Category Archives: EuroSun2008-3

Driving Forces and Resistance to Air Flow in the Duct

The magnitude of the natural convection heat transfer is related to the mass flow rate of the air, which is established by the dynamic balance of two opposing effects: buoyancy and friction. Inherent to the flow inside the duct, are the pressure difference between the inlet and outlet air of the channel since the mean air temperature along the axial length of the duct in the flow direction will change (constant heat flux).

2.3 Driving Forces

It would be expected that the presence of these structural element will increase both the heat transfer rate and the hydraulic pressure loss. Under natural convection, the pressure drop due to the buoyancy forces is a result of the temperature difference between the heated surface and the column of the air in the duct. At a typical height (x) from the base corresponding to length (Lx) of the duct, the buoyancy pressure drop is given by [3].

Подпись: (13)APbx = PmgPexp(Ta, x — Ta, i )Lx sin P

4.2. Resistance to Flow

In the absence of hydraulic losses (variable cross sections, losses through valves, orifices, elbows), the resistance to flow in the channel is resumed to the friction pressure drop (Ap) and was computed as

[10] :

APf = pghf (14)

where, the friction head loss ( h ) is given by:

L V2

duct m

2 gDh

Therefore the pressure drop is expressed as:

Подпись: APf =P йиеУm

2 gDh

For a given BIPVT system, the choice of the duct length (Lduc{) is determined by the dimension of the

roof and therefore any design to optimise energy and heat transfer will be determined by the duct dept. The friction factor (f) for laminar and turbulent flow were respectively evaluated as suggested by Tsuji

[11] , and Smolec [12].

Подпись: (17) (18) f = 1.906(Gr Pr)1/12

f = 1.368(Gr Pr)1/119

3. Experimental Results

5.1. Data Analysis

Подпись: Friction pressure drop Ви yan су pressure drop 50 250 450 650 850 Heat fluxes (W/rn2!

The steady state values were recorded over a period of time. Due to measurement fluctuations in the experiment a statistical uncertainty analysis was conducted. Initial analysis of the raw data yielded the mean and standard deviation of the measurements. Assuming the measurement fit a normal Gaussian distribution, the uncertainty was then calculated with a confidence level of 95%. The error propagation method was used and the average data evaluated. Figure 6 gives the magnitude of friction losses.

Figure 7. Magnitude of pressure drop under Figure 7. Temperature distribution on top plate along

natural convection the duct length at H = 4 cm, slope angle = 44°

It can be seen from figure7, that at a specific heat flux, buoyancy forces can be neglected.

In figure 7, the temperature decrease at the entrance and at the exit is due to radiation losses. Applying a polynomial form of the 6th order to the test data, the temperature distribution as shown in figure 10 can be expressed as:

T(x) = 36.92×6 — 245.8×5 + 605.0×4 — 673.4×3 + 316.8×2 + 0.248x + 55.37

R2 = 0.99

Подпись: Figure 8. Typical temperature profiles of components to steady state for constant heat flux of 350W/m2 Подпись: Figure 9. Temperature profile in ducts

Figure 8 shows a typical temperature profile of components at steady state at a constant heat flux of 350W/m2, while illustrates the variation of the local air velocity as function of various heat fluxes.

As illustrated in figure 8, the air temperature under the wood strips Ta2, Ta4, and Ta6 (figure 2) remained lower than the air temperature in the cavities (Ta1, Ta3, Ta5, Ta7). At steady state the air in the cavities and the bottom plate have the same temperature.

As expected, the presence of the structural elements in the channel constituted an obstacle to the air flow inside the channel due to the increase in pressure drop and friction losses. Consequently, under the same constant heat flux, the reduced air flow rate in the channel due to the wood strips led to an increase in the components temperature as compared to the system without wood strips as illustrated in figure 9.

4. Conclusion

Experimental investigation of temperature distribution in a BIPV system under natural convection has been done. The results of the experiment show that the framing structure of BIPV under natural convection does not contribute to the temperature reduction of photovoltaic module cells. The temperature at the boundaries and the velocity profiles are used to create and validate CFD numerical models [13].


The current ongoing research work is supported by the Solar Building Research Network, a NSERC Strategic Research Network. A special thank to the Solar Calorimetry Laboratory at Queen’s University (Ontario) and the Department of Building, Civil, and Environmental Engineering at Concordia University (Quebec) for hosting the research work.


Symbols Definition

A Cross section area of the duct (m2) L Thickness of bottom insulation (m)

duct oms

C Specific heat at bulk mean air L Thickness of side insulation (m)

p sin s

7th to 10th October, Lisbon — Portugal

temperature [K/kg°C]


Hydraulic diameter of channel (m)


T bp

Bottom plate temperature (K)


Friction coefficient in the channel


a, e

Air temperature at the exit of the channel


Gravitational acceleration (m/s2)


a, г

Mean air temperature at the inlet of the channel

h c

Convective heat transfer coefficient


Mean air temperature (K)

at the bottom plate side (Wm"2K-1).


Depth of cooling duct (m)


sin s

Temperature at the side insulation (K)


Friction head loss



Top plate (heated wall) temperature of the cooling duct (K)


Convective heat transfer coefficient at mean air temperature (Wm-2K-1)



Mean air velocity (m/s)

hsin s

Convective heat transfer coefficient

on the side insulation (Wm-2K-1)


Radiative heat transfer coefficient


Wide of cooling duct (m)


Convective heat transfer coefficient at the top heated side (Wm-2K-1)


Minimum fan pumping power required



Mean air conductivity (W/mK)


Normal random variable


Thermal conductivity of bottom insulation (W/mK)


Standard normal random variable


sin s

Thermal conductivity of side insulation (W/mK)


Thermal conductivity of top side insulation (W/mK)


Total pressure drop in the duct (kPa)


Length of the channel (2.4m)


Pressure drop due to the buoyancy (kPa)


Thickness of top insulation (m)


Friction losses


Typical location at a distance x in the channel (m)

Greek Symbols


Mass flow rate of air (kg/s)


Channel inclination angle [°]


Number of variables

ft exp

Coefficient of volume expansion (1/K)


Nusselt number at the bottom plate


Mean air density (kg/m3)



Nusselt number at the top plate side


Longwave emissivity of top/bottom plates


Energy carried by the air (W)


Stefan-Boltzmann constant (5.67×10-8


Total heat flux [W/m2]


Standard deviation


Heat flux at the bottom plate (W/m2).


Mean dynamic viscosity of air (kg/ms)


Heat loss flux (W/m2)


Kinematic viscosity of air (m2/s)


Heat flux at the top plate (W/m2)

Ohmic heat flux (W/mA2)

T Ambient air temperature (K)


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