Influence of oriented magnetic field on natural convection in an equilateral triangular enclosure filled with water- and kerosene-based ferrofluids using a two-component nonhomogeneous thermal equilibrium model

Figures & data

Figure 1. Physical model of the problem with boundary conditions.

Table 1. Thermophysical properties of base fluids and solid nanoparticles

Physical properties	Water $\left({\text{H}}_2\text{O}\right)$	Kerosene	${\text{Fe}}_3{\text{O}}_4$	Cobalt
${\text{c}}_{\text{p}}\left[\text{J/kgK}\right]$	4,179	2,090	670	420
$\mathit{\rho }\left[{\text{kg/m}}^3\right]$	997.1	780	5,180	8,900
$\text{k}\left[\text{W/mK}\right]$	0.613	0.149	80	100
$\mathit{\mu }\left[{\text{Ns/m}}^2\right]$	0.001003	0.00164	–	–
$\mathit{\beta }\left[1/\text{K}\right]$	21 × 10^−5	99 × 10^−5	20.6 × 10^−5	1.3 × 10^−5
$\mathit{\sigma }\left[\text{W/mK}\right]$	5.5 × 10^−6	6 × 10^−10	0.112 × 10^6	16.02 × 10^6
Pr	6.8377	23.004	–	–

Figure 2. Mesh structure of the physical domain with triangular finite elements.

Table 2. Grid sensitivity check for ${\text{Fe}}_3{\text{O}}_4$-water ferrofluid at Pr = 6.8377, Ra = 10⁵, Ha = 20, Nr = 0.1, γ = 15⁰and d_p = 10 nm

Nodes	368	579	877	3,834	14,998
Elements	661	1,063	1,636	7,417	29,510
Nuav	0.93329	0.94424	0.95234	0.96945	0.96947

Figure 3. (a–c) Streamlines, isotherms and isoconcentrations for different values of Ra.

Figure 4. (a–c) Streamlines, isotherms and isoconcentrations for different values of Ha.

Figure 5. (a–c) Streamlines, isotherms and isoconcentrations for different values of γ.

Table 3. Variation of the average Nusselt number (Nu_av) for ${\text{Fe}}_3{\text{O}}_4$-water and cobalt-kerosene ferrofluids with different values of Hartmann number (Ha) and magnetic field inclination angle (γ)

Ha	γ	${\text{Fe}}_3{\text{O}}_4$-water	Cobalt-kerosene
		Nuav	Nuav
1	0	0.96448	1.45328
	30^°	0.96457	1.46345
	45^°	0.96469	1.47432
	60^°	0.96478	1.48763
	90^°	0.97546	1.49342
50	0	0.94342	1.32456
	30^°	0.94359	1.33365
	45^°	0.94368	1.34564
	60^°	0.94379	1.35432
	90^°	0.95354	1.36574
100	0	0.92426	1.24325
	30^°	0.92435	1.25675
	45^°	0.92443	1.26453
	60^°	0.92457	1.27345
	90^°	0.93452	1.28654