HEAT EQUATION EXAMPLES
1. Find the solution to the heat conduction problem:
4ut
=
uxx , 0 x 2, t > 0
u(0, t)
=
0
u(2, t)
=
0
u(x, 0)
=
2 sin
x
2
sin(x) + 4 sin(2x) = f (x)
Solution:
We use separation of variables. Let u(x, t) = X(x)T (t). Then 4ut = ux

QMT6Y5HB87O - [ebook] Heat Transfer with Applications.
Heat Transfer with Applications
by Kirk D. Hagen
Heat Transfer with Applications by Kirk D. Hagen
This guide on the basics of heat transfer focuses on applications and problemsolving rather than theor

Francis Turbine
1. A Francis turbine works under a head of 120 m. The outer diameter and width are 2 m and 0.16
m. The inner diameter and width are 1.2 m and 0.27 m. The flow velocity at inlet is 8.1 m/s. The
whirl-velocity at outlet is zero. The outlet b