Modeling How External Factors Affect Air‑Conditioned Room Temperature with MATLAB/Simulink

Air conditioners have become essential household appliances, providing temperature regulation, air purification, and dehumidification, especially during hot summer days.

Model Establishment

Physical Model

The study models a typical office in Qingdao, divided into three zones, with dimensions (length, width, height) and a full‑air, side‑supply air‑conditioning system.

Mathematical Model

The air‑conditioned room is treated as a complex thermodynamic system with large inertia, many influencing factors, and strong nonlinearity. To simplify, the following assumptions are made:

The temperature field inside the room is uniform.

Only major heat sources are considered; other factors are ignored.

The building envelope exchanging heat with indoor air is limited to walls; windows and direct solar radiation are neglected.

Air Temperature Model

Based on the energy conservation principle, the rate of change of stored thermal energy equals the net energy gain from the air‑conditioning system minus losses to the environment.

Heat exchange between occupants and air includes respiration, radiation, and natural convection, each described by standard heat‑transfer equations (details omitted for brevity).

Envelope Temperature Model

Heat transfer through walls is modeled without latent heat exchange, using wall density, volume, specific enthalpy, surface area, thermal conductivity, thickness, and solar absorption ratio. Solar radiation on inclined surfaces and the comprehensive outdoor air temperature are also incorporated.

Simulation Results

The MATLAB/Simulink model was initialized with indoor temperature, supply air temperature, airflow rate, solar radiation intensity, wall inner‑surface temperature, and outdoor temperature. The system diagram is shown below.

Effect of Solar Radiation

Increasing solar radiation intensity raises indoor temperature gradually; however, the rise remains within acceptable human comfort limits.

Effect of Occupant Number

With no occupants, temperature stays stable. Adding 12 people causes the temperature to increase until a new steady state is reached, higher than the unoccupied case by a noticeable margin.

Effect of Airflow Rate

Step increases in supply airflow (e.g., to higher values) lead to a gradual temperature drop and faster convergence to a lower steady‑state temperature.

Conclusion

Dynamic mathematical models for indoor air temperature and building envelope were established based on energy conservation, and MATLAB/Simulink was used for simulation. The study shows that supply airflow, occupant count, and solar radiation each have measurable impacts on indoor temperature, providing insights for energy‑efficient HVAC control.

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