# An analysis of the numerical model influence on the ground temperature profile determination

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## Abstract

The estimation of the ground temperature profile with respect to the depth and time is the key issue in many engineering applications which use the ground as a source of thermal energy. In the present work, the influence of the model components on the calculated ground temperature distribution has been analysed in order to develop an accurate and robust model for the prediction of the ground temperature profile. The presented mathematical model takes into account all the key phenomena occurring in the soil and on its top surface. The impact of individual model elements on the temperature of the soil has been analysed. It has been found that the simplest models and the most complex model result in a similar temperature variation over the simulation period, but only at a low depth. A detailed analysis shows that a larger depth requires more complex models and the calculation with the use of simple models results in an incorrect temperature and a theoretical COP estimation.

## Keywords

heat transfer ground heat transport ground temperature profile ground source heat pump## Nomenclature

*ρ*_{z},*ρ*_{w}ground, water density, kg/m

^{3}*c*_{pz},*c*_{w}ground, water specific heat, J/(kg·K)

*k*_{z}ground thermal conductivity, W/(m·K)

*t*time, s

*v*_{i}the Darcy velocity, m/s

- ε
emissivity

- σ
Stefan–Boltzmann constant, W/(m

^{2}·K^{4})*f*fraction of evaporation rate

*r*_{h}air relative humidity

*T*_{sky}reference (sky) temperature, K

*T*_{air}air temperature, K

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## Notes

### Acknowledgments

The paper was carried out under the Statutory Research at the Faculty of Drilling, Oil and Gas, AGH University of Science and Technology, financed from the funds of the Polish Ministry of Science and Higher Education, grant 11.11.190.555

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