Forced Convection (in a cross flow heat exchanger)

3rd Year Thermodynamics Lab Report

Mechanical Engineering Science 10

Forced Convection (in a cross flow heat exchanger)

Summary
The aim of this lab is to determine the average convective heat transfer coefficient for forced convection of a fluid (air) past a copper tube, which is used as a heat transfer model.

Introduction
The general definition for convection may be summarized to this definition "energy transfer between the surface and fluid due to temperature difference" and this energy transfer by either forced (external, internal flow) or natural convection.
Heat transfer by forced convection generally makes use of a fan, blower, or pump to provide high velocity fluid (gas or liquid). The high-velocity fluid results in a decreased thermal resistance across the boundary layer from the fluid to the heated surface. This, in turn, increases the amount of heat that is carried away by the fluid. [1]

Theory Background [2]

Considering the heat lost by forced convection form the test rod. The amount of heat transferred is given by (1)

Where = rate of heat transfer, unknown value.
 = film heat transfer coefficient, this is what we need to found out.
A = area for heat transfer, this is the area of the cross section area of test section.
T = temperature of the copper rod, the temperature after heating. Ta = temperature of air, surrounding temperature.

So, in any period of time, dt, then the fall in temperature, dT, will be given as:

(2) Where m = mass of copper rod, cp = specific heat of the copper rod, J/kgK

Eliminating Q from (1) and (2) then

Since Ta is constant, dT=d(T-Ta)

Integrating gives:

At t = 0, T=To, hence C1 = ln(T-To), hence:

Or

Therefore a plot of ln((T-Ta)/(Tmax-Ta))) against t should give a straight line of gradient from which the heat transfer coefficient, , can be found.

To find the velocity of air passing the rod, first the velocity upstream must be found.

From basic fluid flow theory in the air stream And in the measuring manometer

Therefore (3) Where a = density of air w = density of fluid in manometer v = mean velocity of air h = head in manometer

Therefore measuring the air temperature and air pressure the density can be found,

Where R=289 J/kg K. if w is taken as 1000 kg/m3 and h is measured in m, then

however the velocity, u, used in heat transfer calculations is normally based on the minimum flow area.

Therefore with the single rod , since the inclusion of the rod reduces the cross section and increases velocity.

Practical forced convection heat transfer relationships are often expressed in the dimensionless form
Nu = C.Ren.Prm

However for gases, Pr is virtually constant, therefore

Nu = K.Ren

Typical K and n values are (for Pr  0.7)

Re
K
n
3 - 35
0.795
0.384
35 - 5000
0.583
0.471
5000 – 50 000
0.148
0.633
50 000 – 230 000
0.0208
0.814

Apparatus
Figure 1 shows the test section which contains 18 removable Perspex rods. Any slot can be inserting with a test rod which made of copper and connect with computer. This test section are sealed in an enclosed box made from isolating material which make sure that no heat will escape to the surrounding. The heat flow rate from the test rod is found by heating the cylinder in an electrical heater.

The cooling is provided by a cooling fan, the cooling rate can be change by controlling the inlet area of the fan.

Procedure

1. Insert the test rod in electrical heater leave it until the temperature reading does not rise anymore.
2. Switch on cooling fan and change the inlet area to 20%.
3. Take the reference temperature using the thermometer by the test section.
4. Replace any Perspex rod with test rod and start recording the temperature change against time.
5. Switch off the cooling fan pull out test rod and insert it back to heater, keeping heating until reached maximum temperature again.
6. Switch on cooling fan and change the inlet area to 40%.
7. Repeat step 3 and change adjusting cooling fan inlet area to 60%, 80% and 100%.
8. Organize the results and put them in table then plot diagram.

Results
Plot the time against temperature change in the tube due to different inlet velocities.

From theroy background we know that the gradient of this diagram should equal to the gradient of - .
, this should equal to since the mass and specific heat of the copper rod does not change, we can found α.

From above results we can conclude that heat transfer coefficient can be changed by: (1) Change the area of cross section (2) Plug in more tubes

Discussion
1. Perform the necessary calculations to find the influence of free stream velocity, V, on the heat transfer coefficient, , over the entire range of velocities measured.
2. Convert the above experimental data to a dimensionless form, and plot the Nusselt Number as a function of the Reynolds number, Re , on a linearlized plot, where: and d is the diameter of the disk.
3. Estimate the uncertainty of the experimental data and plot appropriate uncertainty bands on the above plot.
4. What is the main error in this lab and how can we minimize it?
5. Due to the resistance-temperature characteristics of the thermistor, it is very easy to overheat the thermistor and destroy it. The thermistor overheat protective circuit used in this experiment guards the thermistor, against overheating, by switching off the system when a certain temperature is exceeded. Explain how it determines this temperature. Also, is it possible to adjust this temperature? If yes, explain, how? [3]

Conclusions
The flow of fluids and heat transfer in tube banks represents an idealization of many industrially important processes. Typical examples include filtration, flow in biological systems, tubular heat exchangers, flow and heat transfer in fibrous media as encountered in polymer processing and in insulation materials, etc. Additional examples where this flow configuration is of relevance include flow in the fluidized bed drying of fibrous materials (such as coconut shell, rice husk) and paper pulp suspensions and in food processing applications (Kiljanski & Dziubinski, 1996; Mauret & Renaud, 1997). Notwithstanding the importance of the detailed kinematics of the flow and temperature fields, it is readily agreed that the variables of central interest in all these applications are the frictional pressure gradient and the convective heat transfer coefficient (or the rate of heat transfer) as functions of the pertinent system variables. Consequently, over the years, considerable research effort has been expended in developing satisfactory methods for the prediction of pressure drop for the flow of incompressible Newtonian fluids in cross-flow configuration over a collection of circular cylinders, as can be gauged from the number of books and survey articles in this field (e.g., [Zukauskas 1987a] and [Zukauskas 1987b], Chap. 6; Drummond & Tahir, 1984; Nishimura, 1986; Satheesh, Chhabra, & Eswaran, 1999; Shibu, Chhabra, & Eswaran, 2001). Perhaps it is fair to point out here that a bulk of the literature relates to momentum transfer or the estimation of frictional pressure drop incurred during the cross flow of fluids over tube banks in the low Reynolds number region. This work addresses the question of the prediction of the Nusselt number as a function of the Reynolds and Prandtl numbers for a range of voidages of tube banks. It is, however, instructive and useful to briefly summarize the pertinent studies available in the literature. [5]

References
[1]: http://mizisystem.blogspot.co.uk/2011/10/force-convection.html
[2]: Laboratory Handbook
[3]: Experiment 8 Forced Convection on a Flat Disk
[4]: http://dspace.mit.edu/bitstream/handle/1721.1/61456/HTL_TR_1969_064.pdf?sequence=1
[5]: FLUENT - Forced Convection by Yong Sheng Khoo, last edited by Rajesh Bhaskaran
Fig.1 Laboratory Handbook

References: [1]: http://mizisystem.blogspot.co.uk/2011/10/force-convection.html [2]: Laboratory Handbook [3]: Experiment 8 Forced Convection on a Flat Disk [4]: http://dspace.mit.edu/bitstream/handle/1721.1/61456/HTL_TR_1969_064.pdf?sequence=1 [5]: FLUENT - Forced Convection by Yong Sheng Khoo, last edited by Rajesh Bhaskaran Fig.1 Laboratory Handbook