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Numerical analysis of flow and forced convection heat transfer of non-Newtonian fluid in a pipe based on fractional constitutive model

Ailian Chang (State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing, China)
HongGuang Sun (Hohai University, Nanjing, China)
K. Vafai (Department of Mechanical Engineering, University of California Riverside, Riverside, California, USA)
Erfan Kosari (Department of Mechanical Engineering, University of California Riverside, Riverside, California, USA)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 11 January 2021

Issue publication date: 10 August 2021

269

Abstract

Purpose

This paper aims to use a fractional constitutive model with a nonlocal velocity gradient for replacing the nonlinear constitutive model to characterize its complex rheological behavior, where non-linear characteristics exist, for example, the inherent viscous behavior of the crude oil. The feasibility and flexibility of the fractional model are tested via a case study of non-Newtonian fluid. The finite element method is non-Newtonian used to numerically solve both momentum equation and energy equation to describe the fluid flow and convection heat transfer process.

Design/methodology/approach

This paper provides a comprehensive theoretical and numerical study of flow and heat transfer of non-Newtonian fluids in a pipe based on the fractional constitutive model. Contrary to fractional order a, the rheological property of non-Newtonian fluid changes from shear-thinning to shear-thickening with the increase of power-law index n, therefore the flow and heat transfer are hindered to some extent.

Findings

This paper discusses two dimensionless parameters on flow regime and thermal patterns, including Reynolds number (Re) and Nusselt number (Nu) in evaluating the flow rate and heat transfer rate. Analysis results show that the viscosity of the non-Newtonian fluid decreases with the rheological index (order α) increasing. While large fractional (order α) corresponds to the enhancement of heat transfer capacity.

Research limitations/implications

First, it is observed that the increase of the Re results in an increase of the local Nusselt number (Nul). It means the heat transfer enhancement ratio increases with Re. Meanwhile, the increasement of the Nul indicating the enhancement in the heat transfer coefficient, produces a higher speed flow of crude oil.

Originality/value

This study presents a new numerical investigation on characteristics of steady-state pipe flow and forced convection heat transfer by using a fractional constitutive model. The influences of various non-dimensional characteristic parameters of fluid on the velocity and temperature fields are analyzed in detail.

Keywords

Acknowledgements

The work was partially funded by the Fundamental Research Funds for the Central Universities, China under Grants Nos. 2018B680X14, 2019B16014 and B210202092, the National Natural Science Foundation of China under Grant Nos. 11972148, the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX18_0524) and the China Scholarship Council (CSC 201806710044).

Conflict of interest: There is no conflict of interest. This manuscript has not been submitted to anywhere else.

Citation

Chang, A., Sun, H., Vafai, K. and Kosari, E. (2021), "Numerical analysis of flow and forced convection heat transfer of non-Newtonian fluid in a pipe based on fractional constitutive model", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 31 No. 8, pp. 2680-2697. https://doi.org/10.1108/HFF-10-2020-0637

Publisher

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Emerald Publishing Limited

Copyright © 2020, Emerald Publishing Limited

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