Effect of Viscous Dissipation on Heat Transfer in Laminar Flow
Effect of Viscous Dissipation on Heat Transfer in Laminar Flow
Out[]=
This Demonstration shows the effect of axial conduction and viscous dissipation on heat transfer between a fluid in laminar flow and a tube at constant temperature.
Consider the fully developed laminar flow of a fluid in a tube with a wall temperature ; the fluid enters at a uniform temperature . Assuming constant physical properties and axial symmetry, the dimensionless energy equation is:
T
w
T
0
2(1-)=T+r+
2
r
∂T
∂x
1
2
Pe
2
∂
∂
2
x
1
r
∂
∂r
∂T
∂r
2
Br
dU
dr
with boundary conditions:
T(0,r)=0
∂T
∂x
T(x,R)=
T
w
∂T(x,0)
∂r
x=
ξ
2PeR
r=
2R
T=-
-
o
w
o
U=
u
u
avg
u=21-
u
avg
2
r
R
Pe==
ρR
C
p
2
u
avg
k
heatconvected
heatconducted
Br==
μ
2
U
avg
k(-)
T
w
T
0
heatproducedbyviscousdissop[ation
heattransportedbymolecularconduction
where
ξ
R
L
ρ
C
p
u
avg
k
The dimensionless equation is solved using the built-in Mathematica function NDSolve; the effect of the Péclet number and the Brinkman number on the temperature distribution is shown.