Heat Transfer

ME-305
Lab Report No. 7
Temperature Distribution along Extended Surfaces

Submitted by

NUST Scholar Hania Irfan (99-A) 222614

NUST Scholar Koaib Kaleem (99-A) 222611
Avn Cdt Abdullah Khan (99-A) 22099027
Avn Cdt Muhammad Sennan Khan (99-A) 22099018
Avn Cdt Najm-us Saqib (99-A) 22099039

Submitted to
Lab Engineer Zeeshan Khan
Objective
(i) To measure the temperature distribution along an extended surface
(ii) To compare the calculated results with the theoretical analysis.
Theory
The extended surface heat transfer is the most conventional method enhancement of heat
transfer by extending the net effective area available for heat transfer.
For the extended heat transfer surfaces (fins), there are two parallel heat transfer processes. The
one is the convective heat transfer from the unfinned surface to the fluid, and the other is the
conductive heat transfer through the fins and then from the fin surface to the fluid by heat
convection.
The expression of fin efficiency depends on the fin profile. Some typical examples of the fin
profiles are longitudinal fins of rectangular, trapezoidal, or parabolic profiles; radial fins of
these profiles; and cylindrical, truncated conical, or truncated parabolic spines.

The fin in the experiment is an adiabatic one so we used those conditions to calculate its
parameters like fin temperature distribution and fin heat transfer rate.
Apparatus

HEAT TRANSFER SERVICE UNIT (H111)

The Hilton Heat transfer service unit H111 is a benchtop unit designed to support and
instrument various optional heat transfer experiments to demonstrate one or more fundamental
methods of heat transfer. It consists of:

a. Steel fabricated console which contains main input and a variable voltage 0-240 Volts at
2 amps, and a power outlet point for connecting optional equipment.

b. 12 Type K input sockets for thermocouples. These are connected using miniature plugs
which are suitable for temperatures in the range of 0-999.9 oC.
 c. It has a 30mA residual current circuit breaker for disconnecting the system from the
mains in case of current leakage.

EXTENDED SURFACE HEAT TRANSFER SERVICE UNIT (H111E).

The Hilton Extended surface heat transfer H111E accessories allow the investigation of one-
dimensional conduction from a pin. A small diameter metal rod is heated at one end and the
remaining exposed length is allowed to cool by natural convection and radiation. This results in
a dimensioning temperature distribution along the bar that is measured by regularly spaced
thermocouples. The H111E is designed to be used with and installed alongside the heat transfer
service unit service H111.
a. The accessories compare a 10mm diameter brass rod of approximately 350mm
effective length mounted horizontally with support at the heated end and a mounting at
the opposite end.
b. Inside an insulated hosing is a 240 Volt electric heater in direct contact with the
brass rod. The heater has a normal power rating of approximately 30 Watts at 240 Volts
AC. The power supplied to the heated cylinder is provided by the heat transfer service
unit H111. The transfer service unit H111 also allows the operator to vary the power
input to the heater by controlling the voltage supply to the heater element.
c. For safety purposes, a thermostat limits the maximum temperature of the heater to
approximately 150 °C.
d. Eight thermocouples are located at 50mm intervals along the rod to record the
surface temperature. These are connected to the heat transfer service unit H111 through
miniature plugs. The thermocouples are attached to the rod to minimize errors from
conduction effects. An additional thermocouple is mounted on the unit to record the
ambient air temperature.
e. To protect the thermocouple from damage, all lead termination is mounted firmly
into turning and conduit. Also, the rod is coated with a heat resistant matt black paint to
provide a constant radiant emissivity close to 1.

Procedure
1. Ensure that the main switch is in OFF position.
2. Switch on the apparatus.
3. Make sure the thermocouple components are in contact with each other.
4. Take the reading for the voltage and the current supplied from the digital display.
5. Take readings for temperatures T1, T2, T3, T4, T5 and T6 for the thermocouples 1, 2, 3,
4, 5 and 6. These are the experimental values.
6. To calculate theoretical values of temperatures, first we need to calculate value of m by
iterative process. (initially m = 7.4)
 7. Calculate (Tx –Ta) / (T1 – Ta) and coshm (L –x) / coshmL for number of temperatures
and compare these results.
8. Based upon the result, change the assumed value of ‘m’ remembering that reducing the
value of ‘m’ will increase the value of coshm (L –x) / coshmL.
9. Repeat till a reasonably accurate value of ‘m’ has been achieved, then Tx can be
calculated using the following equation
Tx = (T1 – Ta) (coshm (L –x))/coshmL + Ta
10. Compare theoretical and experimental values.

