The plate gradually oxidizes over time so that the surface emissivity increases to 0.5. Calculate the resulting temperature in the plate including radiation heat transfer to the surroundings at the same temperature as the ambient temperature.
GIVEN
Plate in Problem 4.34 oxidizes
FIND
(a) New temperature distribution considering radiation heat transfer
ASSUMPTIONS
(a) Neglect temperature gradients through the plate thickness
SKETCH
Addition of radiative heat transfer from the plate can be most easily handled by computing the radiative heat transfer coefficient for each node (using the temperature for the node calculated from the previous iteration) and by then adding this radiative heat transfer coefficient to the convective heat transfer coefficient for the present iteration. The radiative heat transfer coefficient for node i is
hri= ? ? (Ti2 + T?2) (Ti + T?). The following table gives the results for the Gauss-Seidel iteration. (Recall that temperature must be expressed in Kelvins.)
The peak temperature has been reduced by about 9.8 K due to radiation.
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