Butterfly valve half opened
The butterfly is positioned half opened for a reduce airflow velocity. After a 30 second period of time within in a 1 degree temperature range a temperature for the cylinder was taken (T10). Free stream temperature was then taken at T9
Centrifugal Fan turned off
Fan is turn off meaning zero airflow is happening in the duct. After a 30 second period of time within in a 1 degree temperature range a temperature for the cylinder was taken (T10). Free stream temperature was then taken at T9
Measurements taken for calculations of results
Table 1 Measurements taken from cylinder
Table 2 Temperature readings during different airflow velocities
Results
Table 3 Comparison of experimental power and theoretical power from combined heat transfer rates
Figure 1 Effects of changing airflow velocities on heat transfer rates
Analysis
To calculate the heat transfer rates from the cylinder requires finding the energy balance of the system. This means the energy into the cylinder (Electric power to heat cylinder) is equal to the sum of the heat transfer from the cylinders.
Figure 2 Diagram of the different heat transfer rates occurring from the cylinder
Three types of heat transfer were looked at for the analysis. Force convection due to the free stream airflow over the cylinder, free convection due to the temperature differences and radiation emitted from the cylinder surface.
Energy balance equation for heat transfer rates
Forced Convection
This form of convection involves external flow normal to the axis of the cylinder
Determining forced convection from the cylinder required using the fallowing formula
Heat transfer coefficient, Area of the cylinder A, Cylinder Surface Temperature Ts (K) and Free Stream Temperature (K)
Heat transfer is found from determining the Nusselt number
Nusselt Number , Thermal Conductivity k (W/m.K), Diameter of cylinder
Nusselt Number calculated using the Churchill-Bernstein correlation
This requires the Reynolds Number based on the diameter of the cylinder
Table 4 Force convection from cylinder at different velocities
Free Convection
Convection currents induced by buoyancy forces as a result of the density differences caused by the temperature variations. i.e. Temperature of cylinder surface relative to the surround free stream temperature
Determining free convection from the cylinder required using the fallowing formula
Heat transfer coefficient , Area of the cylinder A, Cylinder Surface Temperature Ts (K) and Free Stream Temperature (K)
Heat transfer is found from determining the Nusselt number
Nusselt Number , Thermal Conductivity k (W/m.K), Diameter of cylinder
Nusselt Number calculated using the Churchill-Chu correlation
This requires the Rayleigh Number based on the diameter of the cylinder
Volumetric thermal expansion coefficient (β) is proportional to the film temperature
Table 5 Free convection from cylinder at different velocities
Radiation
As a result of heating the cylinder thermal radiation occurs. This involves radiation been emitted and absorb by the cylinder. The fallowing equation represents the heat transfer rate of radiation from the cylinder
Radiation emitted from the surface = E (emissive power), Absolute rate at which radiant energy is absorbed on to the cylinder surface =
Determining the Radiation exchange meant analysing the cylinder as a diffuse-gray surface relative to large surroundings
= emissivity of cylinder = 0.95, Stefan-Boltzmann constant σ
Table 6 Radiation from cylinder at different velocities
Experimental Power
The experimental power used to heat the cylinder is determined from the reading taken of the RMS voltage and current. Using Ohms law power is calculated as fallows
Table 7 Voltage and current from the Heat transfer service unit H111 that provided power to the cylinder
Assumptions
Steady state conditions
Negligible power lose dissipated by conduction through the end pieces of the cylinder
Uniform cylinder temperature
Radiation exchange is between diffuse-gray surface (cylinder) to large isothermal surroundings
Discussion
Experimental
Through an electric resistance heater the cylinder is brought to a steady state temperature determined by the voltage and current applied. The centrifugal fan provides a free stream temperature and as a result heat transfer occurs. For the experiment convective and radiation heat transfers were looked at. Ideally the conduction losses through the ends of the cylinders should have been taken into account. Varying the free stream velocity allowed for comparison of the effects on the heat transfer rates to be looked at.
Comparisons of Theoretical and experimental
Comparing experimental power results to calculated theoretical results shows a significant difference. In theory all margins of error would be ruled out and the experiment would be performed in a perfect environment for unbiased results.
Comparison of velocity effects on heat transfer rates
Comparing experimental heat transfer rates for the varied airflow showed the effects on each heat transfer rate.
When airflow velocity is at its maximum, forced convection contributes to largest amount of heat transfer. Due to the constant flow and temperature of air over the cylinder surface a temperature difference is maintained resulting in the main heat transfer occurring as forced convection. Free convection and radiation show similar low values.
Reducing the airflow shows force convection still as the main heat transfer rate. Free convection and radiation in this case contributes a larger amount to heat transfer. The reduced constant flow and temperature of air over the cylinder surface results in less forced convection heat transfer occurring
With no airflow force convection is reduced significantly. This occurs due to the temperature difference between the surface of the cylinder and surrounding air becoming significantly smaller. Radiation in this case makes up the largest part of the heat transfer rates. As the temperature of the cylinder increases thermal radiation occurs resulting in heat transfer through emissivity to the surroundings.
Conclusions
Appling a uniform heat source to a cylinder enclosed in a cross-flow air configuration allows for the calculations of the cylinder heat transfer rates. Comparison can be performed between theoretical and experiment results. Results show force convection contributing to the most amount of heat transfer during the max airflow velocity. In the case of a zero airflow velocity, radiation is the main source of heat transfer. Assumptions in the calculations of theoretical results may have lead to differences in comparison.
References
[1] Moran, Shaprio, Munson, Dewitt. 2003. Introduction to thermal systems engineering. New York: Wiley
