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=ASIA6AP2G7AKA74IGDKQ%2F20260123%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260123T222014Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDUaDGV1LWNlbnRyYWwtMSJGMEQCICsXG91CIZuNzLTmjqfyL0U4e%2BnwCgDh5q5ZDk7gsXx5AiAyo85gC6haHjUSsPYD46c9O61Z8uf1TruzGKAa32AXwyrGBQj%2B%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM6LlOi%2BBjaXP64YY%2FKpoFM%2BXPcViFvQgrcikIY4ugdWoNKslFVkI0sawgsJbLfO%2Fid9ApXd2oVCh6eDbK7oC6V5Avn2lD09cqqyngjKwbO6SqmvJRznDjmgHQiJs7Wx8f7GR8daSl75plXDr96wrS2ywOQYDiUE%2Fk9yzRPHc2p%2B8W%2B75ww9s%2BcVfHu7Ign1HHcykJ2w825Oyvg1%2Bcz1yLmi1N1caAcmWyls3vqf%2BYGXd9p45AdRLoKiohmfne3NUCqaF2PsreTdO5HQZTtkOnMyIYpNc1yhvPOKFuqIJJ5mN2PfFtrtml0%2BKErI4CxsF8EHSg43puFBayAXGTtCy0XLSuFU3dZEQUJengF8Ujqsv%2BD3Ck3AHZIGSK9OamTcrAa%2B%2FPya3Qbtjvvu0Dvv9R%2F%2BNnyXTHSNXNy2x%2BlDM7wo6jtAQYpLJG3U1UdDc3tmmvLZTppMdOvFReOx7L96gqRCYPgDmhQ5KqOSL1IPSO8125bcKgQTV20vMJ36PKb1%2BL%2F9Gr4lTuLvidbUA55%2FmYM9vlOphlEUVGLFguSD7ddcS2%2BCwkok16pv3CQy8wBJEqPaH3iayC0L9nEe4QoDZ46dQRyhisoa%2BVQDqhfiAk%2FwTmq825%2FmMiPpSpRSqRyPX0erdAgQPzjvm1WucRj2oT7EdUSDxCMs40zfEDn5CclPspyutGC8qdMoAdgh%2BXwi3I8t0xEQ1epP5oTiuSxt6iQ5u5L%2FlOZm24OQLdP6TZEvMZwoBci0o4xFOpWKyKQt77e6yFFoNLtaTjUqPMdbC%2BhdtaNrUz1hTyuPaq1P0iAwJ3ppWahlZRT05XHd1sgIwisiyHOdKor68LPtKM%2BLJqF1fj5z3KBKsU2XGIgS9gOiHGi4P1ZyQz%2F%2FOMKh4%2FOz9le%2F9GqdbEM8c3MP68z8sGOrIBBiuNW5Vc%2Fb4Qm75dm%2Fxraywb9TzN1hXANUXmLZ%2FpAT5qD0jwzJZQbNBeNNIFz14kUpHtmafKImSNNXHdcguCf7evK4wUn7ye6Vv4v2HhKMkjmPTl3tjtmNNCnPwBPCPo4gw1opXVhIT4C5knGfNIul7gj%2BZCbHtfl4opCgBVZ92gK%2F2cpy8FwSMQUi4mHz7SKjfUspQcs9pCVAmnxZj%2FKezyaakHDZ0yXkx3bjjlLmYGbg%3D%3D&X-Amz-Signature=f421536065962e3ed9c887e57f1737854e83cb8e14b4ed22b3183b9d64c19c0f&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=ASIA6AP2G7AKA74IGDKQ%2F20260123%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260123T222014Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDUaDGV1LWNlbnRyYWwtMSJGMEQCICsXG91CIZuNzLTmjqfyL0U4e%2BnwCgDh5q5ZDk7gsXx5AiAyo85gC6haHjUSsPYD46c9O61Z8uf1TruzGKAa32AXwyrGBQj%2B%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM6LlOi%2BBjaXP64YY%2FKpoFM%2BXPcViFvQgrcikIY4ugdWoNKslFVkI0sawgsJbLfO%2Fid9ApXd2oVCh6eDbK7oC6V5Avn2lD09cqqyngjKwbO6SqmvJRznDjmgHQiJs7Wx8f7GR8daSl75plXDr96wrS2ywOQYDiUE%2Fk9yzRPHc2p%2B8W%2B75ww9s%2BcVfHu7Ign1HHcykJ2w825Oyvg1%2Bcz1yLmi1N1caAcmWyls3vqf%2BYGXd9p45AdRLoKiohmfne3NUCqaF2PsreTdO5HQZTtkOnMyIYpNc1yhvPOKFuqIJJ5mN2PfFtrtml0%2BKErI4CxsF8EHSg43puFBayAXGTtCy0XLSuFU3dZEQUJengF8Ujqsv%2BD3Ck3AHZIGSK9OamTcrAa%2B%2FPya3Qbtjvvu0Dvv9R%2F%2BNnyXTHSNXNy2x%2BlDM7wo6jtAQYpLJG3U1UdDc3tmmvLZTppMdOvFReOx7