Question

For a residential building with 5000W of heating demand, estimate:

a)     the number of required vertical ground heat exchangers (borehole heat exchangers) to fulfill the heating demand (round up the number).

b)    the heat exchange rate for each ground heat exchanger if boreholes are 30m deep (W/m).

Design parameters and assumptions:

The circulating fluid in the pipes is water with a temperature difference of 5°C between inlet and outlet pipes (T_out - T_in= 5°C) and Reynolds number of 5,000. Pipe outer diameter is 25mm with 1.8mm wall thickness. Circulating fluid density is 1000 kg/m³, the heat capacity is 4180 J/(kgK) and dynamic viscosity of 0.001 Pa.s.

Answer 1

Ans) Given,

Heating demand = 5000 W

Temperature difference (T) = 5^oC or 278 K

Reynold number (Re) = 5000

Pipe outer diameter (d) = 25 mm

Wall thickness (t) = 1.80 mm

Heat capacity (c_m) = 4180 J/ kgK

Dynamic viscosity () = 0.001 Pas

a) We know ,

E = q c_mT

To determine flow rate q , first determine velocity using below relation,

Re = V D /

D = pipe internal diameter = d - 2t = 25 - 3.60 = 21.4 mm or 0.0214 m

=> 5000 = 1000 x V x 0.0214 / 0.001

=> V = 0.234 m/s

Hence, q = A x V

=> q = (/4) x 0.0214² x 0.234

=> q = 8.41 x 10^-5 m³/s

=> E = 8.41 x 10^-5 x 1000 x 4180 x 278

=> E = 97728 W

Number of required exchanger = 97728/5000

= 20 (approx)

Ans b) We know, heat transfer rate (q')

  = q' = k A T/ H ,

where k = heat transfer coefficient of water = 800 W/m²K

H = depth of borehole

A= surface are of pipe

=> q' = 800 x 2 x 3.14 x 0.0125 x 30 x 278 / 30

=> q' = 17458.4 W/m