MOMENTUM, HEAT AND MASS TRANSFER 315
viscosityEare equal, calculate the value of the temperature gradient in a liquid flowing
over the surface atyCD15 (which lies within the buffer layer) for a surface heat flux
of 1000 W/m^2. The liquid has a Prandtl number of 7 and a thermal conductivity of
0.62 W/m K.
Solution
a)In the region where eddy effects considerably exceed molecular contributions:
E×/
Outside the laminar sub-layer and the buffer-layer but still close to the surface:
RDEdux/dywhereRis shear stress at surface
WritingEasEuE, and approximating,uEDEjdux/dyjgives:
R
D^2 E
(
dux
dy
)(
dux
dy
)
where the modulus sign is dropped as dux/dyis positive near a surface.
PuttinguŁD
p
R/, the shearing stress velocity:
uŁ
2
D^2 E
(
dux
dy
) 2
uŁDE
dux
dy
Using the Prandtl approximationED 0. 4 ygives:
uŁD 0. 4 y
dux
dy
∴
dux
dy
D 2. 5
uŁ
y
WritingyCDyuŁ/anduCDux/uŁ, then:
uŁ
duC
dyC
D 2. 5
uŁ
yC
and:
duC
dyC
D
2. 5
yC
b) In the buffer zone:
It is given that:
duC
dyC
D 2
(
2. 5
yC
)
D
5
yC
The shear stress is given by:
RDCE
dux
dy
∴ uŁ
2
D
R
D
(
CE
)
dux
dy