**AME 517, Fall 2009**

**Problem set #4**

**Assigned: 10/21/2009**

**Due: 10/30/2009, 4:30 pm**

** **

**Chapter 8: **

8.1

8.3 (assume that the
needle is a gray body with e
= a = 0.8, donÕt worry about the non-gray effects.)

8.4

**Other problem: **

Repeat problem 6.8
assuming that plate 2, instead of having a fixed temperature of 600K, has an
unknown temperature but receives conductive heat transfer from the bottom side
with a heat transfer coefficient of U_{2} = 10 W/m^{2}K and T_{°}
= 600 K.

**Notes on text
problems:**

Problems 8.1 and 8.3 are
different from most of the problems weÕve done in previous chapters because
they are not modeling radiative transfer via a finite number of discrete
surfaces (² 4 for the cases we've been doing), but rather treating the antenna
or needle as a continuous surface with conduction along the antenna or
needle. In this case you have to
use Eq. 8.1 to solve the problem.
The difficulty is that q_{R}(x) is not constant (though you
might try q_{R}(x) = constant for a reality check of your result.) You need to compute q_{R}(x) as
a function of the distance (x) from the base of the antenna or needle, then
integrate 8.1 with the appropriate boundary conditions. Note that problems 8.1 and 8.3 are MUCH
easier than the examples given in the text (sections 8.2 and 8.3) because in
the text examples you don't know q_{R}(x) beforehand - you have to
determine it as part of the solution, which is why you wind up with the
integro-differential equations in the text: 8.8 or 8.18+8.21.

Problem 8.4 can be
treated via the spreadsheet as we've been doing in class since the bead is
assumed to be isothermal; in part a there are only 2 surfaces, the tube and the
thermocouple bead. In part b there
is a 3rd surface, namely the shield, which you may choose to model as 2
separate surfaces, one being the inside of the shield and the other being the
outside.