Thermal modeling of the convective heat transfer in the large air cavities of the 3D concrete printed walls

Figures & data

Figure 1. 3D Printed Concrete Walls Classification based on their patterns. The classification also applies to slanted, curved, and organic shape walls. (Source: classification and figures by the authors)

Table 1. Examples of densities of 3D printed concrete mixture

Constituent (as described by the authors)	Density (kg/m^3)	Reference
Cement, calcium sulfoaluminate (CSA), fly ash, silica fume	700–1400	(Cho et al., 2021)
Cement, silica sand, gravel, cork, polypropylene fiber, and air	986	(Alkhalidi & Hatuqay, 2020)
Silica sand, gravel, sulfur, polypropylene fibers, and air	1,254	(Alkhalidi & Hatuqay, 2020)
Silica sand	1,522	(Alkhalidi & Hatuqay, 2020)
Cement, fly ash, silica fume, fine aggregate, water, and superplasticizer	2,084	(Cicione et al., 2021)
Cement, siliceous sand, silica fume, fly ash, ladle furnace slag, limestone filler, water. and superplasticizer	2,100	(Papachristoforou et al., 2019)
Cement, silica fume, fly ash, water. and superplasticizer	2,168	(Lithium et al., 2019)
Cement, siliceous sand, silica fume, fly ash, ladle furnace slag, limestone filler, water. and superplasticizer	2,225	(Papachristoforou et al., 2019)
Cement, Sand, Fly ash, Silica fume, water (5 Mixtures—same materials, different proportions)	2,300	(Le et al., (2012))
Five concrete mixtures densities—no constituent information	1,800–2,400	(Suntharalingam et al., 2021)

Figure 2. Examples of 3D printed concrete walls with large cavities. As per the classification in Figure 1, the walls in the photo correspond to “3D printed exterior layers” (at the left) and “3D printed wall with straight stiffeners” (at the right). (Source: Dubai Electricity and Water Authority©).

Table 2. Thermal studies on wall cavities, hollow masonry units, and glazing air spaces

Element	Topic	Findings	Reference
Brick wall with air cavities	Thermal and mechanical optimization	When the influence of natural convection rises, the optimal number of air gaps increases. When the influence of natural convection in the air gaps is smaller, the thermal resistance of the wall increases.	(Lorente & Bejan, 2002)
Hollow block wall	Effect of the blocks’ holes configurations on the thermal performance of the wall	The thermal performance might be improved by reducing the ribs’ width and hole number in each row. It is preferable to increase hole rows rather than hole thickness.	(Y. Zhang & Wang, 2017)
Hollow clay bricks	Study of the insulation performance of hollow bricks filling the cavities with perlite The conjugate heat transfer analysis includes conductive, convective, and radiative heat transfer in three cavities scenarios (unfilled, half-filled, and full-filled with perlite)	Filling the cavities with perlite inhibits radiative and convective heat transfer. The insulation performance can improve by 15.6% and 27.5% for half and full-filled cases.	(Arici et al., 2016)
Hollow concrete blocks	Conjugate heat transfer across a hollow block, considering conductive and convective heat transfer in the cavity.	The block’s thermal resistance significantly increases, raising the number of cavities without changing its width.	(Antar & Baig, 2009)
Hollow concrete blocks	Thermal transmittance for different cavity configurations of concrete blocks	Large cavities provide higher transmittance values due to convection	(Henrique Dos Santos et al., 2017)
Hollow concrete blocks	Conjugate heat transfer of a hollow block on the roofs	With the same size and materials, the block with more holes has the best thermal performance. The thermal load of blocks with three hollows was 7% lower than the blocks with two holes.	(Xamán et al., 2017)
Enclosure air layers on building envelopes	Study the convective and radiative heat transfer in the air layer of building envelopes	The optimum thickness of the air layers ranges from 20 to 30 mm, depending on the climate. The higher the air layer, the lower the convective heat transmission.	(Zhang & Yang, 2018)
Clay bricks with air cavities	Studies on air cavities of various design	A change in cavities configuration could alter the thermal resistivity by 20%	(Bouchair et al., 2008)
Multiple pane windows	Study the fluid flow and heat transfer in double, triple, and quadruple pane windows, varying the gap widths and including and excluding the radiative heat transfer in the calculations.	Heat loss through windows can be considerably reduced by increasing the number of panes, which slows the heat flow in the cavity, suppressing the convective transfer. By replacing a double pane window with a triple or quadruple pane window, the energy-saving can reach 50% or 67%, respectively.	(Arici et al., 2015)
3D printed concrete cavity walls	Parametric study of thermal performance of 32 models based on eight 3D printed cavity wall configurations.	There was an evident relationship between air cavities area and energy performance walls with the integration of insulation material. Adding an intermediate row (more and smaller cavities) reduces the U value significantly. The thermal performance was improved with cavity insulation (Min. U value = 0.34 W/m2·K). Propose an equation to determine the U-values of 10 cm-thick 3D printed cavity walls with different configurations.	(Suntharalingam, Upasiri et al., 2021)
3D printed lightweight foam concrete wall with cavities	Thermal performance of two 3D printed lightweight foam concrete walls with cavities (effect of the number and size of cavities)	The thermal performance of a solid lightweight foam concrete wall is better than a 3D printed lightweight foam wall section with large and wide cavities. However, a wall with four cavities has a better thermal performance than a solid lightweight foam wall. More cavities of smaller leads to improved thermal resistance.	(Marais et al., 2021)

