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Illustration 5.1
A hot oven is maintained at 180 ^{o}C having vertical door 50 cm high is exposed to the atmospheric air at 20^{o}C. Calculate the average heat transfer coefficient at the surface of the door.
The various air properties at the average temperature [(180+20)/2 = 100^{o}C] are,
k = 0.032 W/m ^{o}C; Pr = 0.7; Kinematic viscosity = 24 x 10^{6} m^{2}/s
At T_{b} = 20^{o}C,
Solution 5.1
First we have to find the Grashof number,
With the help of Gr and Pr, we can estimate the R_{a} number,
Ra = G_{r}P_{r} = 1.16 X 10^{8} X 0.7 = 8.12 X 10^{7}
As Ra < 10^{9}, the eq.5.7 can be used,
5.3 Combined natural and forced convection
As we know that there is hardly any situation in which only natural or forced convective heat transfer occurs. Generally, in all the processes natural and forced convection heat transfer occur but depending upon the contribution made, the process may be approximated as either natural or forced convection problem. However, certain situation needs to be addressed as combined natural and forced convection problem. The following is a thumb rule to determine the individual situations.
In this situation, the following equation may be used,
where, Nu is the Nusselt number due to mixed convection, Nu_{n} is the Nusselt number due to natural convection, and Nu_{f} is the Nusselt number due to forced convection. The value of m is generally taken as 3, whereas positive and negative signs can be used for the convection in the same and opposite directions, respectively.
Illustration 5.2
In the oven door described in illustration 5.1 is subjected to an upward flow of air (that is forced convection). What would be the minimum free stream velocity for which natural convection may be neglected?
Solution 5.2.
Section 5.3 above shows that for the following condition the effect of natural convection may be neglected,
The value of Gr number calculated in the previous illustration was 1.16 X 10^{8}
Thus,
U >> 0.24 m/s
Therefore, the bulk velocity of the air should be far greater that 0.24 m/s.
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