Chapter 13, Problem 13.41P

Many products are processed in a manner that requires a specified product temperature as a function of time. Consider a product in the shape of long, 10-mm-diameter cylinders that are conveyed slowly through a processing oven as shown in the schematic. The product exhibits near-black behavior and is attached to the conveying apparatus at the products ends. The surroundings are at 300 K, while the radiation panel heaters are each isothermal at 500 K and have surfaces that exhibit near-black behavior. An engineer proposes a novel oven design with a tilting top surface so as to be able to quickly change the thermal response of the product.

1. Determine the radiation per unit length incident upon the product at $x=0.5\text{m}$ and $x=1\text{m}$ for $\alpha =0$ .
2. Determine the radiation per unit length incident upon the product at $x=0.5\text{m}$ and $x=1\text{m}$ for $\alpha =\pi /15$ . Hint: The view factor from the cylinder to the left-hand side surroundings can be found by summing the view factors from the cylinder to the two surfaces shown as id dashed lines in the schematic.