A cabin is heated by the combined power provided by a fan and the hotend. The cabin walls, ceiling, and floor consist of a layer of MDF sandwiched between two layers of insulation. The insulation has a thickness of $0.06 \text{ m}$ and a thermal conductivity of $k_{\text{ins}} = 0.04 \text{ W/m} \cdot \text{K}$, while the central MDF layer has a thickness of $0.02 \text{ m}$ and a thermal conductivity of $k_{\text{MDF}} = 0.15 \text{ W/m} \cdot \text{K}$.
The total wall, ceiling, and floor area of the cabin is $600 \text{ m}^2$. One vertical wall has an opening for the fan to introduce heat. The area of the fan opening is $1 \text{ m}^2$. The inside air temperature is maintained at $22^\circ\text{C}$, while the outside temperature drops to $-5^\circ\text{C}$. The convective heat transfer coefficient inside the cabin is $h_i = 15 \text{ W/m}^2 \cdot \text{K}$, and outside is $h_o = 25 \text{ W/m}^2 \cdot \text{K}$.
Task:
How much heat flux should the hotend and fan provide to maintain these conditions in steady state?
Tip: Use energy balance and thermal resistances to solve the problem.