In Section 3.3, a rectangular plate was analyzed, and the two-dimensional conduction Equation 3.7 was solved subject to four boundary conditions (Equations 3.8). Suppose we again solve the...

In Section 3.3, a rectangular plate was analyzed, and the two-dimensional conduction Equation 3.7 was solved subject to four boundary conditions (Equations 3.8). Suppose we again solve the two-dimensional conduction equation for the rectangular plate of Figure 3.2, but with diff erent boundary conditions. Obtain the temperature profi le for the following boundary conditions: a. x = 0 θ = 0 b. x = W θ = 0

Equation 3.7

Figure 3.2

c. y = 0 θ = 0 d. y = H θ = T2 sinh(πx/W) for x ≤ W/2 For x ≥ W/2, the temperature profi le is symmetric about x/W = 0.5. A graph of the fourth boundary condition is as shown in Figure P3.6.