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

Autor:	Muhammad Waris Saeed Khan, Nasir Ali, Zeeshan Asghar
Rok vydání:	2021
Předmět:	Materials science Carreau fluid Rotational symmetry General Physics and Astronomy 02 engineering and technology Mechanics 021001 nanoscience & nanotechnology 01 natural sciences Simpson's rule Nusselt number 010305 fluids & plasmas Runge–Kutta methods 0103 physical sciences Benchmark (computing) Tube (fluid conveyance) Physical and Theoretical Chemistry 0210 nano-technology Mathematical Physics Communication channel
Zdroj:	Zeitschrift für Naturforschung A. 76:589-603
ISSN:	1865-7109 0932-0784
DOI:	10.1515/zna-2021-0042
Popis:	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 W e ≤ 1 $\left(We\le 1\right)$ and power-law index n < 1 $\left(n{< }1\right)$ for shear-thinning trend while n > 1 $\left(n{ >}1\right)$ 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.
Databáze:	OpenAIRE
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