CHEMICAL ENGINEERING

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