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Nanofluid Flows Within Porous Enclosures Using Non-Linear Boussinesq Approximation

Sameh E. Ahmed1,2,*, Dalal Alrowaili3, Ehab Mahmoud Mohamed4,5, Abdelraheem M. Aly1,2
1 Department of Mathematics, College of Science, King Khalid University, Abha, 62529, Saudi Arabia
2 Department of Mathematics, South Valley University, Qena, 83523, Egypt
3 Mathematics Department, College of Science, Jouf University, Sakaka, Saudi Arabia
4 Electrical Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University, Wadi Addwasir, 11991, Saudi Arabia
5 Electrical Engineering Department, Aswan University, Aswan, 81542, Egypt
* Corresponding Author: Sameh E. Ahmed. Email:

Computers, Materials & Continua 2021, 66(3), 3195-3213.

Received 01 July 2020; Accepted 20 October 2020; Issue published 28 December 2020


In this paper, the Galerkin finite element method (FEM) together with the characteristic-based split (CBS) scheme are applied to study the case of the non-linear Boussinesq approximation within sinusoidal heating inclined enclosures filled with a non-Darcy porous media and nanofluids. The enclosure has an inclination angle and its side-walls have varying sinusoidal temperature distributions. The working fluid is a nanofluid that is consisting of water as a based nanofluid and Al2O3 as nanoparticles. The porous medium is modeled using the Brinkman Forchheimer extended Darcy model. The obtained results are analyzed over wide ranges of the non-linear Boussinesq parameter 0 ≤ ζ ≤ 1, the phase deviation 0° ≤ Φ ≤ 180°, the inclination angle 0° ≤ γ ≤ 90°, the nanoparticles volume fraction 0% ≤ φ ≤ 4%, the amplitude ratio 0 ≤ a ≤1 and the Rayleigh number 104 ≤ Ra ≤ 106. The results revealed that the average Nusselt number is enhanced by 0.73%, 26.46% and 35.42% at , 105 and 106, respectively, when the non-linear Boussinesq parameter is varied from 0 to 1. In addition, rate of heat transfer in the case of a non-uniformly heating is higher than that of a uniformly heating. Non-linear Boussinesq parameter rises the flow speed and heat transfer in an enclosure. Phase deviation makes clear changes on the isotherms and heat transfer rate on the right wall of an enclosure. An inclination angle varies the flow speed and it has a slight effect on heat transfer in an enclosure.


CBS scheme; non-linear Boussinesq approximation; non-uniformly heating; non-darcy flow; nanofluid

Cite This Article

S. E. Ahmed, D. Alrowaili, E. Mahmoud Mohamed and A. M. Aly, "Nanofluid flows within porous enclosures using non-linear boussinesq approximation," Computers, Materials & Continua, vol. 66, no.3, pp. 3195–3213, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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