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How does CTF method work with temperature dependent boundary heat transfer coefficients?

The last paragraph in section Conduction Transfer Function Module of EnergyPlus documentation says:

The coefficients (CTFs) in the equation are constants that only need to be determined once for each construction type.

Following the derivation by Seem (1987), this seems true if the coefficient matrices A, B, C and D in state space representation given in section Calculation of Conduction Transfer Functions are constant matrices. The 2-node example of a simple one layer slab in the same section has convection heat transfer coefficient in A, B, C and D matrices.

How is this handled when a temperature dependent correlation (like Walton etc.) are used for convection coefficients? If the convection coefficient and matrices are updated every time step, wouldn't the transfer function coefficients be computed at every step? What am I missing here?

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The Conduction Transfer Module is used exclusively for heat transfer through surfaces when the properties remain constant or relatively constant. As can be read at the beginning of the section Basic Finite Difference Solution Approach of EnergyPlus documentation:

This has all the usual restrictions of a transformation-based solution: constant properties, fixed values of some parameters, and do not produce results for the interior of the surface.

When the properties of the material may change over time or moisture may be relevant, other methods should be used. One can specify in EnergyPlus (see object HeatBalanceAlgorithm) between:

• Conduction Transfer Function: for constant properties.
• Moisture Penetration Depth Conduction Transfer function: to consider the effect of moisture
• Conduction Finite Difference (CondFD): As the name implies, this directly solves a heat transfer equation through finite differences either using Crank - Nicholson algorithm (second-order in time) or a First-order implicit method. Both are described in the documentation here.
• The Combined Heat and Moisture Transfer (HAMT) Model. Also a finite difference algorithm, It is also described in the documentation here..

The last two are considered for advanced usage or research according to the documentation. As a side note, I've seen in some corners of physics people playing with time-dependent transfer functions and equations or analogous constructions, but it is always with the understanding that it is an approximation and, in many cases, it is not computationally reasonable to do so.

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Thanks for the answer! I get the requirement of constant (temperature-independent) properties of the conducting medium/domain. What about the boundary heat transfer coefficients? For example, in one-dimensional conduction if the convective heat transfer coefficient at the end node is temperature dependent. If it is constant, the boundary heat flux will have a linear relation with the end node temperature and the matrices in the state space representation will be constant (as in the 2-node example in EnergyPlus documentation). How is it done if it is not?

( 2023-10-19 18:52:06 -0500 )edit