10
Analytical Heat Transfer
(b)
(a)
T
x
x
T
T(x, t)
T(x, t)
"
q s
FIGURE 1.9
(a) Finite heat flux. (b) Adiabatic surface.
1.4 Simplified Heat Conduction Equations
1. Steady state ∂T/∂t = 0, no heat generation q ˙ = 0
∂ 2 T
1-D
= 0
∂x 2
∂ 2 T
∂ 2 T
2-D
+
= 0
∂x 2
∂y 2
∂ 2 T
∂ 2 T
∂ 2 T
3-D
+
+
= 0
∂x 2
∂y 2
∂z 2
x
T(x, t)
T(0, t)
T ∞, h
T
FIGURE 1.10
Convective boundary conditions.
T(x, 0) = T i
FIGURE 1.11
Initial condition.