L96gqRCYPgDmhQ5KqOSL1IPSO8125bcKgQTV20vMJ36PKb1%2BL%2F9Gr4lTuLvidbUA55%2FmYM9vlOphlEUVGLFguSD7ddcS2%2BCwkok16pv3CQy8wBJEqPaH3iayC0L9nEe4QoDZ46dQRyhisoa%2BVQDqhfiAk%2FwTmq825%2FmMiPpSpRSqRyPX0erdAgQPzjvm1WucRj2oT7EdUSDxCMs40zfEDn5CclPspyutGC8qdMoAdgh%2BXwi3I8t0xEQ1epP5oTiuSxt6iQ5u5L%2FlOZm24OQLdP6TZEvMZwoBci0o4xFOpWKyKQt77e6yFFoNLtaTjUqPMdbC%2BhdtaNrUz1hTyuPaq1P0iAwJ3ppWahlZRT05XHd1sgIwisiyHOdKor68LPtKM%2BLJqF1fj5z3KBKsU2XGIgS9gOiHGi4P1ZyQz%2F%2FOMKh4%2FOz9le%2F9GqdbEM8c3MP68z8sGOrIBBiuNW5Vc%2Fb4Qm75dm%2Fxraywb9TzN1hXANUXmLZ%2FpAT5qD0jwzJZQbNBeNNIFz14kUpHtmafKImSNNXHdcguCf7evK4wUn7ye6Vv4v2HhKMkjmPTl3tjtmNNCnPwBPCPo4gw1opXVhIT4C5knGfNIul7gj%2BZCbHtfl4opCgBVZ92gK%2F2cpy8FwSMQUi4mHz7SKjfUspQcs9pCVAmnxZj%2FKezyaakHDZ0yXkx3bjjlLmYGbg%3D%3D&X-Amz-Signature=7a4a9d52a42cb374a762c130e229c686e380856ccac25aa2b77adf38ae83725a&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=ASIA6AP2G7AKA74IGDKQ%2F20260123%2Feu-central-1%2Fs3%2Faws4_request&X-Amz-Date=20260123T222014Z&X-Amz-Expires=3600&X-Amz-Security-Token=IQoJb3JpZ2luX2VjEDUaDGV1LWNlbnRyYWwtMSJGMEQCICsXG91CIZuNzLTmjqfyL0U4e%2BnwCgDh5q5ZDk7gsXx5AiAyo85gC6haHjUSsPYD46c9O61Z8uf1TruzGKAa32AXwyrGBQj%2B%2F%2F%2F%2F%2F%2F%2F%2F%2F%2F8BEAIaDDk2MzEzNDI4OTk0MCIM6LlOi%2BBjaXP64YY%2FKpoFM%2BXPcViFvQgrcikIY4ugdWoNKslFVkI0sawgsJbLfO%2Fid9ApXd2oVCh6eDbK7oC6V5Avn2lD09cqqyngjKwbO6SqmvJRznDjmgHQiJs7Wx8f7GR8daSl75plXDr96wrS2ywOQYDiUE%2Fk9yzRPHc2p%2B8W%2B75ww9s%2BcVfHu7Ign1HHcykJ2w825Oyvg1%2Bcz1yLmi1N1caAcmWyls3vqf%2BYGXd9p45AdRLoKiohmfne3NUCqaF2PsreTdO5HQZTtkOnMyIYpNc1yhvPOKFuqIJJ5mN2PfFtrtml0%2BKErI4CxsF8EHSg43puFBayAXGTtCy0XLSuFU3dZEQUJengF8Ujqsv%2BD3Ck3AHZIGSK9OamTcrAa%2B%2FPya3Qbtjvvu0Dvv9R%2F%2BNnyXTHSNXNy2x%2BlDM7wo6jtAQYpLJG3U1UdDc3tmmvLZTppMdOvFReOx7L96gqRCYPgDmhQ5KqOSL1IPSO8125bcKgQTV20vMJ36PKb1%2BL%2F9Gr4lTuLvidbUA55%2FmYM9vlOphlEUVGLFguSD7ddcS2%2BCwkok16pv3CQy8wBJEqPaH3iayC0L9nEe4QoDZ46dQRyhisoa%2BVQDqhfiAk%2FwTmq825%2FmMiPpSpRSqRyPX0erdAgQPzjvm1WucRj2oT7EdUSDxCMs40zfEDn5CclPspyutGC8qdMoAdgh%2BXwi3I8t0xEQ1epP5oTiuSxt6iQ5u5L%2FlOZm24OQLdP6TZEvMZwoBci0o4xFOpWKyKQt77e6yFFoNLtaTjUqPMdbC%2BhdtaNrUz1hTyuPaq1P0iAwJ3ppWahlZRT05XHd1sgIwisiyHOdKor68LPtKM%2BLJqF1fj5z3KBKsU2XGIgS9gOiHGi4P1ZyQz%2F%2FOMKh4%2FOz9le%2F9GqdbEM8c3MP68z8sGOrIBBiuNW5Vc%2Fb4Qm75dm%2Fxraywb9TzN1hXANUXmLZ%2FpAT5qD0jwzJZQbNBeNNIFz14kUpHtmafKImSNNXHdcguCf7evK4wUn7ye6Vv4v2HhKMkjmPTl3tjtmNNCnPwBPCPo4gw1opXVhIT4C5knGfNIul7gj%2BZCbHtfl4opCgBVZ92gK%2F2cpy8FwSMQUi4mHz7SKjfUspQcs9pCVAmnxZj%2FKezyaakHDZ0yXkx3bjjlLmYGbg%3D%3D&X-Amz-Signature=4ccee2ea8f60300962af49a5bc24d926480ca9c846dc454962820d3b12845445&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%) |