For the energy evaluation, the method in the international standard ISO 52016-2:2017(E) [17] is mainly adopted, and the method is applicable to both ventilated and non-ventilated Trombe wall. According to the standard, the total energy that Trombe wall obtains is the sum of heat gain and heat loss through the wall as Eq. (1) shows. The heat gain comes from solar radiation and the heat loss is casued by the tempereature difference between indoor and outside air.

(1)

where *Q*_{Total,t} is the heating load of Trombe wall during the heating period (kWh). *Q*_{Gain} is the accumulated heat gain during the heating period (kWh). *Q*_{Loss} is the accumulated heat loss during the heating period (kWh).

For the convenience of application, two energy indexes are proposed here. The first one is annual accumulated heating load per unit Trombe wall area (*Q*_{HL} ) and the second one is annual accumulated energy saving per unit Trombe wall area compared with conventional wall (*Q*_{ES} ) , which are shown in Eq. (2) and Eq. (3).

(2)

(3)

where *Q*_{HL} is the annual accumulated heating load per unit Trombe wall area (kWh/m^{2}). *Q*_{ES} is the annual accumulated energy saving per unit Trombe wall area compared with conventional wall (kWh/m^{2}). *Q*_{Total,c} is the conventional wall heating load during the heating period (kWh). *A*_{sw} is the area of the Trombe wall (m^{2}).

The energy evaluation of Trombe wall is based on the following assumptions [17, 18].

a. The surface temperatures of the inner and outer walls are uniform, so the Trombe wall is simplified into a zero dimensional lumped parameter model.

b. For ventilated Trombe wall, when the air layer temperature is lower than room temperature, the air flow stops. Otherwise, the air in the layer begins to flow.

c. The heat transfer coefficients of thermal conduction, convection and radiation are constant that are independent of temperature. This assumption turns a nonlinear equation into a linear equation (refer to Eqs. (4) and (6)), so the superposition principle is applicable in the calculation.

d. For the ventilated Trombe wall, the air flow rate in the air layer is known and constant.

e. The air in the air layer is transparent medium without absorption and emission capability.

Next, the calculation method of heat gain and heat loss in Eq. (1) is described according to ventilated and non-ventilated Trombe wall respectively (Please refer to Fig. 1 for the structures).

(1) Ventilated Trombe wall

Heat gain

The solar radiation will be absorbed by the massive wall when the air layer is covered by a transparent envelope, and then the heat absorbed continues to be transferred to the internal environment by conduction and convection. So the heat gain of the Trombe wall can be expressed by solar radiation intensity, as shown in Eq. (4).

(4)

where *I*_{w} is the accumulated total solar incident radiation during heating calculation period (kWh/m^{2}). **_{sol} is solar absorption coefficient of the massive wall behind the transparent envelope. *F*_{F} is the frame reduction factor. *F*_{S} is the shading reduction factor. *F*_{W} is the correction factor for non-scattering glazings. *g*_{w} is total solar energy transmittance of the glazing covering the air layer. *U*_{o} is total thermal transmittance of the Trombe wall (W/(m^{2}·K)). *R*_{e} is external thermal resistance of the transparent envelope, between air layer and external environment (m^{2}·K/W). *R*_{i} is internal thermal resistance of the massive wall, between air layer and interior environment (m^{2}·K/W). *R*_{l} is thermal resistance of the air layer (m^{2}·K/W). *U*_{i} is thermal transmittance of the massive wall containing the air space (W/(m^{2}·K)). *U*_{e} is thermal transmittance of the transparent envelope containing the air space (W/(m^{2}·K)). **_{a} ∙*C*_{a} is heat capacity per unit volume of air (J/(m^{3}·K)). *q*_{v,se} is set value of air flow rate through the ventilated layer (m^{3}/s). **_{sw} is non-dimensional parameter related to the air layer temperature. *ω* is the ratio of the total solar radiation falling on the heat collection element when the air layer is open to the total solar radiation falling on the heat collection element during the calculation period. So its value is between zero and one and it can be calculated byEq. (5).

(5)

where **_{al} is the ratio of solar heat gain to heat loss of the air layer. For the detail explanation of variables in Eq. (4) and Eq. (5), please refer to literature [18] and [17].

**Heat loss**

The heat loss of Trombe wall is caused by the temperature difference between air layer and outdoor environment, and according to the ISO 52016-2:2017(E) it can be expressed by the indoor and outdoor air temperature difference shown in Eq. (6). The temperature difference multiplied by the calculation period is also called heating degree days.

(6)

The effects of heat conduction, convection and radiation in different Trombe wall layers are taken into account in Eq. (6). The layers of Trombe wall refer to the transparent structure, air layer and thermal storage wall.

The factor ** in Eq. (6) is the ‘‘ratio of the accumulated internal-external temperature difference when the ventilation is on, to its value over the whole calculation period’’. The opening and closing of the vents depends on the temperature difference between air layer and internal environment, so the factor ** is greater than zero unless the vents were off all the time (it is equivalent to non-ventilated Trombe wall). The calculation method of the factor ** was given in the standard of ISO 52016 as shown in Eq. (7). *T*_{e} is the external environment temperature (K). *T*_{i} is the internal environment temperature (K). *t* is the total hours of heating period (h). Other variables in Eq. (6) are the same as in Eq. (4).

(7)

(2) Non-ventilated Trombe wall

Compared with the ventilated Trombe wall, it is less complicated for the non-ventilated Trombe wall to calculate the heat loss and solar gain in heating season. As the Trombe wall is non-ventilated, the convection parts in Eqs. (4) and (6) should be deleted, so the heat loss and heat gain of the non-ventilated Trombe wall can be calculated by Eqs. (8) and (9).

(8)

(9)

(3) Conventional wall

The energy saving of Trombe wall is obtained by comparison with conventional wall, so the total energy loss through the conventional wall (i.e. accumulated heating load) should also be calculated.

Similar to the calculation method of Trombe wall, the accumulated heating load of conventional wall can be calculated in the form of heating degree days by Eq. (10). The correction factor for overall heat transfer coefficient of conventional wall (**) in Eq. (10) reflects the heat gain from solar radiation on conventional wall which is between 0 and 1.

(10)

where *Q*_{Total,c} is the conventional wall heating load during the heating period. ** is correction factor of opaque building envelope’s overall heat transfer coefficient. *U*_{c} is the total thermal transmittance of the conventional wall (W/(m^{2}·K)). *A*_{c} is area of the conventional wall (m^{2}).