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Update conduction-through-the-walls.tex
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correct typo "root find algorithms" => "root-finding algorithms"
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Accacio authored Jan 15, 2025
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Expand Up @@ -143,7 +143,7 @@ \subsection{Calculation of Conduction Transfer Functions}\label{calculation-of-c
The accuracy of the state space method of calculating CTFs has been addressed in the literature.~ Ceylan and Myers (1980) compared the response predicted by the state space method to various other solution techniques including an analytical solution.~ Their results showed that for an adequate number of nodes the state space method computed a heat flux at the surface of a simple one layer slab within 1\% of the analytical solution.~ Ouyang and Haghighat (1991) made a direct comparison between the Laplace and state space methods.~ For a wall composed of insulation between two layers of concrete, they found almost no difference in the response factors calculated by each method.
While more time consuming than calculating CTFs using the Laplace Transform method, the matrix algebra (including the calculation of an inverse and exponential matrix for A) is easier to follow than root find algorithms.~ Another difference between the Laplace and State Space methods is the number of coefficients required for a solution.~ In general, the State Space method requires more coefficients.~ In addition, the number of temperature and flux history terms is identical (nz = nq).~ Note that as with the Laplace method that the actual number of terms will vary from construction to construction.
While more time consuming than calculating CTFs using the Laplace Transform method, the matrix algebra (including the calculation of an inverse and exponential matrix for A) is easier to follow than root-finding algorithms.~ Another difference between the Laplace and State Space methods is the number of coefficients required for a solution.~ In general, the State Space method requires more coefficients.~ In addition, the number of temperature and flux history terms is identical (nz = nq).~ Note that as with the Laplace method that the actual number of terms will vary from construction to construction.
Two distinct advantages of the State Space method over the Laplace method that are of interest when applying a CTF solution for conduction through a building element are the ability to obtain CTFs for much shorter time steps and the ability to obtain 2- and 3-D conduction transfer functions.~ While not implemented in the Toolkit, both Seem (1987) and Strand (1995) have demonstrated the effectiveness of the State Space method in handling these situations that can have important applications in buildings.
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