"Mass timber" refers to engineered wood products, laminated from smaller boards into structural components, such as glue-laminated (glulam) beams or cross-laminated timber (CLT) panels. Mass timber products, together with careful forestry management, could help decarbonize the construction industry. Designing mass timber panels as heat exchangers could multiply the potential carbon savings, by obviating extra materials (e.g., insulation) and simplifying HVAC systems.

The optimum spacing of the channels is:

is the optimized channel spacing (center to center),

is the panel thickness,

is the thermal conductivity of the panel material

is the thermal conductivity of the air.

The Bejan number is defined as:

where

is the design pressure,

is the dynamic viscosity of the air, and

is the thermal diffusivity of the air. The void fraction of the panel

is defined as:

where

is the diameter of the channels. A second correlation predicts the total heat transfer through the optimized panel:

.

The number of thermal units (NTU) is the ratio of the total heat transfer coefficient during heat exchange,

, to the baseline heat transfer coefficient when there is no heat exchange,

:

where

is the heat flux at the heated interior surface,

is the temperature of the heated interior surface, and

is the temperature of the exterior air (which enters through the channels). During sensible, steady heat exchange, the surface heat flux

transfers in part to the incoming air

, while the remainder

transfers to the exterior environment:

,

which can also be defined in terms of coefficients of heat transfer:

and

is the heat-exchange efficiency:

.

These definitions of

and

are valid so long as the surface heat flux or the surface temperature is constant and uniform. Either boundary condition can be maintained with integrated hydronics. In either conditions,

is equivalent to the relative temperature increase experienced by the incoming air:

where

is the temperature of the incoming air as it leaves the channels and enters the interior space. Following the convention in the dynamic insulation literature,

can be referred to as the "dynamic

value". However, it is important to emphasize that

. That is, achieving low values for

should not come at the cost of over-ventilating, neither in terms of the heat of ventilation (

) or of the air flow rate. The air flow rate per unit area of panel is defined as:

.

Finally, there is an important sizing limit to take note of:

.

The correlations are invalid if this limit is exceeded.

[1] S. Kim, S. Lorente and A. Bejan, "Vascularized Materials with Heating from One Side and Coolant Forced from the Other Side,"

*International Journal of Heat and Mass Transfer*,

**50**(17–18), 2007 pp. 3498–3506.

doi:10.1016/j.ijheatmasstransfer.2007.01.020.

[2] S. Craig and J. Grinham, "Breathing Walls: The Design of Porous Materials for Heat Exchange and Decentralized Ventilation,"

*Energy and Buildings*,

**149**, 2017 pp. 246–259.

doi:10.1016/j.enbuild.2017.05.036.

[3] S.Craig, A. Halepaska, K. Ferguson, P. Rains, J. Elbrecht, K. Moe, D. Kennedy and A. Freear, "Buildings as a Global Carbon Sink? The Design of Mass Timber Panels as Heat Exchangers (Dynamic Insulation)" (submitted for publication).