Table 3.

Variation of average Nusselt number (Nu_av) along heated wall for different nanoparticles volume (ϕ), diameter (d) and shape (n) of nanoparticles considering with/without Brownian with Ra = 10⁵, Ha = 15, and λ = 3.

Brownian effect (BM)	Nanoparticles volume (ϕ)	Nanoparticles shape (n)	Nanoparticles diameter (d)	Average Nusselt number (Nuav)	Increases (%)
with BM	0	3.0	10 nm	4.267974931830414	–
	0.01			5.140180145823340	20.43
	0.02			5.930500451043041	38.95
	0.05			7.971343224154655	86.77
	0.04	3.0	10 nm	7.254760603941890	–
		3.7		7.334404774458736	1.10
		4.9		7.470160718151543	2.97
		5.7		7.560131307489343	4.21
		8.6		7.882830676803941	8.66
	0.04	3.0	100 nm	5.398074838809371	–
			50 nm	5.779106109891497	7.06
			20 nm	6.519641772718621	20.78
			10 nm	7.334404744750127	35.87
			1 nm	13.02908943936327	141.37
Without BM	0	3.0	–	4.267974931830413	–
	0.01		–	4.309365483763966	0.97
	0.02		–	4.353923846604179	2.01
	0.05		–	4.503711767742641	5.52
	0.04	3.0	–	4.362500816778986	–
		3.7	–	4.451326343833879	2.03
		4.9	–	4.602177643914426	5.49
		5.7	–	4.701783415723639	7.78
		8.6	–	5.056793437004171	15.92