h B , S 4 = A B 2 S 2 3 − 12 B 2 η Cos h B + 3 Cos h 3 B + B − 12 + 13 η Sin h B 32 Cos h B + B η Sin h B ,

S 5 = − 3 32 A B 2 S 2 3 , S 6 = 3 8 A B 3 S 2 3 .

Q 1 = 1 2 − 1 4 ⁢ B 2 ⁢ S 2 2 ⁢ ω − 1 2 ⁢ B 2 ⁢ ξ S 2 2 ⁢ ω + 1 8 ⁢ S 2 2 ω Cos ⁢ h ⁡ 2 B + 1 4 ⁢ B ξ S 2 2 ⁢ ω Sin ⁢ h ⁡ 2 B , Q 2 = 1 2 1 + ξ ,

Q 3 = − 1 8 S 2 2 ω ,

Q 4 = − A B 2 S 2 4 ω Cos h B 64 Cos h B + B η Sin h B − 3 A B 4 η S 2 4 ω Cos h B 32 Cos h B + B η Sin h B + 3 A B 6 η S 2 4 ω Cos h B 16 Cos h B + B η Sin h B + 3 A B 4 η S 2 4 ω Cos h B 16 Cos h B + B η Sin h B − 3 A B 4 η η 2 S 2 4 ω Cos h B 32 Cos h B + B η Sin h B + 3 A B 6 η η 2 S 2 4 ω Cos h B 8 Cos h B + B η Sin h B − 33 A B 2 S 2 4 ω Cos h 3 B 1024 Cos h B + B η Sin h B − 3 A B 4 S 2 4 ω Cos h 3 B 64 Cos h B + B η Sin h B − 3 A B 4 η 2 S 2 4 ω Cos h 3 B 32 Cos h B + B η Sin h B + 27 A B 4 η 1 η 2 S 2 4 ω Cos h 3 B 256 Cos h B + B η Sin h B + 7 A B 2 S 2 4 ω Cos h 5 B 1024 Cos h B + B η Sin h B − 3 A B 4 η 1 η 2 S 2 4 ω Cos h 5 B 256 Cos h B + B η Sin h B + 3 A B 5 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B − A B 3 η 1 S 2 4 ω Sin h B 64 Cos h B + B η Sin h B − 3 A B 5 η 1 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B − A B 3 η 2 S 2 4 ω Sin h B 32 Cos h B + B η Sin h B + 3 A B 5 η 2 S 2 4 ω Sin h B 8 Cos h B + B η Sin h B − 9 A B 5 η 1 η 2 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B − A B 3 η 1 S 2 4 ω Sin h 5 B 1024 Cos h B + B η Sin h B + A B 3 η 2 S 2 4 ω Sin h 5 B 256 Cos h B + B η Sin h B ,

Q 5 = − 3 A B 6 η S 2 4 ω Cos h B 16 Cos h B + B η Sin h B + 3 A B 4 S 2 4 ω Cos h 3 B 64 Cos h B + B η Sin h B − 3 A B 5 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B + 3 A B 5 η 1 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B + A B 5 η 1 S 2 4 ω Sin h 3 B 64 Cos h B + B η Sin h B ,

Q 6 = 3 A B 3 S 2 4 ω Sin h B 16 Cos h B + B η Sin h B , Q 7 = 7 A B 2 S 2 4 ω Cos h B 128 Cos h B + B η Sin h B , Q 8 = 5 A B 2 S 2 4 ω Cos h B 512 Cos h B + B η Sin h B ,

Q 9 = − 3 A B 2 S 2 4 ω 256 Cos h B + B η 1 Sin h B , Q 10 = 3 A B 4 η 1 S 2 4 ω 64 Cos h B + B η 1 Sin h B , Q 11 = 3 A B 4 η S 2 4 ω 64 Cos h B + B η 1 Sin h B ,

Q 12 = − A B 3 η S 2 4 ω 256 Cos h B + B η Sin h B , Q 13 = − A B 3 η S 2 4 ω 256 Cos h B + B η Sin h B , Q 14 = 5 A B 3 η S 2 4 ω 1024 Cos h B + B η Sin h B ,

Q 15 = − 5 A B 3 η S 2 4 ω 256 Cos h B + B η Sin h B + 3 A B 3 S 2 4 η ω 64 Cos h B + B η Sin h B ,

Q 16 = − 5 A B 3 η S 2 4 ω 256 Cos h B + B η Sin h B − 3 A B 3 S 2 4 η ω 64 Cos h B + B η Sin h B , Q 17 = 5 A B 3 η S 2 4 ω 1024 Cos h B + B η Sin h B .

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Received: 2025-01-10
Accepted: 2025-04-10
Published Online: 2025-05-06
Published in Print: 2025-06-26

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
https://doi.org/10.1515/zna-2025-0015
Schlagwörter für diesen Artikel
magnetohydrodynamic flow; porous medium; convective heat transfer; perturbation series method; Carreau fluid model

Artikel in diesem Heft

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Controlling the convective heat transfer of shear thinning and shear thickening fluids in parallel plates with magnetic force
  4. Multistability, chaos and hyperchaos in a novel 3D discrete memristive system: microcontroller implementation and cryptography
  5. Comparative study of thermally intense cilia and non-cilia generated motion of Ellis’s fluid by using MATHEMATICA 14.1
  6. Fundamental Concepts of Physical Science
  7. Nonlinear electrodynamics and its possible connection to relativistic superconductivity: instance of a time-dependent system
  8. Galilean decoherence and quantum measurement
  9. Solid State Physics & Materials Science
  10. A dynamically tunable polarization-insensitive broadband vanadium dioxide-assisted absorber for terahertz applications
  11. Thermodynamics & Statistical Physics
  12. Heat transfer analysis for the Cattaneo–Cristov heat flux model using integral transform technique with isothermal and isoflux wall conditions
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