ABSTRACT
Exact and more accurate solutions of conjugate convective heat transfer problems are considered in following chapters.
In general, the conjugate problem of convective heat transfer in the boundary layer approximation is governed by a system of four equations: continuity, momentum, and energy equations for a fluid and a conduction equation for a body. In the case of a two-dimensional heat transient problem for incompressible fluid, this system is
∂ ∂
+ ∂ ∂
=u x
v y
0 (2.1)
∂ ∂
+ ∂ ∂
+ ∂ ∂
= − + − + ∂ ∂∞
u t
u u x
v u y
dp dx
g T T u
y 1 2
2ρ β ν( ) (2.2)
∂ ∂
+ ∂ ∂
+ ∂ ∂
= ∂ ∂
+ ∂ ∂
T t
u T x
v T y
T y c
u yp
α ν 2
(2.3)
T x
T y
q ∂ ∂
= ∂ ∂
+ ∂ ∂
+
2 (2.4)
The boundary and conjugate condition are
y u v y u U T T= = = →∞ → → ∞0 0, , (2.5)
y T T T y
= = ∂ ∂
= ∂ ∂
= =
, λ λ (2.6)
The initial conditions are usually specified for each particular problem. In the case of forced heat transfer, the second term in the right-hand part
of Equation (2.2) should be omitted, and the first should be substituted by U(dU/dx) = − (1/r)(dp/dx). This relation follows from Equation (2.2), written for the free stream of the boundary layer. In the case of natural convective heat transfer, the first term in the right-hand part of Equation (2.2) should be omitted.
