3D internal forced convection heat-transfer correlations from CFD for building performance simulation

Figures & data

Figure 1. The geometric parameters of: (a) the 3D enclosure with inlet and outlet openings; (b) the vertical 2D plane; (c) the horizontal 2D plane.

Figure 2. The geometric parameters of: (a) the vertical 2D plane; (b) the horizontal 2D plane.

Table 1. Boundary conditions of the vertical 2D, horizontal 2D, and 3D simulations.

Variable	3D	Vertical 2D	Horizontal 2D
Vin (m/s)	0.5–1.0–1.5	0.5–1.0–1.5	0.5–1.0–1.5
Tin (°C)	20	20	20
Twall (°C)	30	30	30
H (m)	3	3	–
L (m)	5	5/cosαv	5/cosαh
A (m)	3	–	3
Win (m), Wout (m)	0.42	0.42	–
Xin (m), Xout (m)	0.70	–	0.70
Hin (m), Hout (m)	2.59–1.40–0.21	2.59–1.40–0.21	–
Ain (m), Aout (m)	2.59–1.40–0.21	–	2.59–1.40–0.21

Figure 3. Symmetric and asymmetric configurations for the 3D model.

Figure 4. General geometric parameters for the 2D models.

Figure 5. 2D configurations for different inlet and outlet opening positions.

Figure 6. Uniform-growth mesh for: (a) a 2D model; (b) a 3D model.

Figure 7. Grid sensitivity analysis for the 3D geometry case (where H = L = A = 3.00 m, W_in = W_out = X_in = X_out = 0.42 m, H_in = 2.78 m, A_in = 0.22 m, H_out = 1.50 m, A_out = 1.50 m, Re_in = 119,293, T_walls = 30°C, T_in = 10°C).

Table 2. 3D correlation coefficients according to the 2D planes.

Wall	ai	bi	ni	R^2
1	.4352	.4352	1	.985
2	–	.9124	1	.995
3	.5123	.5123	3	.987
4	–	.8112	1	.986
5	.4491	–	1	.979
6	.5512	–	1	.989

Figure 8. Comparison of the correlated and simulated 3D Nu values for: (a) Walls 1 and 3; (b) Walls 2 and 4; (c) Walls 5 and 6.

Table 3. Application range of the variables in the 2D models (dimensionless).

Variable	Minimum	Average	Maximum
Win/H	0.017	0.067	0.400
Wout/H	0.017	0.067	0.400
Hin/H	0.025–0.083–0.217	0.500	0.975–0.917–0.783
Hout/H	0.025–0.083–0.217	0.500	0.975–0.917–0.783
L/H	0.5	1.0	2.0
Rein (Win, Vin)	1657–3314– 4971	6627–13,255– 19,882	39,764–79,529– 119,293

Figure 9. Comparison of the Nusselt numbers obtained by correlation and CFD simulation for: (a) Wall 1; (b) Wall 2; (c) Wall 3; (d) Wall 4.

Table 4. Correlation coefficients for the 2D models.

Coefficient	Wall 1	Wall 2	Wall 3	Wall 4
a	.019512	.041169	.066311	.009220
b	−.006984	−.016679	−.027515	−.004926
c	−.005944	−.033410	.005247	−.002107
d	.003044	−.024028	.005527	.006855
e	−.005913	−.002876	−.003623	−.001066
f	.016337	.041022	.020702	.003956
n	.770041	.782311	.771561	.868345
R^2	.987	.978	.988	.986

Figure 10. Test case for validating the methodology: (a) the vertical 2D plane; (b) the horizontal 2D plane.

Table 5. Test case input parameters for the 3D and 2D models and the CHTCs for the six walls (h₁ to h₆) obtained by simulation and correlation.

Inputs			3D simulation						3D correlation
Vin	Ain	Aout	h1	h2	h3	h4	h5	h6	h1	h2	h3	h4	h5	h6
0.5	0.2	0.2	1.05	3.23	3.49	5.35	1.78	1.24	0.87	3.43	3.56	5.29	1.75	1.11
0.5	0.2	1.5	0.93	3.46	3.52	5.06	1.71	1.16	0.89	3.88	2.89	5.31	1.65	1.17
0.5	0.2	2.8	0.74	3.39	3.48	4.89	1.71	1.26	0.72	2.91	3.41	4.60	1.70	1.05
0.5	1.5	0.2	1.05	3.40	3.07	5.37	1.15	1.10	1.04	3.74	2.52	6.07	0.92	1.26
0.5	1.5	1.5	0.88	3.65	3.09	5.34	1.25	0.88	0.74	3.43	2.63	4.38	1.45	0.93
1.5	0.2	0.2	2.28	7.63	8.03	12.14	4.15	2.77	1.89	8.63	8.99	14.45	4.77	3.10
1.5	0.2	1.5	2.06	7.82	8.03	11.25	3.89	2.69	2.16	7.82	9.23	10.24	3.35	2.45
1.5	0.2	2.8	1.62	7.82	7.89	10.92	3.80	2.84	1.44	8.99	8.60	9.83	3.61	2.84
1.5	1.5	0.2	2.42	7.67	7.26	12.11	2.98	2.55	2.10	6.29	6.89	11.50	3.13	2.75
1.5	1.5	1.5	1.80	7.95	6.77	11.00	2.83	1.93	1.51	7.95	7.38	12.31	2.26	1.84

Note: V_in (m/s), A_in (m), A_out (m), H_in = H_out = 0.1 m, L = 5 m, H = 3 m, A = 3 m, h_i (W/m²K), λ = 0.0264 W/mK, Pr = 0.72.

Figure 11. Comparison of the CHTCs according to ACH with the correlations developed by other authors.

Table 6. Application range of the variables of the 3D models.

Variable	Minimum	Maximum
H (m)	3.0	3.0
L (m)	0.5	6.0
A (m)	0.5	6.0
Win (m), Wout (m)	0.05	2.10
Xin (m), Xout (m)	0.05	2.10
Hin (m), Hout (m)	0.025	3.000
Ain (m), Aout (m)	0.025	6.000
Rein	1657	119,293