Forced Convection Cooling of the Finned Insert:
Please refer to Table #4 for the raw data and Table #6 for the calculated data.
Discussion
Natural Convection Cooling of a Flat Plate:
The heat transfer coefficients found by using the equations:
were in the range specified for the free convection of gases, 2-25 W/(m*K), therefore the percent error is 0 %. [1]
Similarly the heat transfer coefficient calculated by using the equation:
was in the range specified for the free convection of gases, 2-25 W/(m*K), therefore the percent error is 0 %. [1]
It can be confirmed that natural convection is taking place since the fluid motion is caused by buoyancy forces that are induced by the density differences due to variation in temperature of the fluids. [1] The results obtained fit the theory learned from the text book and the lecture notes.
Forced Convection Cooling of a Flat Plate:
The heat transfer coefficient calculated by using the equation:
was not in the range specified for the forced convection of gases, 25-250 W/(m*K), and the percent error was calculated to be 17.3 %.
An error that can explain the difference between the calculated and the theoretical values may be that the fan was not working efficiently; also there may not have been steady state heat transfer, hence there was no forced convection.
The generic methods for the calculation for the heat transfer coefficient were not used since the temperature difference was found to be zero, hence the heat transfer coefficient was found to be zero (this is not true since it can be shown from more complex calculations that h = 20.674).
Natural Convection Cooling of the Finned Insert:
The heat transfer coefficients were found by using the equations:
The latter equation used the recommended relation for the average Nusselt number with spacing between the fins whereas the former equation used the generic equation for the calculation of heat transfer coefficients. [1]
In both cases, the heat transfer coefficients were in the range specified for the free convection of gases, 2-25 W/(m*K), therefore the percent errors were 0 %. [1]
Forced Convection Cooling of the Finned Insert:
The heat transfer coefficients found by using the equations:
were not in the range specified for the free convection of gases, 25-250 W/(m*K), therefore the percent errors were 17%, 4.548% & 7.704%, respectively. [1]
Again the errors can be attributed to the fan not functioning properly and causing the less than intended forced convection in the channel and the heat transfer being in a transient state.
A relationship that can be formed from the calculation of the heat transfer coefficients is that as the air flow in the channel is increased, the heat transfer coefficient increases as well since there is a greater amount of heat exchange taking place.
Conclusion
The objective of the laboratory, investigate some important aspects of free and forced convection heat transfer, was achieved with moderate results. The heat transfer coefficients of both the flat plate and the finned insert for natural convection were found to be in the theoretically specified range. This was not the case for the forced convection of both inserts; therefore relatively small percent errors were present. Overall a firm understanding of the concept of convection was gained.
References
[1] Cengel, Y. A., & Ghajar, A. J. (2011). Heat and Mass Transfer: Fundamentals & Applications (4th ed.). The McGraw-Hill Companies.
[2] Equipment for Engineering Education, Instruction & Operation. (1998). Heat Transfer Lab Manual. Hamburg, Germany.
[3] Ledezma, G., & Bejan, A. (1996, June). Heat Sinks with Sloped Plate Fins in Natural and Forced Convection. International Journal of Heat & Mass Transfer, 39(9), 1773-1783.
[4] Tahat, M., Kodah, Z. H., Jarrah, B. A., & Probert, S. D. (2000). Heat Transfers from Pin-Fin Arrays Experiencing Forced Convection. Applied Energy, 419-442.
Appendix A – Tables & Figures
Table 1: Experimental Data for Natural & Forced Convection of a Flat Plate
Table 2: Calculated Data for Natural Convection of a Flat Plate
Table 3: Calculated Data for Forced Convection of a Flat Plate
Table 4: Experimental Data for Natural & Forced Convection of the Finned Insert
Table 5: Calculated Data for Natural Convection of the Finned Insert
Table 6: Calculated Data for Forced Convection of the Finned Insert
Table 7: Percent Error between Theoretical & Calculated Heat Transfer Coefficients
Appendix B – Sample Calculations
Calculations for Natural Convection Cooling of a Flat Plate:
Since RaL is in the range of 104 < RaL <109, the Nu number is calculated in the following manner:
Calculations for Forced Convection Cooling of a Flat Plate:
Calculations for Natural Convection Cooling of the Finned Insert:
The Characteristic Length with respect to the height of the fins:
The Characteristic Length with respect to the spacing between the fins:
Since the fin thickness (t = 0.003 m) is sufficiently smaller than the spacing between the
fins the optimal fin spacing is determined to be:
However the optimal fin spacing and the actual fin spacing do not match therefore this concludes any further calculations with respect to SOpt.
Calculations for Forced Convection Cooling of the Finned Insert:
The air flow is assumed to be turbulent.
Calculations for Percent Error between Theoretical and Calculated Heat Transfer Coefficients:
Natural Convection of a Flat Plate:
Forced Convection of a Flat Plate:
Natural Convection of the Finned Insert:
Forced Convection of the Finned Insert:
Appendix C – Formulas Used
Natural Convection of the Finned Insert:
The first method used to obtain the heat transfer coefficient was by using the generic heat transfer coefficient equation. [2]
The second method used for obtaining the heat transfer coefficient was by using the equation that utilizes the Nusselt number, calculated at optimum spacing and characteristic length. The equation was developed by Bar-Cohen and Rosenhow (1984), in which they employed data under various boundary conditions to gain a correlation for the Nusselt number. [1]
Forced Convection of the Finned Insert:
The first and second methods used to obtain the heat transfer coefficients was by using the generic heat transfer coefficient equations outlaid in the laboratory manual. [2]
The third method used to obtain the heat transfer coefficient was by using the heat transfer coefficient equation that applies the Nusselt’s number and the characteristic length. [1] The equation that is employed for the calculation of the Nusselt number is the same as the equation for the average Nusselt’s number over a flat plate with turbulent flow (since the Reynolds number was less than/equal to 107 or greater than/equal to 5*105; and the Prandtl number was less than/equal to 60 or greater than/equal to 0.6). [1]
It was understood that the correlation used is an equation for turbulent flow across a flat plate but was used anyways because it embodies the flow across the vertical flat plates of the finned insert.
