laminar flow convective heat transfer
DESCRIPTION
Laminar Flow Convective Heat Transfer Goals: By the end of today’s lecture, you should be able to: obtain laminar flow heat transfer coefficients for: parallel plate exchangers apply the applicable equations to determine: the exchanger outlet cup mixing temperature the required exchanger surface areaTRANSCRIPT
CBE 150A – Transport Spring Semester 2014
Laminar Flow Convective Heat Transfer
CBE 150A – Transport Spring Semester 2014
Goals:
By the end of today’s lecture, you should be able to:
obtain laminar flow heat transfer coefficients for: parallel plate exchangers
apply the applicable equations to determine: the exchanger outlet cup mixing temperature the required exchanger surface area
Laminar Flow Convective Heat Transfer
CBE 150A – Transport Spring Semester 2014
Outline:
I. Relevant equations
• Flat plate exchanger
II. Example – blood substitute heat exchanger
CBE 150A – Transport Spring Semester 2014
xy
- H
+ H
Uniform Plate Temperature TH
Temperature Profile (x,y)x = 0Fluid in laminar flow
Uniform Inlet Temperature T1
Laminar Flow Between Two Heated Parallel Plates
W
CBE 150A – Transport Spring Semester 2014
The Differential Equation (Basic Equations)
2
2
2
2
2
2
2
)(:
)(
2
:
123)(
yT
xTyuSimplify
xT
yT
xTyu
HUq
channeltheacrossvelocityaverageUWhere
HyUyu
w
CBE 150A – Transport Spring Semester 2014
The Differential Equation (Dimensionless Form)
Dimensionless variables:
H
H
TTTT
1 H
yy *1
2*
4PrRe
xH
UHxx
kC
WQUH
p
Pr
24Re
CBE 150A – Transport Spring Semester 2014
Subject to boundary conditions:** 01 yallforxat
*** 00 xallforyaty
010 ** xallforyat
2*
2
*2*1
23
yxy
Differential equation:
CBE 150A – Transport Spring Semester 2014
Yields:
0 0
**2
32exp
m n
nnm
mm yaxA
CBE 150A – Transport Spring Semester 2014
The solution yields T (temperature in the streamline) as a function of y (distance from the plate surface) but we probably don’t care !!
What we want is the average temperature in the exit fluid – the “cup mixing” temperature. So:
Cup Mixing Temperature
Temperature Profile (x,y)
H
H
mixingcup
dyHyU
dyyxHyU
0
2
2
0
123
,123
CBE 150A – Transport Spring Semester 2014
Cup Mixing Temperature
Temperature Profile (x,y)
*)89.1exp(91.0
3*2exp
0
2
x
ionapproximattermOne
xG
cm
m
mmcm
Equation12.5.17
CBE 150A – Transport Spring Semester 2014
Cup-mixing temperature along the axis of a parallel plate, laminar flow heat exchanger.
CBE 150A – Transport Spring Semester 2014
0
2
0
22
3/*2exp
3/*2exp38
4
mmm
mmmm
locloc
cm
Hcmloccmp
xG
xGNu
kHh
forsolutiontheingIncorporat
dxTThdTHUC
Local heat transfer coefficient
CBE 150A – Transport Spring Semester 2014
Local Nusselt numbers along the axis of a parallel plate laminar flow heat exchanger. Both surfaces at the same constant temperature. Also shown is the average Nusselt number plotted against x*, Dh = 4H
CBE 150A – Transport Spring Semester 2014
CFD Exercise – Blood substitute heat exchanger
In a surgical procedure on a kidney it is necessary to take the kidney “off-line” andnourish it with a blood substitute using an extracorporeal(outside the body) system. The blood substitute is passed through an oxygenator before it enters the organ, and it is necessary to raise the temperature of the liquid from 32 C to 38 C before returning it to the organ. A preliminary design under consideration has the following features. The blood substitute will flow through a parallel plate exchanger with a width (W) = 10 cm. and a channel height (2H) = 2 mm. The plates are maintained at TH = 40 C. The required capacity of the exchanger is a flowrate of 1 Liter /min
The liquid has the following properties:
Pr = 4.5 k = 0.6 W/ m K = 3 mPa s = 1250 kg / m3
What is the required length of the exchanger plate: