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The convection heat transfer coefficient on a vertical plate from surface temperature measurements: results

Answers to questions

A1 Pointed screws are used in an effort to minimise the heat lost to the holding rig. The area available for heat flow by conduction into the clamp and then to the rig is very small by having sharp–pointed screws and therefore conduction heat loss can be neglected.

A2 One method would be to use a least squares method and by regression analysis obtain a better value for h. However, there is usually considerable uncertainty in the convection coefficient therefore a more accurate calculation of h is unnecessary.

A3 At the start of cooling, using the initial temperature (80 °C), surface area of the plate (1.848 * 10-2 m2), the Stefan-Boltzmann constant (5.669 * 10-8 W/m2 K) , typical emissivity (0.09) and the ambient temperature (18 °C), an instantaneous initial radiation heat rate as well as an initial convection heat rate can be computed. Care is taken to convert all temperatures to kelvin for the radiation calculation.

Evaluating we get 0.79 watts for radiation and 11.45 watts for convection using an assumed h = 10 W/m2 °C. As the temperature falls the radiation rate will decay much quicker than the convection rate due to the fourth power temperatures.

From the curves of Figure 4, The following observations can be made in relation to the best match h=10 theoretical curve chosen:

The measured temperature is more concave or decays more rapidly than the h=10 curve initially at the higher temperatures from time zero up to about 400 seconds of cooling time. This confirms the rapid radiation heat rate decay.

From about 400 to 850 seconds on the time line, the measured temperature lines up almost perfectly with the h=10 theoretical curve. Then at about 850 seconds of cooling time the measured temperature starts to separate from the h=10 curve. As radiation loss would have almost disappeared, its effect on heat loss would also disappear.
It is interesting to observe that the measured temperature line follows almost exactly the curvature of the h = 9 theoretical curve, except for a shift in values. About a 2-degree temperature difference is maintained throughout cooling between these curves. Then, if radiation were not present, the value of h = 9 or somewhere between 9 and 10 should probably be chosen as its curvature more closely matches the curvature of the measured temperature. With radiation not present, the curves would probably line up because the 2-degree temperature shift would disappear. However, radiation even though minimal can not be eliminated.

Therefore, we can conclude that radiation can be neglected if the value h=10 is selected as best match because this value already compensates somewhat for the radiation loss.

Teachers’ notes
Further study

The convection coefficient is not constant throughout the surface of a vertical plate. How is its variation for the case of a vertical plate in free convection?

The convection heat transfer coefficient depends on a large number of factors. It is usually very difficult to determine and there is usually considerable uncertainty associated with it. For more detail and insight into convection, the boundary layer theory used to explain the convection heat transfer phenomena presented in many heat transfer textbooks should be consulted.

REF.1 Holman, J. P., "Heat Transfer", 7th ed., McGraw-Hill, NY, USA, 1992, p. 139-142.

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