Experiment 5

Objectives:
To determine the combined heat transfer (Qradiation + Qconvection) from a horizontal cylinder in natural
convection over a wide range of power inputs.

Apparatus:
• TXC-CC Heat Transfer Accessory.
• TSTCC Service Unit with Computer.
Description:
The equipment is divided into two parts: the forced or free convection unit and the radiation unit.
The forced or free convection part carries out the following functions:
• Create the flux of necessary air and face it towards the cylinder.
• Measurement of the air flow.
• Measurement of inlet and outlet air temperatures.
How the Combined Convection and Radiation Module works:

Theory:
If a surface having a temperature greater than its surroundings is located in stationary air at the
same temperature as the surroundings, then heat will be transferred from the surface to the air and
the surroundings. This transfer of heat will be a combination of natural convection to the air and
radiation to the surroundings.
In case of natural convection the Nusselt number (Nu) depends on the Grashof number (Gr) and
Prandtl numbers (Pr) and the heat transfer correlation can be expressed in the form:
Nu = f ( Gr , Pr ) and the Rayleigh number Ra = ( Gr x Pr )
The following theoretical analysis uses an empirical relationship for the heat transfer due to natural
convection proposed by VT Morgan in the paper “ The Overall Convective Heat Transfer from
smooth Circular Cylinder ” published in TF Irvine and JP Hartnett (eds.), Advances in Heat
Transfer vol. 16, Academic, New York, 1975, pp 199-269
If
Ts = surface temperature of cylinder (K)
D = Diameter of cylinder (m)
L = Heated Length of cylinder (m)
Ta = Ambient Temperature of air (K)
Heat Transfer Area (surface area) As = (πDL) (𝑚2)
Heat loss due to natural Convection Qc = HcmAs(Ts-Ta) (W)
Heat loss due to radiation Qr = HrmAs(Ts-Ta) (W)
Total Heat Loss from the cylinder Qtotal = Qc+Qr (W)
The average heat transfer coefficient for radiation Hrm can be calculated using the following
relationship:

𝑇𝑠 4 − 𝑇𝑎 4
𝐻𝑟𝑚 = 𝜎𝜉𝐹 [ ]
𝑇𝑠 − 𝑇𝑎
Where,
σ = 5.67×10−8 W𝑚−2𝐾−4 (Stephen Boltzmann constant)
ξ = Emissivity of surface
F = 1 (View Factor)
The average heat transfer coefficient for natural convection Hcm can be calculated using the
following relationship:
𝑘. 𝑁𝑢. 𝑚
𝐻𝑐𝑚 = (Wm−2 K −1 )
𝐷
𝑁𝑢 = 𝑐(𝑅𝑎𝐷 )𝑛 (From Morgan, where c and n are obtained from the Table 1)
𝑔β(𝑇𝑠 − 𝑇𝑎 )𝐷3
𝑅𝑎𝐷 =
𝜈2
 1
β=
𝑇𝑓𝑖𝑙𝑚
(K-1)

𝑇𝑠 +𝑇𝑎
𝑇𝑓𝑖𝑙𝑚 = (K)
2

𝑔β(𝑇𝑠 − 𝑇𝑎 )𝐷3
𝐺𝑟𝐷 =
𝜈2
𝑅𝑎𝐷 = 𝐺𝑟𝐷 x 𝑃𝑟
Where,
Ra = Rayleigh number
Gr = Grashof number
Nu = Nusselt Number
g = Acceleration due to gravity = 9.81 m/s2
β = Volume expansion coefficient (𝐾−1)
ν = Dynamic Viscosity of air (m2s-1)
k = Thermal conductivity of air (Wm-1K-1)
Note: k, Pr, and ν are physical properties of air taken at film temperature and can be found
from the table-2.
Table listing constant c and exponent n for natural convection on a horizontal cylinder (source-
Morgan):
Table 1:

Table 2:

Alternatively, a simplified equation may be used to calculate the heat transfer coefficient for free
convection from the publication “Heat Transmission”, 3rd edition, McGraw-Hill, New York, 1959.
 𝑇𝑠 − 𝑇𝑎 0.25
𝐻𝑐𝑚 = 1.32 [ ] (Wm−2 K −1 )
𝐷
Procedure:
1. Setup the Equipment
2. Set the heater to the desired power input.
3. Allow the system to reach a steady-state temperature
4. Measure and record the temperatures.
5. Find the other parameters given in the table

Readings and Calculations:

Heater T1 T2 Hcm Hrm Qc Qr Qout = Qc + Qr

1.
2.
3.
4.
5.
6.
7.
Results and Discussion:

This experiment investigated the combined heat transfer due to natural convection and radiation
from a heated horizontal cylinder. The results showed that as power input increased, the surface
temperature of the cylinder rose, leading to greater heat loss. Convection contributed more to
heat transfer at lower temperatures, while radiation became more significant at higher
temperatures.

The experiment also highlighted the practical importance of these heat transfer modes in
engineering applications like heat dissipation in machinery and insulation systems. Minor
variations in results could be due to measurement inaccuracies or external factors like air
currents. Overall, the experiment successfully demonstrated the effects of convection and
radiation in heat transfer.