Safety Precautions
 Follow proper start-up and shut-down procedures to prevent sudden temperature changes.
 Adhere to SOPs provided by lab supervisor.
Observations & Calculations
Ambient Temperature T9 or Ta = 31°C

Sample No Readings Distance from T1 (m)

V Volts 215 -
I Amps 0.004 -
T1 °C 85.5 0
T2 °C 71.2 0.05
T3 °C 59.5 0.1
T4 °C 50 0.15
T5 °C 43.6 0.2
T6 °C 40.7 0.25
T7 °C 38.5 0.30
T8 °C 37 0.35

Calculation of m by iterative process,

(Tx−Ta) coshm(L – x )
T 1−Ta coshmL
True
m=6.3 m=6.5 m=6.6 m=6.7 m=6.8 m=6.9 m=7.0 m=7.1 m=7.2 m=7.3 m=7.4 m=7.5 m=7.6 m=7.7 m=7.8 m=7.9 m=8.0 m=8.1 m=8.2
Values
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0.7376 0.7375 0.7294 0.7255 0.7216 0.7177 0.7138 0.71 0.7062 0.7024 0.6987 0.695 0.6913 0.6877 0.684 0.6804 0.6769 0.6733 0.6698 0.6664
0.5229 0.5487 0.5366 0.5307 0.5248 0.5191 0.5134 0.5078 0.5023 0.4968 0.4915 0.4862 0.481 0.4758 0.4707 0.4657 0.4608 0.4559 0.4511 0.4463
0.3486 0.4149 0.401 0.3942 0.3876 0.3811 0.3747 0.3685 0.3624 0.3564 0.3505 0.3447 0.339 0.3335 0.328 0.3227 0.3175 0.3123 0.3073 0.3023
0.2312 0.3226 0.3081 0.3011 0.2942 0.2876 0.2811 0.2747 0.2686 0.2626 0.2567 0.2509 0.2454 0.2399 0.2346 0.2294 0.2243 0.2194 0.2146 0.2099
0.178 0.2625 0.248 0.241 0.2342 0.2276 0.2212 0.215 0.209 0.2031 0.1975 0.1919 0.1866 0.1814 0.1763 0.1714 0.1667 0.1621 0.1576 0.1532
0.1376 0.2288 0.2143 0.2074 0.2007 0.1942 0.188 0.1819 0.176 0.1704 0.1649 0.1595 0.1544 0.1494 0.1446 0.1399 0.1354 0.131 0.1268 0.1227
0.1101 0.2179 0.2034 0.1966 0.1899 0.1835 0.1773 0.1713 0.1655 0.1599 0.1545 0.1492 0.1441 0.1392 0.1345 0.1299 0.1255 0.1212 0.117 0.113

Temperatur T2 T3 T4 T5 T5 T7 T8 AVG
e
Value of m 6.3 6.7 7.3 7.8 7.7 7.9 8.2 7.41
So, to calculate the theoretical value of T1-T8 we will use m = 7.41 in following formula
Tx = (T1 – Ta) (coshm (L –x) )/coshmL + Ta

Result

Supporting Material (MATLAB Code)

Individual Analyses:
N/S Hania Irfan
We took readings from the temperature sensors and used an iterative process to reach our value
of ‘m’. For the given dataset, the iterations yielded mostly accurate results in comparison with
the theoretical results. We noticed that by taking an average of m, we were able to calculate the
temperature distribution as being very close to accuracy.
NS Koaib:
The comparison between theoretical and actual value shows very little error, which indicates
that the value of m calculated through iterative process holds good, as well as the value of
temperatures taken by thermocouple are somewhat accurate.
A/C Sennan Khan:
In this lab, the readings obtained from the thermocouples helped us calculate the value of m
using iterations, which were reasonably accurate when compared with the theoretical vals.
A/C Najam:
Assessment is that using a high-conductivity fin, temperatures were recorded from base to tip.
These readings were compared to theoretical predictions, with expected trends generally
aligning. Deviations were attributed to experimental errors or unaccounted heat losses. The
calculated efficiency and effectiveness demonstrated the fin's performance in enhancing heat
transfer.
A/C Abdullah:
The extended surface heat transfer method enhances heat transfer by increasing the effective
area. Fins improve heat dissipation but reduce efficiency with longer lengths or higher
resistance. In the experiment using an adiabatic fin and the Hilton Heat Transfer Service Unit
(H111), temperature distribution and heat transfer rate were measured. The unit, equipped with
a variable voltage supply and power outlet, supports various heat transfer experiments

Lab Assessment Rubrics

Below
Assessment Outstanding Good Average Poor
SNO Average
Parameters (05) (04) (03) (01)
(02)
Safety Procedures
1 (x1.5)
Equipment Handling
2 and Operations (x1.5)

Group Participation
3 (x1)
Individual Performance
4
(x 6)
Methodology adopted
5 (x5)
Accuracy and Critical
6 Analysis of Results
(x5)