THERMAL SCIENCE

International Scientific Journal

SIMULATION ON NATURAL CONVECTION OF CARREAU FLUIDS IN A LOCALLY HEATED TRAPEZOIDAL CAVITY

ABSTRACT
The laminar natural convection of non-Newtonian Carreau fluids in a trapezoidal cavity with a local heat source at the bottom is numerically investigated. A stabilized streamline-upwind/Petrov-Galerkin (SUPG) finite element algorithm is proposed, in which equal low-order finite elements are used. Effects of Rayleigh number (i.e., Ra = 104 and 105), power-law index (i.e., 0.6 ≤ n ≤ 1.4), Prandtl number (i.e., 0.1 ≤ Pr ≤ 100), and local heat source length (i.e., 0.1 ≤ η ≤ 1.0) are researched. Results show that for different power-law indexes, as Prandtl numbers increase, the convective heat transfer is enhanced; as power-law indexes increase, influences of Prandtl numbers decrease, as local heat source length increase, the convective heat transfer is enhanced.
KEYWORDS
PAPER SUBMITTED: 2025-06-01
PAPER REVISED: 2025-07-27
PAPER ACCEPTED: 2025-08-08
PUBLISHED ONLINE: 2025-09-13
DOI REFERENCE: https://doi.org/10.2298/TSCI250601160L
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2026, VOLUME 30, ISSUE No. 2, PAGES [1439 - 1451]
REFERENCES
[1] Das, D., et al., Studies on Natural Convection within Enclosures of Various (Non-Square) Shapes - A Review, International Journal of Heat and Mass Transfer, 106 (2017), Mar., pp. 356-406
[2] Xia, Y. W., et al., Direct Numerical Simulation of Double Diffusive Natural Convection in a Closed Mixture Cavity Heated from Below, Thermal Science, 27 (2023), 5B, pp. 4261-4275
[3] Mohebbi, R., et al., Heat Source Location and Natural Convection in a C-Shaped Enclosure Saturated by a Nanofluid, Physics of Fluids, 29 (2017), 12, 122009
[4] Nouri, R., et al., Non-Newtonian Natural-Convection in a Square Box Submitted to Horizontal Heat Flux and Magnetic Field, Thermal Science, 28 (2024), 4A, pp. 3049-3061
[5] Horimek, A., Non-Newtonian Natural-Convection Cooling of a Heat Source of Variable Length and Position Placed at the Bottom of a Square Cavity, Thermal Science, 27 (2023), 5B, pp. 4161-4178
[6] Bird, R. B., et al., Dynamics of Polymeric Liquids, Fluid Mechanics, John Wiley, New York, USA, 1987, Vol. 1
[7] Kefayati, G. R., et al., Three-Dimensional Lattice Boltzmann Simulation on Thermosolutal Convection and Entropy Generation of Carreau-Yasuda Fluids, International Journal of Heat and Mass Transfer, 131 (2019), Mar., pp. 346-364
[8] Turan, O., et al., Laminar Natural Convection of Power-Law Fluids in a Square Enclosure Submitted from below to a Uniform Heat Flux Density, Journal of Non-Newtonian Fluid Mechanics, 199 (2013), Sept., pp. 80-95
[9] Alloui, Z., et al., Natural Convection of Carreau-Yasuda Non-Newtonian Fluids in a Vertical Cavity Heated from the Sides, International Journal of Heat and Mass Transfer, 84 (2015), May, pp. 912-924
[10] Malkeson, S. P., et al., Numerical Investigation of Steady State Laminar Natural Convection of Power- Law Fluids in Side-Cooled Trapezoidal Enclosures Heated from the Bottom, Numerical Heat Transfer, Part A, Applications, 83 (2023), 7, pp. 770-789
[11] Li, S. G., et al., Numerical Simulation of Heat Transfer and Entropy Generation Due to the Nanofluid Natural Convection with Viscous Dissipation in an Inclined Square Cavity, Numerical Heat Transfer, Part A, Applications, 86 (2024), 14, pp. 4956-4986
[12] Makayssi, T., et al., Natural Double-Diffusive Convection for the Carreau Shear-Thinning Fluid in a Square Cavity Submitted to Horizontal Temperature and Concentration Gradients, Journal of Non- Newtonian Fluid Mechanics, 297 (2021), 104649
[13] Cengizci, S., et al., Natural Convection in Nanofluid-Filled Quadrantal Cavities under Magnetic Field: Application of the SUPS Formulation, Numerical Heat Transfer, Part B, Fundamentals, 86 (2024), 11, pp. 3953-3975
[14] Brooks, A. N., et al., Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows with Particular Emphasis on the Incompressible Navier-Stokes Equations, Computer Methods in Applied Mechanics and Engineering, 32 (1982), 1, pp. 199-259
[15] Kim, N., et al., The 3-D Least-Squares Finite Element Analysis of Flows of Generalized Newtonian Fluids, Journal of Non-Newtonian Fluid Mechanics, 266 (2019), Apr., pp. 143-159
[16] Li, S. G., et al., Least Squares Finite Element Simulation of Local Transfer for a Generalized Newtonian Fluid in 2-D Periodic Porous Media, Journal of Non-Newtonian Fluid Mechanics, 316 (2023), 105032
[17] Gonzalez, A., et al., Numerical Study of the Use of Residual- and Non-Residual-Based Stabilized VMS Formulations for Incompressible Power-Law Fluids, Computer Methods in Applied Mechanics and Engineering, 400 (2022), 115586
[18] Cengizci, S., et al., Stabilized Finite Element Simulation of Natural Convection in Square Cavities Filled with Nanofluids under Various Temperature Boundary Conditions, International Communications in Heat and Mass Transfer, 156 (2024), 107655
[19] Cengizci, S., A SUPS Formulation for Simulating Unsteady Natural/Mixed Heat Convection Phenomena in Square Cavities under Intense Magnetic Forces, The European Physical Journal Plus, 139 (2024), 8, 713
[20] Wang, D. G., et al., The SUPG Finite Element Method Based on Penalty Function for Liddriven Cavity Flow up to Re = 27500, Acta Mechanica Sinica, 32 (2016), Sept., pp. 54-63
[21] Li, S. G., et al., Mathematical Modeling for the Local Flow of a Generalized Newtonian Fluid in 3-D Porous Media, Applied Mathematical Modelling, 105 (2022), pp. 551-565
[22] Cengizci, S., et al., A Computational Study for Simulating MHD Duct Flows at High Hartmann Num- bers Using a Stabilized Finite Element Formulation with Shock-Capturing, Journal of Computational Science, 81 (2024), 102381
[23] Huang, C., et al., A Semi-Implicit Three-Step Method Based on SUPG Finite Element Formulation for Flow in Lid Driven Cavities with Different Geometries, Journal of Zhejiang University-Science A, 12 (2011), 1, pp. 33-45
[24] Yu, P. X., et al., Compact Computations Based on a Stream-Function-Velocity Formulation of Two-Dimensional Steady Laminar Natural Convection in a Square Cavity, Physical Review E, 85 (2012), 3, 036703
[25] Tian, Z. F., et al., A Fourth-Order Compact Finite Difference Scheme for the Steady Stream Functio Vorticity Formulation of the Navier-Stokes/Boussinesq Equations, International Journal for Numerical Methods in Fluids, 41 (2003), 5, pp. 495-518

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence