MHD natural convection in a wavy nanofluid enclosure with an internally corrugated porous cylinder

Figures & data

Figure 1. Physical domain for different thermal source locations of the corrugated cylinder.

Table 1. Thermophysical properties of Nanoparticle and basic fluid at T = 25⁰ C [32].

Properties	${\displaystyle \frac{\rho }{\text{kg}{\text{m}}^{-3}}}$	${\displaystyle \frac{C_{\mathrm{p}}}{\text{Jk}{\text{g}}^{-1}{\text{K}}^{-1}}}$	${\displaystyle \frac{K}{\text{W}.{\text{m}}^{-1}{\text{K}}^{-1}}}$	${\displaystyle \frac{\text{β}}{{\text{K}}^{-1}}}$
Water	997	4180	0.614	$2.1\ast {10}^{-4}$
$\text{A}{\text{l}}_2{\text{O}}_3$	3970	765	40	${0.85}^{\ast }{10}^{-5}$

Table 2. Coefficients included in non-dimensional G.E.

Coefficients	Nanofluid Domain	Nano – Pours Domain
C1	1	ε^2
C2	1	ε
C3	0	ε^2
C4	${\alpha }_{\mathrm{na}}/{\alpha }_f$	${\alpha }_{\mathrm{eff}}/{\alpha }_f$

Figure 2. Mesh generation of proposed geometry.

Table 3. Sensitivity of Grid generation on the dimensionless value of Nusselt number.

Grid size	Number of elements	Nu	Percentage error $=\left|{\displaystyle \frac{N{U}_{\mathrm{new}}-N{U}_{\mathrm{old}}}{\mathrm{NU}\mathrm{\_new}}}\right|$	CPU time (sec)
Extremely coarse	4082	6.8986	-	36
Extra coarse	4484	6.9059	0.0150	48
Coarser	7514	7.0314	0.0179	58
Coarse	11436	7.1201	0.0125	96
Normal	17544	7.0934	0.0038	146
Fine	30824	7.1328	0.0055	182
Finer	45540	7.1595	0.00373	300
Extra fine	75880	7.2577	0.0135	578
Extremely fine	90144	7.2564	0.00018	621

Table 4. Validation of Nu_avg at φ = 0.04, Ha = 80 of the current study with Malekpour et al.[37].

Ra	Precent study	Malekpour et al.[37]	Percentage change%
10^4	6.2	6.35	2.2
10^5	6.34	6.59	3.7
10^6	18	18.2	1.09

Figure 3. Validation with significant researchers in terms Nu and Ra.

Figure 4. Validation in terms of streamlines of CFD results for present work and Hussain and Rahomey [38].

Figure 5. (a) validation the dynamic viscosity ratio with experimental of Ho et al. [39] (b) validation of thermal conductivity ratio with Chon et al. [40].

Figure 6. Iso thermal contour at different Ra number (Ha = 60 and Da = 10⁻³).

Figure 7. Stream functions for different Ra number (at Ha = 60 and Da = 10⁻³).

Figure 8. Isothermal counter for different Ha number (at Ra = 10⁶, and Da = 10⁻³).

Figure 9. Stream function counter for different Ha numbers (at Ra = 10⁶, and Da = 10⁻³).

Figure 10. The isothermal counter varies the magnetic source’s inclination angle (Ha = 60, Ra = 10⁶, Da = 10^−3, and δ = 0.3).

Figure 11. The stream function counter varies the magnetic source’s inclination angle (Ha = 60, Ra = 10⁶, Da = 10⁻³ and δ = 0.3).

Figure 12. Isothermal counter for different Da numbers (at Ra = 10⁶ and Ha = 60).

Figure 13. Stream function counter for different Da numbers (at Ra = 10⁶ and Ha = 60).

Figure 14. The isothermal counter varies at different positions (Ha = 60, Ra = 10⁶, Da = 10⁻³).

Figure 15. Stream function varies at different positions (Ha = 60, Ra = 10⁶, Da = 10⁻³).

Figure 16. Values of Nu interfaces with ϕ for different locations of the hot cylinder at Ha = 60, Ra = 10⁶, and γ  = 90⁰.

Figure 17. Nu interfaces with γ, on the first cylinder at δ = 0.3, at different volume fractions Ra = 10⁶ and Ha = 60, Da = 10⁻³.

Figure 18. Nu interfaces with Ha on the first cylinder at δ = 0.3, at a different angle of inclination, Ra = 10⁶ and ϕ =  0.02, Da = 10⁻³.

Figure 19. Nu interfaces with volume fraction on the first cylinder at δ = 0.3, at different Ra, Ha = 60 and Da = 10⁻³,γ=p/2.

Figure 20. Nu interfaces Ra on the first cylinder at δ = 0.3, at different Da, Ha = 20 and, γ = 0.

Figure 21. Nu varies with the number of undulations of the hot corrugated cylinder at δ = 0.3 (Ra = 10⁶, Ha = 30, Da = 10⁻³, ϕ=0.06, γ = 0⁰).

Figure 22. Contour shows the max stream function for different numbers of undulations.

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