Download The combined forced and free convection heat transfer from

Introduction:
In the unbounded condition, the phenomenon of flow separation, bluff body wake and
prediction of heat transfer from a cylinder have been intensely studied for a long time
because of their fundamental significance in flow physics and their practical importance
in aerodynamic and heat transfer applications. The generation and evolution of vertical
structures in the wake region have a big effect on the drag, heat transfer, flow-induced
vibration and noise problems [2]. The combined forced and free convection heat transfer
from cylinders (of circular or square cross-section) has numerous industrial applications
such as cooling towers, oil and gas pipelines, tubular and compact heat exchangers,
cooling of electronic components, flow dividers in polymer processing applications and
so on. The analysis of mixed convection is more complicated than that of the pure forced
or free convection alone. For low flow velocity and larger temperature difference
between the body and the fluid, the flow and heat transfer are strongly influenced by the
buoyancy force [1]. When the flow velocity is not very high and the temperature
difference between the body surface and ambient fluid is large. The free and forced
convection effects are comparable under such situations. The vortex shedding also
becomes more complicated. Most previous investigations of combined flow and heat
transfer in such situations have focused on circular cylinders. However, flow around the
square cylinder is also an important fundamental problem of engineering interest [3], but
beyond our scopes. The objective of this lab is to calculate the drag coefficient using the
drag force exerted on the cylinder. The purpose of this work is to numerically study the
velocity profiles as well as the Reynolds number associated with force acting on the
control volume causes by an arbitrary flow.
Another paragraph for a brief overview of what we did/found in the lab…
Theory:
Bernoulli’s equation can be most generally expressed as
1
1
U 12  gh1  P2  U 22  gh2
2
2
To measure the pressure in moving fluid, Bernoulli’s equation can be used and expressed
as:
1
1
P1  U12  P2  U 22
(1)
2
2
where  is the density of air under standard conditions, U is the velocity and P is the
pressure. The second term of the right hand side is zero because at the stagnation point,
U is 0. Assuming P2 equal to Pstatic, the velocity can be expressed as:
2( Ptotal  P1 )
U1 
(2)
P1 

The momentum balance equation is express as:

(3)
Fb  Fs   VdV   UU .dA
t cv
cs
where the first term of the right hand side is zero due to the assumption of steady,
incompressible flow. The surface force (Fs) is the sum of drag force and lift force. Lift
force is also zero due to the flow is perpendicular to the plate. The drag coefficient can
be calculated using equation 4 below
(4)
CD 
FD
1
U 2 Ap
2
where Ap is the projected area.
Method:
Air bench free jet station:
Figure 1 is the set up of the experiment. After turned on the air flow, we first determine
the drag force exerted on the cylinder by put enough weight on the weight pan to balance
the cylinder (keep horizontally). The weight then recorded for each different flow.
Along the path of the air flow, we then measured the velocity profiles in the vertical
direction at the outlet surface by adjusted the free stream nozzle at different location.
With each location, the pressure can be measure by reading off the different height from
the manometers.
Figure 1
The pressure of a moving fluid can be determined by using Bernoulli’s equation as shown
in equation 1. From there, the velocity was determined using equation 2. Equation 2
then substitute into equation 4 to get the drag coefficient for a cylinder.
Wind tunnel station:
The set up of the wind tunnel is shown in figure 2 below. With an arbitrary velocity
flow, the pressure distributions along one side of the cylinder surface can be calculated
by measuring the height of multiple tap water manometers. The same procedures are
repeated for two other velocity flows. The velocity for each flow then calculated using
Bernoulli’s equation.
Figure 2
References:
[1] A.K. Dhiman, R.P. Chhabra and V. Eswaran. Steady mixed convection across a
confined square cylinder. International Communications in Heat and Mass Transfer.
A.K. Dhiman, R.P. Chhabra and V. Eswaran
[2] H.S. Yoon, J.B. Lee and H.H. Chun. A numerical study on the fluid flow and heat
transfer around a circular cylinder near a moving wall. International Journal of Heat and
Mass Transfer, Volume 50, Issues 17-18, August 2007, Pages 3507-3520
[3] Atul Sharma and V. Eswaran. Effect of channel-confinement and aiding/opposing
buoyancy on the two-dimensional laminar flow and heat transfer across a square cylinder
International Journal of Heat and Mass Transfer, Volume 48, Issues 25-26, December
2005, Pages 5310-5322