Question

The straight fin with a parabolic profile y-1-xL)² is of particular interest since it can give the maximum heat loss for a given weight of any profile. By substituting appropriate values of Ae and sp in Eq. (2.30), show that the governing differential equation is where z = L-x. This is an Euler equation.

Answer 1

The given equation represents the heat loss of a straight fin with a parabolic profile. By substituting appropriate values of Ae and sp in Eq. (2.30), we can show that the governing differential equation is obtained by substituting z = L - x into the equation. This equation is known as an Euler equation and describes the behavior of the heat loss for this particular fin profile.

Step-by-step explanation:

The given equation represents the heat loss of a straight fin with a parabolic profile. By substituting appropriate values of Ae and sp in Eq. (2.30), we can show that the governing differential equation is obtained by substituting z = L - x into the equation.

For example, if we have Ae = 2 and sp = 3, we substitute these values into Eq. (2.30) to obtain the governing differential equation.

This equation is known as an Euler equation and describes the behavior of the heat loss for this particular fin profile.