Startseite Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
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Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study

  • Muhammad Waris Saeed Khan EMAIL logo , Nasir Ali und Zeeshan Asghar
Veröffentlicht/Copyright: 21. Mai 2021
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 76 Heft 7

Abstract

The thermal entrance problem (also known as the classical Graetz problem) is studied for the complex rheological Carreau fluid model. The solution of two-dimensional energy equation in the form of an infinite series is obtained by employing the separation of variables method. The ensuing eigenvalue problem (S–L problem) is solved for eigenvalues and corresponding eigenfunctions through MATLAB routine bvp5c. Numerical integration via Simpson’s rule is carried out to compute the coefficient of series solution. Current problem is also tackled by an alternative approach where numerical solution of eigenvalue problem is evaluated via the Runge–Kutta fourth order method. This problem is solved for both flat and circular confinements with two types of boundary conditions: (i) constant wall temperature and (ii) prescribed wall heat flux. The obtained results of both local and mean Nusselt numbers, fully developed temperature profile and average temperature are discussed for different values of Weissenberg number and power-law index through graphs and tables. This study is valid for typical range of Weissenberg number We≤1 and power-law index n<1 for shear-thinning trend while n>1 for shear-thickening behaviour. The scope of the present study is broad in the context that the solution of the said problem is achieved by using two different approaches namely, the traditional Graetz approach and the solution procedure documented in M. D. Mikhailov and M. N. Ozisik, Unified Analysis and Solutions of Heat and Mass Diffusion, New York, Dover, 1994.

Keywords: bvp5c; Carreau fluid; Graetz problem; Runge–Kutta method; Simpson’s rule; Sturm–Liouville boundary value problem
Corresponding author: Muhammad Waris Saeed Khan, Department of Mathematics and Statistics, International Islamic University, Islamabad44000, Pakistan, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

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Received: 2021-02-17
Revised: 2021-04-17
Accepted: 2021-04-21
Published Online: 2021-05-21
Published in Print: 2021-07-27

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Simultaneous effects of Brownian motion and thermophoretic force on Eyring–Powell fluid through porous geometry
  4. Gravitation & Cosmology
  5. A cyclic non-singular universe from Gauss–Bonnet and superstring corrections
  6. Hydrodynamics
  7. Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
  8. Solid State Physics & Materials Science
  9. Enhancement of thermal conductivity and ultrasonic properties by incorporating CdS nanoparticles to PVA nanofluids
  10. Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic
  11. Thermodynamics & Statistical Physics
  12. Analytical treatment of the critical properties of a generalized van der Waals equation
  13. Thermodynamic equilibrium of a fluid column under the influence of gravity
https://doi.org/10.1515/zna-2021-0042
Schlagwörter für diesen Artikel
bvp5c; Carreau fluid; Graetz problem; Runge–Kutta method; Simpson’s rule; Sturm–Liouville boundary value problem

Artikel in diesem Heft

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Simultaneous effects of Brownian motion and thermophoretic force on Eyring–Powell fluid through porous geometry
  4. Gravitation & Cosmology
  5. A cyclic non-singular universe from Gauss–Bonnet and superstring corrections
  6. Hydrodynamics
  7. Mathematical modelling of classical Graetz–Nusselt problem for axisymmetric tube and flat channel using the Carreau fluid model: a numerical benchmark study
  8. Solid State Physics & Materials Science
  9. Enhancement of thermal conductivity and ultrasonic properties by incorporating CdS nanoparticles to PVA nanofluids
  10. Pressure and size dependent investigation of ultrasonic and thermal properties of ScRu intermetallic
  11. Thermodynamics & Statistical Physics
  12. Analytical treatment of the critical properties of a generalized van der Waals equation
  13. Thermodynamic equilibrium of a fluid column under the influence of gravity
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