# a reference model for ground coupled heat transfer

Recently, successive reductions in building fabric and infiltration heat losses have increased the relative importance of heat loss to ground. However, because of the complexity of the problem, model predictions for uninsulated slab-on-grade heat transfer, for example, can differ by between 25% and 60%. This discrepancy has motivated further validation efforts in an extension to IEA BESTEST of which the work described here forms part. The novel validation methodology prescribed in the extended BESTEST calls for putative reference models/programs to be gauged first against a known exact solution to a ground coupled heat transfer problem, and then to agree closely with the predictions of other proposed reference models when all are applied to progressively more complex and realistic test problems for which analytical solutions do not exist. The closely agreeing reference solutions produced in this manner can then be used to test the performance of more general whole-building models in this demanding aspect.

The reference model described here was programmed specifically for this task within a general purpose mathematical package, MATLAB, which includes an extensive catalogue of algebraic and differential equation solvers. A three-dimensional finite difference approximation to the Heat Diffusion Equation was prepared and applied to ground coupled heat transfer in the environs of a building for a range of geometries and boundary conditions. The problem is challenging in three ways: (i) it is large – about a million nodes were used, (ii) it is mathematically stiff and (iii) it possesses an exceedingly lengthy thermal time constant. Nevertheless, the results achieved were well within the tolerances prescribed in the extended BESTEST, for example, the reference model prediction was within 0.032% of the analytical solution to the initial test problem. It can therefore be concluded that the model is fit for purpose.

Another conclusion emerging from the work concerns the very lengthy thermal time constants for ground coupled heat transfer problems such as slab in/on grade – also basements, labyrinth cooling systems and buried coils – when this heat transfer mode is a significant fraction of the total thermal load. Normally one discards the initial output of a simulation run, that is, the output calculated during the pre-conditioning period. If, however, the pre-conditioning period is decades in duration, then load predictions are inaccurate for a significant fraction of the building life unless initial conditions are directly measured – using bore-holes for example. Typical sub-surface temperature profiles are of little use on most sites which will have been disturbed by site excavation during the construction phase and probably by road works, pipe laying and construction of adjacent buildings prior to that.

## Personnel

DIT - School of Civil & Building Services Engineering

Dr Michael Crowley

### Collaborators

International Energy Agency (IEA) Testing and Validation of Building Energy Simulation Tools Experts Group