Laminar Flow Convective Heat Transfer

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Presentation transcript:

Laminar Flow Convective Heat Transfer

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

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

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)

The Differential Equation (Basic Equations)

The Differential Equation (Dimensionless Form) Dimensionless variables:

Differential equation: Subject to boundary conditions:

Yields:

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

Temperature Profile (x,y) Equation 12.5.17 Cup Mixing Temperature

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

Local heat transfer coefficient

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

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: