Gases after combustion are discharged from a flue in a facility to the atmosphere at a temperature of250 °C and a flow rate of 25000 m3/h. It is desired to benefit from the heat of this waste gas in heating.There is a site with 40 residences, each with a heating load of approximately 8 kW, located 3 km fromthe facility.1- Determine the substation capacity to be used, taking into account the hot water requirement foreach house on the site.2- Determine the substation inlet/outlet temperature and the heat exchanger water inlet/outlettemperatures. The temperature of the water leaving the heat exchanger is required not to exceed 95° C. The pipeline between the facility and the site is underground pipeline. Determine the requireddata by considering the region where the facility is located, calculate the heat losses in the line andfind the required insulation thickness.3- Calculate the total capacity including losses and determine the required exchanger dimensions.(Can you solve it with the formulas given in the pictures.) 8 Underground pipelines8.1 GeneralPipelines are laid in the ground with or without thermal insulation, either in channels or directly in the soil.8.2 Calculation of heat loss (single line) without channels8.2.1 Uninsulated pipeThe heat flow rate per metre, qe, for a single underground pipe is calculated by Equation (73):LE(73)R + REwheree, is the medium temperature;ee is the surface temperature of the soil;Ri is the linear thermal resistance of the insulation;RĘ is the linear thermal resistance of the ground for a pipe laid in homogeneous soil;iE is the design thermal conductivity of the ambient soil;HẸ is the distance between the centre of the pipe and the ground surface.The linear thermal resistance of the ground for an uninsulated pipe, as shown in Figure 11, is given byEquation (74):REarcosh 2HE(74)which, for HE/D, > 2, may be simplified to Equation (75): The intermal diameter, D, is identical to D (where - 1). The linear thermal resistance of the ground, RE.becomes, in this case, as given by Equation (78):(78)2 dD.which, for HeD, > 2, may be simpified to Equation (79):4 HED.1(79)Figure 11- Underground pipe without insulation8.2.2 Insulated pipeFor underground pipes with insulating layers, as shown in Figure 12, the themal resistance is caloulated byEquation (76):(76)NOTEThe concentric layers can consist ot for example, insularing material and sheathing (eg jacket pipe)embedded in a bottoming (eg. sand) with a square cross-section.Figure 12- Underground pipe comprising several concentric layersThe square cross-section of the outer layer with side length, a, is taken into consideration with an equivalentdiameter as given by Equation (77D,= 1.073 a(77)

Temperature of flue gases, T=250o CFlow rate, Q=25000 m3/h or 6.944 m3/s

Answered: Gases after combustion are discharged…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

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Gases after combustion are discharged from a flue in a facility to the atmosphere at a temperature of
250 °C and a flow rate of 25000 m3
/h. It is desired to benefit from the heat of this waste gas in heating.
There is a site with 40 residences, each with a heating load of approximately 8 kW, located 3 km from
the facility.
1- Determine the substation capacity to be used, taking into account the hot water requirement for
each house on the site.
2- Determine the substation inlet/outlet temperature and the heat exchanger water inlet/outlet
temperatures. The temperature of the water leaving the heat exchanger is required not to exceed 95
° C. The pipeline between the facility and the site is underground pipeline. Determine the required
data by considering the region where the facility is located, calculate the heat losses in the line and
find the required insulation thickness.
3- Calculate the total capacity including losses and determine the required exchanger dimensions.

(Can you solve it with the formulas given in the pictures.)

8 Underground pipelines
8.1 General
Pipelines are laid in the ground with or without thermal insulation, either in channels or directly in the soil.
8.2 Calculation of heat loss (single line) without channels
8.2.1 Uninsulated pipe
The heat flow rate per metre, qe, for a single underground pipe is calculated by Equation (73):
LE
(73)
R + RE
where
e, is the medium temperature;
ee is the surface temperature of the soil;
Ri is the linear thermal resistance of the insulation;
RĘ is the linear thermal resistance of the ground for a pipe laid in homogeneous soil;
iE is the design thermal conductivity of the ambient soil;
HẸ is the distance between the centre of the pipe and the ground surface.
The linear thermal resistance of the ground for an uninsulated pipe, as shown in Figure 11, is given by
Equation (74):
RE
arcosh 2HE
(74)
which, for HE/D, > 2, may be simplified to Equation (75):

The intermal diameter, D, is identical to D (where - 1). The linear thermal resistance of the ground, RE.
becomes, in this case, as given by Equation (78):
(78)
2 d
D.
which, for HeD, > 2, may be simpified to Equation (79):
4 HE
D.
1
(79)
Figure 11- Underground pipe without insulation
8.2.2 Insulated pipe
For underground pipes with insulating layers, as shown in Figure 12, the themal resistance is caloulated by
Equation (76):
(76)
NOTE
The concentric layers can consist ot for example, insularing material and sheathing (eg jacket pipe)
embedded in a bottoming (eg. sand) with a square cross-section.
Figure 12- Underground pipe comprising several concentric layers
The square cross-section of the outer layer with side length, a, is taken into consideration with an equivalent
diameter as given by Equation (77
D,= 1.073 a
(77)

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