How to estimate dynamic effects in a more or less simplified way


Explanation of thermal inertia and the differences between internal and external insulation. PDF slides


Heat stored in a building component is defined by the difference between its temperature and a reference temperature . In a wall of thickness , mass density and heat capacity , it can be estimated in the unit [J/m] as:

The total inertia of an -layered wall is the sum of these accumulated energies over all layers:

In a transient state, we can calculate the evolution of temperatures in time as a function of R and C values of a building component. These values depend on the discretization size and material properties. In the example shown here, the following equation is to be solved: $$ C \dfrac{\partial T}{\partial t} = \frac{1}{R} (T_1-T) + \frac{1}{R} (T_2-T) $$


Consider a wall made of three layers:

Layer 1 (concrete)  Layer 2 (insulatin) Layer 3 (finishing)
cm cm cm
W/m.K W/m.K W/m.K
J/kg.K J/kg.K J/kg.K
kg/m kg/m kg/m

The outdoor temperature is and the indoor temperature is . The outdoor heat transfer coefficient is W/m.K and the indoor one is W/m.K

Exercise 1: inertia

Suppose an internal insulation.

  • Calculate the thermal resistance of each layer and the heat flux through the wall.
  • Calculate the temperature distribution across the wall and the average temperature of each material.
  • Calculate the total stored heat and estimate the heat inertia.

Answer the same questions as above in the case of an external insulation

Exercise 2: transient simulations

Simulate the evolution of temperature inside the wall by following these steps:

  • Discretise each material layer with a sufficient number of resistances and capacities (this is similar to a finite difference scheme)
  • Write the equations for the temporal evolution of temperature on each point. You can select either an implicit or an explicit scheme for time discretization.
  • Solve and plot the evolution of temperature at the interface between concrete and insulation, by supposing a uniform initial temperature

The solution will be shown here soon.