Figure 3. Two-dimensional computational domain with concrete and air segments and boundary conditions.

Table 3. Properties of concrete mixture and the air

Material	Thermal conductivity W/(m.K)	Density (kg/m3)	Specific heat kJ/(kg K)	Dynamic viscosity* (kg/m-s)
Concrete	1.8	2300	1
Air	0.0255	1.225	1.005	1.849x10^−5

*At standard atmosphere pressure and a temperature equal to 25°C.

Table 4. Number of subdivisions of the original cavity and resulting sub-cavities sizes

Number of subdivisions	Number of dividers (Per axis)	Cavities arrangement	Size of the resulting cavities (mm)
1	0	1	220.00 x 220.00
4	1	2 x 2	109.50 x 109.50
16	3	4 x 4	54.25 x 54.25
64	7	8 x 8	26.63 x 26.63
256	15	16 x 16	12.82 x 12.82
1024	31	32 x 32	5.91 x 5.91
4096	63	64 x 64	2.45 x 2.45

Figure 4. Comparison between the present numerical model temperature contours for Ra = 10⁴, 10^5, and 10⁶ in a square cavity at the first row and the benchmark solution (Wakashima & Saitoh, 2004) at the second row.

Table 5. Normal heat flux in each of the studied cases

Number of cavities	Heat Flux (W/m^2) Tout—Tin = 20°C		Difference (%)
	Low Conductivity Divider (0.032 W/m·K)	High Conductivity Divider (0.270 W/m·K)
1	40.37	40.37	-
4	19.65	20.30	1.03
16	9.05	9.70	1.07
64	4.20	4.90	1.17
256	2.51	4.20	1.67
1024	2.46	6.00	2.44
4096	2.80	10.50	3.75

Figure 5. Normal heat flux vs. number of air cavities.

Figure 6. Air velocity profiles and temperature on the cavities with 1, 4, 16, 64, and 256 subdivisions.

Figure 7. 3D projection of temperature profiles for cavities with no subdivisions and with 4 and 256 sub-cavities.

Figure 8. Non-dimensional temperature gradient inside the air space with four cavities for Ra = 10⁴, 10⁶, and 10⁷.

Figure 9. Non-dimensional temperature gradient inside the air space with 16 cavities for Ra = 10⁷ and case of no flow, i.e., Nu = 1, temperature gradients still are significant.

Figure 10. Non-dimensional temperature gradient inside the air space with 64 cavities for Ra = 10⁷ and case of no flow, i.e., Nu = 1, temperature gradients are becoming less significant.

Figure 11. Variation of heat transfer coefficient (h) with air cavity width between vertical plates.

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Data availability statement

“Some or all data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.”