.IDEAS.Buildings.Components.BaseClasses.ConductiveHeatTransfer.MonoLayerDynamic

Information

For the purpose of dynamic building simulation, the partial differential equation of the continuous time and space model of heat transport through a solid is most often simplified into ordinary differential equations with a finite number of parameters representing only one-dimensional heat transport through a construction layer. Within this context, the wall is modelled with lumped elements, i.e. a model where temperatures and heat fluxes are determined from a system composed of a sequence of discrete resistances R_n+1 and capacitances C_n. The number of capacitive elements n used in modelling the transient thermal response of the wall denotes the order of the lumped capacitance model.

C_c · dT_c / dt = Σ_i=1ⁿ Q̇_res,i + Q̇_source

where

• T_c is the temperature of the lumped capacity,
• Q̇_res is the heat flux through the lumped resistance,
• R_res is the total thermal resistance of the lumped resistance,
• Q̇_source are internal thermal sources that represent the added energy to the lumped capacity, and
• C_c is the thermal capacity of the lumped capacity, equal to (ρ · c_p · d_c · A), where
• ρ denotes the density,
• c_p is the specific heat capacity of the material,
• d_c is the equivalent thickness of the lumped capacity, and
• A is the surface area of the wall.

Revisions

• June 17, 2025, by Lucas Verleyen:
  Replaced images with inline equations. See #1440.
• January 25, 2019, by Filip Jorissen:
  Revised initial equation implementation. See issue #971.
• January 25, 2018, by Filip Jorissen:
  Propagated T_start in the declaration of T. See issue #692.
• December 8, 2016, by Filip Jorissen and Damien Picard:
  Revised implementation of placeCapacityAtSurf_b, which has been renamed to addRes_b. This is for solving problems when linearising a model. See issue 591.
• February 10, 2016, by Filip Jorissen and Damien Picard:
  Revised implementation.