Insertion within a Partition Wall on the Energy Consumption of a Conditioned Room under Adjacent Local Periodical Temperature Effect

The aim of this work is to study the combined insertion effect of Phase Change Materials (PCM) and thermal insulation within a partition wall separating a conditioned room from an adjacent local which is under a periodic thermal activity. This is done by a comparative study with a reference wall under the same thermal conditions. The comparison criterion is the energy density transmitted to the local conditioned in established regime. The results show that the inclusion of thermal insulation and phase change material provides a significant reduction of energy consumption of the conditioned local; thereby a judicious choice of phase change material with thermal level and range melting temperature reduces further this reduction.


Indices
o / i Outside /Inside m Melting

Introduction
Currently, modern life is causing a huge problem of energy consumption. Climatic conditions generate a discomfort situation, which requires the increasing use of air conditioning systems.
There are several techniques to reduce the use of air-conditioning systems and improve the energy efficiency of buildings. Among the proposed solutions: insulation of walls and roofs [1], use of light colours on external surfaces [2] and energy storage devices in the building structure [3,4,5]. The last technique uses frequently phase change materials (PCM). Phase change material is known by its ability to store more energy and temperature fluctuations [6]. The investigation of PCM is made for the case of conditioned local [7,8,9] and non-conditioned local [10]. Criteria of these works are the daily and annually energy per unit area [1,8] or the flux density transmitted to the local [7,11].
In the case of conditioned premises, the results of the various studies have shown that the insertion of thermal insulation or phase change materials is advantageous and reduces the energy consumption involved in these premises.
The aim of our study is to evaluate the simultaneous insertion effect of thermal insulation and phase change materials within a partition wall on the reduction of energy consumption. The partition wall separates two locals. The conditioned one is considered at constant temperature and corresponds to comfort temperature. The adjacent local is subject to a periodical thermal activity.

Illustration of problem
The reference partition wall is shown in Figure 1. It is a structure of total thickness L , consisting of concrete, subjected to two different thermal boundary conditions: constant temperature corresponding to the conditioned room comfort temperature i T and a sinusoidal temperature o T relative to the adjacent local.

Analysis and modelling
The thermal behaviour of the multilayer wall system is given by the equations below. The equation 1 is applicable to the concrete and the insulation, while the equations 2 and 3 concern the phase change material, according to the enthalpy method. These equations are coupled with the continuity of temperature and flux at the different interfaces (equations 4 and 5 ) and are associated with the boundary conditions ( 6 , 7 and 8 ).  Concrete and insulation (subscript 1 ): T is the melting temperature, and f L the heat latent.  Interfaces between concrete, phase change material and insulation : are respectively the average temperature value and the amplitude, while  is the pulsation. This parameter is related to the daily period of the adjacent room temperature sinusoidal oscillations.
The system of previous equations associated to the boundary and interfaces conditions has been solved by a scheme with implicit finite differences. This scheme is unconditionally stable which leads to a tridiagonal matrix system solved by Thomas algorithm. This resolution provides the evolution of temperature profile at each point of the wall. Choice of step time t  and space x  is a result of a consensus between computational time and accuracy.

Validation of numerical solution
Before presenting the numerical results the multilayer wall, provided with phase change material and thermal insulation, the numerical code is validated by comparison with analytical solution available in the literature relative to classic problem of Newman [12]. A phase change material is initially at the melting temperature

Results and discussion
We In order to apprehend the effect of melting range of PCM, we have introduced a melting factor parameter  taking values from 1% to 3%. The merge interval Concrete-Insulation-Concrete-PCM-Concrete (CICPC). The combinations insertion effects are estimated by the relative deviation of energy  transmitted toward the partitions wall, comparatively to that corresponding to the reference wall. This parameter is deduced from the internal daily energy density  , transmitted to the conditioned local in established periodic regime according to :  . This is done with the values from 1 to 3 of the melting parameter for these two PCMs.
Values of daily energy for the two PCMs and comfort temperatures are reported in Figures 5 and 6, whereas Table 2 and Figure 7 illustrate the corresponding relative deviation parameter  . This leads to a comparison of daily energy for the two combinations of PCM and insulation (CPCIC and CICPC).

Conclusion
This study deals with the insertion effect of thermal insulation and phase change material within a conventional partition wall. The various configurations are compared under the same thermal conditions corresponding to a local conditioned and a second whose temperature evolves periodically. Based on a numerical code and the energy consumption as criterion, the results show that the insertion of the thermal insulation and the phase change material reduces significantly the energy consumption. The phase change material reduces further this consumption if level and range melting temperature are appropriate. The most suitable phase change material is that of a melting temperature slightly greater than a comfort temperature, associated with an adequate melting range.
The first author thanks the French -Maghreb project PHC (Volubilis side) for the training period in the University of Lorraine.