# Model development and performance evaluation of an earth air heat exchanger under a constrained urban environment

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## Abstract

An earth air heat exchanger (EAHE) is an underground heat exchanger that captures or dissipates heat to the ground and hence moderates the temperature of the air flowing through it. Though a promising energy efficient option for thermal comfort, EAHE has not diffused much in the society. One reason for its limited application is space constraint. This includes restrictions on the length and route of the EAHE pipe, positioning of the EAHE, the forced interaction between the civil foundations and the EAHE etc. In order to investigate the effectiveness of such a ‘constrained’ EAHE, an EAHE was installed under such urban constraints and its performance was measured. Simultaneously a predictive 3-dimensional numerical transient model was developed to study the impact of model parameters on the EAHE’s performance. The model was coded on the MATLAB^{Ⓒ} platform. The developed mathematical model is robust, and it was validated at sites with and without urban constraints across three climatic zones. Model predictions were in good agreement with the measured values. The data and model predictions confirmed that in a semi-arid climatic zone if a constrained EAHE is placed strategically, its performance is not compromised, and it provides the desired cooling even when it is installed at a shallower depth.

## Keywords

Earth air heat exchanger (EAHE) Urban site Transient Model## Abbreviations

- α
Albedo of the ground surface

- ɛ
Emissivity of the ground

- ɛΔR
Long wave emission from the ground

- ρ
Density (kg m

^{−3})- χ
Volume fraction

- ΔL
Length (m)

- ΔxΔyΔz
Size of the control volume

- a, b
Constants

- C
_{p,air} Specific heat of air (J kg

^{−1}K^{−1})- Cv
Volumetric heat capacity (J m

^{−3}K^{−1})- d
_{i} Inner diameter (m)

- d
_{o} Outer diameter (m)

- EAHE
Earth to air heat exchanger

- E,W,U,D,F,B
Suffixes to indicate parameter values respectively to the right, left, above, below, in front and behind of the control volume under evaluation

- f
Moisture fraction

- G
Solar global irradiance incident on the ground (Wm

^{−2})- h
_{c} Convection heat transfer coefficient (Wm

^{−1}K^{−1})- k
Thermal conductivity (Wm

^{−1}K^{−1})- NTR
Net total radiation (W m

^{−2})- r
_{a} Relative humidity of air near the ground surface

- r
_{i} Inner radius (m)

- S
_{o} Heat source (Wm

^{−3})- SDS
Standard data set

- T
Temperature in (

^{°}C)- t
Time (s)

- u
Velocity (ms

^{−1})- x,y,z
Rectangular co-ordinate axes

## Notes

### Acknowledgements

The authors would like to thank TERI School of Advanced Studies, Delhi, Landmark Design Group, Pune and Dr. VVN Kishore for their expert comments and support.

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