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Improve the calculation accuracy of the optimal insulation thickness in building walls as determined by a dynamic heat transfer model

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Abstract

To improve the calculation accuracy of optimum insulation thickness of building walls, the effects of the initial conditions and the choice of the representative day used as boundary conditions on results have been studied. In this context, the unsteady heat transfer across the multilayer wall was considered as one-dimensional and the problem was solved numerically by an implicit finite difference method. A computational FORTRAN code has been developed and validated to calculate, under real meteorological data (RMD), the cooling transmission loads and the optimum insulation thickness during the summer period in the Sahara of Algeria. For steady periodic conditions, the influence of the initial conditions on the precision of the numerical result has been studied for two cases of representative days (July 15 and 21). By comparing the results with the case of real conditions (RMD), we find that the choice of July 15 as a typical day gives more accurate results than the choice of July 21. In addition, the difference of cooling transmission loads of 76.2% for July 15 and 76.31% for July 21 is observed, between the use of a repeated and another non-repeated typical day.

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Abbreviations

\(a\) :

Thermal diffusivity (m2/s)

\(A_{\text{Es}}\) :

Annual cost of energy saved ($/m2 year)

\(C\) :

Specific heat (J/kg K)

\(C_{\text{c}}\) :

Yearly cost of energy consumed by air-conditioning ($/m2 year)

\(C_{\text{e}}\) :

Cost of electricity ($/kWh)

\(C_{\text{i}}\) :

Cost of insulation material ($/m3)

COP:

Coefficient of performance of the air-conditioning system

\(C_{\text{t}}\) :

Total cost ($/m2)

d :

Inflation rate (%)

\(h_{\text{o}}\) :

Heat transfer coefficient at the outdoor of multilayer wall surface (W/m2 K)

\(h_{\text{i}}\) :

Heat transfer coefficient at the indoor of multilayer wall surface (W/m2 K)

i :

Interest rate (%)

\(I_{\text{T}} \left( t \right)\) :

Total solar radiation (W/m2)

\(k\) :

Thermal conductivity (W/mK)

\(L_{\text{i}}\) :

Insulation thickness (m)

\(L_{\text{opt}}\) :

Optimum insulation thickness (m)

\({\text{MBE}}\) :

Mean bias error

n :

Lifetime period (years)

\({\text{PWF}}\) :

Worth factor

\(P_{\text{b}}\) :

Payback period (years)

\(q_{\text{o}}\) :

Heat flux at outdoor surface of the multilayer wall (W/m2)

\(q_{\text{i}}\) :

Heat flux at indoor surface of the multilayer wall (W/m2)

\(Q_{\text{c}}\) :

Cooling transmission load for insulated wall (MJ/m2 years)

\({Q_{\text{c-unins}}}\) :

Cooling transmission load for uninsulated wall (MJ/m2 years)

\(Q_{\text{h}}\) :

Heat delivered at the hot reservoir (external environment)

RMD:

Reel meteorological data

\({\text{RMSE}}\) :

Root mean square error

\(t\) :

Time (s)

\(T_{\text{Es}}\) :

Total cost saved during the lifetime of building ($/m2)

\(T_{\text{e}} \left( t \right)\) :

Sol–air temperature (K)

\(T_{\text{in}}\) :

Indoor air temperature (K)

\(T_{\text{o}} \left( t \right)\) :

Outdoor air temperature as a function of time (K)

\(T_{\text{wi}}\) :

Indoor wall surface temperature (K)

\(T_{\text{wo}}\) :

Outdoor wall surface temperature (K)

\(W\) :

Compressors dissipated work (MJ/m2 years)

\(x_{i}\) :

Indoor wall surface temperature obtained from Fluent or CodyMur (K)

\(y_{\text{i}}\) :

Indoor wall surface temperature obtained from the FORTRAN code (K)

ρ :

Density (kg/m3)

α :

Solar absorptivity (equal to 0.8)

\(\Delta x\) :

Space step (m)

\(\Delta t\) :

Time step (s)

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This research did not receive any specific grant from funding agencies in the public, commercial or not-for-profit sectors.

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Authors and Affiliations

  1. Département de Physique, Faculté des Mathématiques et des Sciences de la Matière, Université Kasdi Merbah Ouargla, 30000, Ouargla, Algeria

    Hichem Necib

  2. Mechanical Engineering Department, Faculty of Technology Sciences, University of Mentouri Constantine 1, 25000, Constantine, Algeria

    Brahim Necib

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  1. Hichem Necib
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Necib, H., Necib, B. Improve the calculation accuracy of the optimal insulation thickness in building walls as determined by a dynamic heat transfer model. Asian J Civ Eng 21, 903–913 (2020). https://doi.org/10.1007/s42107-020-00248-w

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