Forced Convection Heat Transfer: Theory, Apparatus, and Results

Forced Convection Heat Transfer
Objective:
1) To determine the convective heat transfer coefficient for forced convection.
2) To determine the velocity and temperature distribution in fluid flow.
Introduction:
In many engineering applications, applications of forced convection heat transfer is found.
Thus it is important to have knowledge of this topic specially while designing heat-
exchangers.
Heat Exchanger is a device used to exchange of heat between two fluids at different
temperatures. The fluid at higher temperature loses heat and the fluid at colder temperature
gains heat and its temperature rises. Thus the heat transfer takes from hot fluid to the cold
fluid.
The transfer of heat can occur in 3 different modes, Conduction, Convection and Radiation.
The key principles acting in heat exchangers are convection and conductive heat transfer. In
this case, heat transfer by radiation is negligible in comparison to other two modes of heat
transfer. In this experiment conduction occurs as the heat from the electric heating tape
passes through the copper pipe wall and then heat transferred to the moving fluid is made
through forced convection.
Theory
In a fluid when there is bulk fluid motion, then the heat transfer takes place by convection.
When there is no bulk motion, then heat transfer occurs by conduction.
Convection involves fluid motion as well as heat conduction.
Heat transfer takes place from the heated surface to fluid passing over the surface have lower
temperature. This is illustrated in figure 1. The fluid motion when caused by a fan or pump,
results in forced convection heat transfer. By Newton’s Law of cooling, this forced
convection heat transfer is given by (Bahrami, n.d.):
̇qconv =h As ( T s−T ∞ ) (W/m2) (1)
Where h = convective heat transfer coefficient (W/m2K)
T ∞= fluid average temperature ( oC)
Ts = pipe surface temperature ( oC)

Calculation of mass flow rate
To determine the mass flow rate an orifice plate in the pipe connects to a manometer on the
instrumentation panel. The equation related to the orifice plate is given as
̇m=0.00365∗√ ( horiface(mm))/(ρair ) (2)
Where
horifice is the manometer reading (mm), and
ρair is the local air density (kg/m3)
To determine the air density at the orifice we use the equation of state
𝑝=𝜌×𝑅×𝑇 (3)
Figure 1. Velocity and Temperature profiles developed during forced convection
(Incropera et al., 2007)
We can calculate the air density downstream (just after) the orifice plate since we know the
pressure and temperature.
Pressure downstream of the orifice
= Atmospheric pressure + Fan pressure – Orifice pressure drop
¿ patm+ ( g∗hfan ( mm ) ) − ( g∗horiface ( mm ) ) (N/m2) (4)
Temperature downstream of orifice is the “inlet temperature test section”

Calculation of velocity distribution
The velocity distribution across the duct can be found by using the pitot tube. From the pitot-
static equation:
∆ ppitot = 1
2 ρair V 2 (5)
V = √(2 ∆ p pitot )/( ρair ) (6)
Δppitot is the pressure difference across the pitot manometer in N/m2.
V is the local velocity at the traverse position. The manometer scale is in units of mm H2O.
Therefore
∆ ppitot =ρH 2O∗g∗(h pitot(mm) /1000) (7)
Using the equation h2p = 100 kg/m3 and substituting in (6) and (7), we get,
V = √ (2∗9.81∗hpitot (mm))/(ρair) = 4.429√ hpitot (mm)/ ρair (8)
The air density at the pitot can be determined by the equation of state
𝑝𝑠𝑡𝑎𝑡𝑖𝑐=𝜌𝑎𝑖𝑟 *𝑅*𝑇𝑎𝑣 (9)
There is variation in the local air temperature across the duct so an average temperature 𝑇𝑎𝑣
is used
pstatic at pitot is the local static pressure
= Fan pressure + Atmospheric pressure – Orifice pressure drop – test length pressure drop.
= (g*hfan (mm)) + patm – (g*horifice (mm)) – (g*hlength (mm)) (N/m2) (10)
Density at the pitot is
ρat pitot= ( pstatic at pitot )
R Tav
(11)
The energy added per metre length of the pipe to the air by the heating tape is found from the
electrical work. There is a heat loss of approximately 4% through the lagging so
The Heat energy added to the air per unit length is given by:
Q=V ∗I∗0.96 /Lheat tape (W/m) (12)
Where
I is the heater current (amps),

V is the heater voltage (volts)
and
Lheattape is the length of the pipe wrapped with heating tape (m)
Since L is 1.75m then
̇Q=0.55V ∗I (W/m) (13)
Using the Newton’s law of cooling , we determine the Heat transferred by convection from
the wall
̇Q=h Aw ( T w−T AV ) (14)
Where:
Aw is the inner surface area of the pipe from start of heating to pitot tube
h is the convective heat transfer coefficient (W/m2.K)
Inner surface area at a distance of 1.475m from datum is given by
𝐴𝑤=𝜋𝐷𝐿=𝜋*0.033*1.475=0.153𝑚2 (15)
Tw is the average wall temperature. The average of temperatures 1 to 7 in table 2
Tav is the average air temperature (Tout + Tin)/2
Where
Tin is the inlet temperature test section, and
Tout is the average of the thermocouple traverse reading (readings 1-30) in table 3
Hence forced convection heat transfer coefficient is found from
Using equation 14 the heat added from the datum to the pitot tube at L = 1.475m is
𝑄̇=1.475 *0.55𝑉 * 𝐼 (W) (16)
𝑄̇= *(ℎ 𝑇𝑤−𝑇𝐴𝑣)=1.475*0.55𝑉*𝐼 (17)
h=(1.475∗0.55 V∗I )/¿ (Tw – Tav) = (5.3 * V * I ) / ( Tw –Tav) (18)
Description of Apparatus
The apparatus used in the experiment is the TD1 Forced Convection Heat Transfer apparatus
(TecQuipment, n.d.).