ALEXANDRIA UNIVERSITY
FACULTY OF ENGINEERING
MECHANICAL ENGINEERING DEPARTEMENT
Energy and Environment
Assignment 1
‫االسم‪ :‬مصطفى سعيد شعبان حسن‬
‫سيكشن‪10 :‬‬
‫رقم الجلوس‪436 :‬‬
‫‪Page | 1‬‬
Table of Contents
Flat plate system data assumption used for the thermal analysis: .................................. 3
Flat-plate collectors connected in series (case 1): ........................................................... 3
Flat-plate collectors connected using mixed configuration (case 2): ............................. 5
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Flat plate system data assumption used for the thermal analysis:
Ul: Overall heat transfer coefficient
W: Tube spacing
Do: Outer diameter of tubes
Di: Outer diameter of tubes
δ: Plate thickness
K: Thermal conductivity of pate material
hi: Heat transfer coefficient Inside tubes
L: Length of fin
Ac: Collector area
τα: Optical efficiency
Cp: Specific Heat of Water
Gt: Solar irradiance
Ti: Inlet temperature of the water
Ta: Ambient temperature
6.9 W/m2 C
0.12 m
0.015 m
0.0135 m
0.0004 m
385 W/m k
320 W/m2 K
0.0525 m
4 m2
0.8
4186 J/kg C
800 W/m2
20 C
15 C
Flat-plate collectors connected in series (case 1):
Thermal analysis results (ignoring bond resistance):
Assuming using 4 flat plates in a series configuration and total mass flow rate of
water equals 0.06 (kg/s), the results of the thermal analysis would be:
Qu overall: Overall useful heat gain
η overall: Overall efficiency of the series configuration
To: Outlet water temperature
7278.855 W
57%
48.98 C
Equations used for calculating the useful heat gain and the thermal efficiency of
flat plates connected in series with N number of plates:
𝑸𝒖 (𝟏) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝟏) − 𝑻𝒂)]
𝑸𝒖 (𝟏) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝟏) − 𝑻𝒊 (𝟏))
Ac: Collector area.
FR: Heat removal factor.
Ul: Overall heat transfer coefficient.
Ta: Ambient temperature.
Ti: Inlet temperature.
Qu (1): Useful heat gain from the first flat plate collector.
To (1): Output fluid temperature from the first flat plate.
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𝑸𝒖 (𝟐) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝟐) − 𝑻𝒂)]
𝑸𝒖 (𝟐) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝟐) − 𝑻𝒊 (𝟐))
Qu (2): Useful heat gain from second flat plate collector.
To (2): Output fluid temperature from second flat plate.
Ti (2): Input fluid temperature to the second flat plate.
As:
𝑻𝒊 (𝟐) = 𝑻𝒐(𝟏)
𝑸𝒖 (𝑵) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝑵) − 𝑻𝒂)]
𝑸𝒖 (𝑵) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝑵) − 𝑻𝒊 (𝑵))
Qu (N): Useful heat gain from last flat plate collector.
To (N): Output fluid temperature from the last flat plate.
Ti (N): Input fluid temperature to last flat plate.
As:
𝑻𝒊 (𝑵) = 𝑻𝒐 (𝑵 − 𝟏)
To (N-1): Output fluid temperature from the second to last flat plate.
𝑸𝒖 (𝒔𝒆𝒓𝒊𝒆𝒔) = 𝑸 (𝟏) + 𝑸 (𝟐) + ⋯ + 𝑸 (𝑵)
Qu (series): Total heat gain from all plates connected in series.
𝜼 (𝒔𝒆𝒓𝒊𝒆𝒔) =
𝑸𝒖 (𝒔𝒆𝒓𝒊𝒆𝒔)
𝑨𝒄 𝑮𝒕 𝑵
η (series): Overall efficiency of total plates connected in series.
N: number of plates connected in series.
Gt: Solar irradiance.
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Flat-plate collectors connected using mixed configuration (case 2):
Thermal analysis results (ignoring bond resistance):
Assuming using 4 flat plates in mixed configuration and total mass flow rate of
water equals 0.12 (kg/s), the results of the thermal analysis would be:
Qu overall: Overall useful heat gain
η overall: Overall efficiency of the mixed configuration
To: Outlet water temperature
8005.87 W
63%
35.9 C
Equations used for calculating the useful heat gain and the thermal efficiency of
flat plates connected used mixed configuration with N number of plates:
Mixed connections consist of both series and parallel connected plates to form the
mixed configuration of the system.
Series connection part:
𝑸𝒖 (𝟏) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝟏) − 𝑻𝒂)]
𝑸𝒖 (𝟏) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝟏) − 𝑻𝒊 (𝟏))
Ac: Collector area.
FR: Heat removal factor.
Ul: Overall heat transfer coefficient.
Ta: Ambient temperature.
Ti: Inlet temperature.
Qu (1): Useful heat gain from the first flat plate collector.
To (1): Output fluid temperature from the first flat plate.
𝑸𝒖 (𝟐) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝟐) − 𝑻𝒂)]
𝑸𝒖 (𝟐) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝟐) − 𝑻𝒊 (𝟐))
Qu (2): Useful heat gain from second flat plate collector.
To (2): Output fluid temperature from second flat plate.
Ti (2): Input fluid temperature to the second flat plate.
As:
𝑻𝒊 (𝟐) = 𝑻𝒐(𝟏)
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𝑸𝒖 (𝑵) = 𝑨𝒄 𝑭𝑹 [𝑮𝒕𝝉𝜶 − 𝑼𝒍 (𝑻𝒊 (𝑵) − 𝑻𝒂)]
𝑸𝒖 (𝑵) = 𝒎˚ 𝑪𝒑(𝑻𝒐 (𝑵) − 𝑻𝒊 (𝑵))
Qu (N): Useful heat gain from last flat plate collector.
To (N): Output fluid temperature from the last flat plate.
Ti (N): Input fluid temperature to last flat plate.
As:
𝑻𝒊 (𝑵) = 𝑻𝒐 (𝑵 − 𝟏)
To (N-1): Output fluid temperature from the second to last flat plate.
𝑸𝒖 (𝒔𝒆𝒓𝒊𝒆𝒔) = 𝑸 (𝟏) + 𝑸 (𝟐) + ⋯ + 𝑸 (𝑵)
Qu (series): Total heat gain from all plates connected in series.
𝜼 (𝒔𝒆𝒓𝒊𝒆𝒔) =
𝑸𝒖 (𝒔𝒆𝒓𝒊𝒆𝒔)
𝑨𝒄 𝑮𝒕 𝑵
η (series): Overall efficiency of total plates connected in series.
N: number of plates connected in series.
Gt: Solar irradiance.
Parallel connection part:
It will be parallel to those plates that are connected in series so that the heat gain of the
system can be doubled depends on the number of parallel connections we made, the
flow rate of the working fluid also will be increased.
This is called a mixed connection so that we mix parallel and series configurations.
As:
𝑸𝒖 (𝒎𝒊𝒙𝒆𝒅) = 𝑴 ∗ 𝑸𝒖 (𝒔𝒆𝒓𝒊𝒆𝒔)
𝜼 (𝒎𝒊𝒙𝒆𝒅) = 𝜼 (𝒔𝒆𝒓𝒊𝒆𝒔)
Qu (mixed): Total heat gain from all plates connected in a mixed configuration.
η (mixed): Overall efficiency of total plates connected in a mixed configuration.
M: number of parallel paths of the series connections.
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