Example

Bread is being baked on a stainless steel sheet. The top is cooking nicely but the bottom is not getting done. The oven (ceiling, wall, and floor) temperature is 400°F (204.4°C) and the emissivity and absorptivity are 0.90

1. The bottom of the stainless steel sheet has emissivity absorptivity of 0.25. Assuming a view factor of 1.0, what is the net rate of radiant heat transferred to the bottom of the sheet? Assume that the surface of the bread while cooking and vaporizing water is 212°F (100°C) and that the conduction heat transfer to the stainless steel sheet is to a surface at the same temperature.

2. What is the net rate of heat transfer to the top of the bread, which has emissivity—absorptivity equal to 0.90?

Solution. (1) By substituting the values in equation 22, the net heat that is being transferred to the bottom of the sheet is:

In English units:

q = (0.1713)(10)-8[(0.9)(0.25)(1.0)(860)i - (0.25X0.9X1.0X672)4] = 132 Btu/(h)(ft2)

In SI units:

q = (5.6697)(10)-8[(0.9)(0.25)(1.0)(478^ - (0.25X0.9X1.0X373)4] = 417 W/m2

Checking units:

(2) By substituting the values in equation 22, the net heat that is being transferred to the top of the bread is:

In English units:

q = (0.1713)(10)-8[(0.9)(0.9)(1.0)(860)4 - (0.9X0.9X1.0X672)4] = 476 Btu/(h)(fl?)

In SI units:

q = (5.6697)(10)-8[(0.9)(0.9)(1.0)(478)4 - (0.9X0.9X1.0X373)4] = 1508 W/m2

It is clear that the top portion of the bread is receiving more than 3.5 times the amount of heat being received on the bottom where it is in contact with the stainless steel sheet. This explains why the top, the portion receiving the most heat, is baking at a faster rate than the bottom. It should be noted that often cookies or items being baked in an oven burn on the bottom and are obviously being heated at a faster rate than the top of the item. This is due to the fact that often the metal container is in contact with a hot shelf and is thus receiving heat by conduction.

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