Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.
![Comparison of the local Nusselt number along the hot wall between the present results and numerical results by Lai and Yang [34]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0029_fig_004.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251206%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251206T145039Z&X-Amz-Expires=3600&X-Amz-Signature=6d47e74335c5763a8cb2d9904995c096e829aa77843eb8168471108a35c17821&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 5.
![Comparison of the temperature on axial midline between the present results and numerical results by Ghassemi et al. [35] (ϕ =3.10-2, Ra=105)](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0029_fig_005.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251206%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251206T145039Z&X-Amz-Expires=3600&X-Amz-Signature=985e7833173f76bffc221b4df383d4cd6692b810e4b94ffc38b0b31a087decc8&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig. 6.
![a) Horizontal component of velocity b) vertical component of velocity with those of Talebi et al. [36]](https://sciendo-parsed.s3.eu-central-1.amazonaws.com/68432e85f788d76dad45bfe1/j_ama-2025-0029_fig_006.jpg?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Content-Sha256=UNSIGNED-PAYLOAD&X-Amz-Credential=AKIA6AP2G7AKOUXAVR44%2F20251206%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20251206T145039Z&X-Amz-Expires=3600&X-Amz-Signature=3df12f8f6788092bba125731fa5f997b76f0109a09c04093fe12433cfbb0c599&X-Amz-SignedHeaders=host&x-amz-checksum-mode=ENABLED&x-id=GetObject)
Fig.7.

Fig.8.

Fig.9.

Fig.10.

Fig.11.

Fig. 12.

Fig. 13.

Fig.14.

Fig. 15.

Thermophysical properties of fluid and nanoparticles
| Physical Properties | Fluid phase (H2O) | Nanoparticle (CuO) |
|---|---|---|
| Cp(J/kg.K) | 4179 | 385 |
| ρ (kg/m3) | 997.1 | 8933 |
| k (W/m.K) | 0.631 | 401 |
| β×10-5 (1/K) | 21 | 1.67 |
| σ (Ω/m)-1 | 0.05 | 5.69 10-7 |
Grid independence test for Nu¯m at ϕ=4_10-2; Ha = 0
| Average Nusselt number | ||
|---|---|---|
| Lattice size | Re=1 | Re=100 |
| 50×50 | 1.7632 | 7.3423 |
| 75×75 | 2.1482 | 8.8753 |
| 100×100 | 2.5483 | 9.6128 |
| 120×120 | 2.5502 (0.07%) | 9.6412 (0.2%) |