Green Energy and Sustainability

Green Energy and Sustainability 2021;1(2):0007 |

Original Research Open Access

Analytical model for the simulation of Trombe wall operation with heat storage

Catherine Baxevanou , Dimitrios Fidaros , Aris Tsangrassoulis

  • Department of Architecture Engineer, University of Thessaly, Pedion Areos, 38334, Volos, Greece
  • These authors contributed equally to this work.

Correspondence: Catherine Baxevanou

Academic Editor(s): Thomas Kotsopoulos, Georgios Martinopoulos, Giorgos Panaras

Received: Sep 27, 2021 | Accepted: Nov 10, 2021 | Published: Dec 17, 2021

This article belongs to the Special Issue

Cite this article: Baxevanou C, Fidaros D, Tsangrassoulis A. Analytical model for the simulation of Trombe wall operation with heat storage. Green Energy Sustain 2021; 1(2):0007.


Passive solar systems, such as the Trombe wall, are cost-effective ways to reduce the energy consumption of buildings for heating, cooling, and ventilation. The operation of these systems can be simulated either with Building Energy Simulation Tools—BES like TRNSYS, EnergyPlus, etc either with Computational Fluid Dynamics—CFD. In both cases, the purchase of special software and/or special programming skills are required. In parallel analytical calculating tools are being developed, which also require some programming to solve an implicit system of non-linear equations but with fewer software requirements. The majority of analytical models concerns energy balance models for steady-state conditions with the result that heat storage is not taken into account, which in the case of a Trombe wall has a significant effect on the developed transport phenomena.

In the present work, an analytical energy balance implicit model was developed for the simulation of the transient operation of a Trombe wall taking into account the heat storage. Using this model, the operation of a Trombe wall for 7 typical days of the year was simulated. The results are presented in terms of the daily evolution of the temperature with which the air enters the room served by the passive system, of the temperature of the Trombe wall surface adjacent to the served room, and of the airflow rate inside the air gap. These results are compared with the results that a system without heat storage would give. Both systems are assessed based on annual performance as calculated by a quasi-steady explicit model. The developed model can be used to calculate the operation of a Trombe wall as well as to supply explicit quasi-steady models with values for airflow rate inside the air gap for Trombe wall operation without mechanical ventilation. Feeding these values to a quasi-steady model developed by authors it was found that the increase of storage wall heat capacity, either changing the storage wall material, either using phase change materials, can offer better utilization of Trombe wall heat gains up to 35% yearly.

Background: The present work aims to develop an analytical model for simulating the operation of a Trombe wall in a transient state taking into account the heat storage in the wall.

Methods: A closed system of equations is developed, based on 5 energy balances and a series of assumptions and auxiliary relations, to calculate the operation of a wall Trombe with heat storage with an hourly time step.

Results: Characteristics Trombe wall temperatures and mass flow rate through the air gap are calculated for typical days of 7 winter months. These are used for the calculation of utilizable heat gains from Trombe wall.

Conclusions: The model that does not take into account heat storage predicts higher temperatures and air mass flow rate in the gap than the present model by 10%. However heat storage increase the utilizable heat gains by 35% compared with a system without heat storage.


Trombe wall, heat storage, energy balance model, analytical model, implicit model

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