1. Laminar Flow Convective Heat Transfer

2. 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 area

3. Outline: Relevant equations Flat plate exchanger
Example – blood substitute heat exchanger

4. Laminar Flow Between Two Heated Parallel Plates
Uniform Plate Temperature TH
Uniform Inlet Temperature T1 W
+ H x y
- H
Fluid in laminar flow
x = 0
Temperature Profile (x,y)

5. The Differential Equation (Basic Equations)

6. The Differential Equation (Dimensionless Form)
Dimensionless variables:

7. Differential equation:
Subject to boundary conditions:

8. Yields:

9. 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:
Temperature Profile (x,y)
Cup Mixing
Temperature

10. Temperature Profile (x,y)
Equation
Cup Mixing
Temperature

11. Cup-mixing temperature along the axis of a parallel plate, laminar
flow heat exchanger.

12. Local heat transfer coefficient

13. 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

14. CFD Exercise – Blood substitute heat exchanger
In a surgical procedure on a kidney it is necessary to take the kidney “off-line” and
nourish 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 m = 3 mPa s r = 1250 kg / m3
What is the required length of the exchanger plate: