ME 345 Heat Transfer

ME 345 Heat Transfer

Lecture 24 Please bring text-we will do an example

Lecture Outline:

1)   Convection: Fluids review

2)   Special Cases:

-unheated entry length

-boundary Condition of q” = constant

3) Cautions in using correlations; mixed turbulent and laminar flow

EXTERNAL CONVECTION: Continued

Fluids Review:

1)   The Peclet number is defined as: Pe = Re Pr

2)   For turbulent flow: d » dt because of the extra motion of the molecules

3)   Cf,x is the local friction factor; and
where ts,x is the local shear stress

4)   If you have separation, all of these equations no longer apply!!!!!

Correlations for special cases:

I) Unheated starting length: the boundary layers start at different locations

1)   Laminar correlation: Eqn. 7.47:

NOTE: x starts at the leading edge

and Nuxôx=0 = hxx/k = 0.332Rex1/2 Pr1/3 for 0.6 < Pr < 50 is the regular Nux that you would calculate without the unheated length .

2)   Turbulent Correlation: Eqn. 7.48:

where the Nux is from Eqn. 7.37

For the unheated length problem, if you need (the average over the plate) you end up having to integrate numerically---there is no closed form solution.

II)   Different Boundary Condition: q” = constant è now you be calculating Ts(x)

1)   Laminar flow: Eqn. 7.50,

Nux = 0.453 Rex1/2 Pr1/3 (Or you can use Eqn. 7.53b to get the average Nusselt number)

2) Turbulent flow: Eqn. 7.51,

Nux = 0..0308 Rex4/5 Pr1/3 (For turbulent flow, you can use the correlation for the constant
temperature case to get the average Nusselt number)

3)   You can also use the above in the equations for the unheated starting length correlation

4)   To calculate Ts(x) using the hx: use q” = hx (Ts(x)-T¥)

5)   Also, calculating q is easy! Just multiply by the area!!! q = q” A

WARNINGS AND CAUTIONS IN USING CORRELATIONS!!!

1) Be sure that you satisfy ALL of the conditions and limits of the correlations, including Pr, etc.

2) Remember that these correlations are based on experiments and will not be exact, especially if you are outside the experimental range of the dimensionless numbers

Example:

For Example: If you need a value of
Nux out here, then you should find a
different correlation!!!

The symbols all represent data points. Different symbols represent measurements using different fluids: i.e. different values of Pr.
Mixed Turbulent and Laminar flow:

If your flow becomes turbulent, you first need to decide where along the surface it becomes turbulent!!! Then, if you need to determine averaged values of h, etc :

1) If it goes turbulent more than 95% of the way down toward the end è use laminar eqns!!

2)   If it goes turbulent less than 5% of the way toward the end è use turbulent eqns!!!

3) If it happens in between, è use mixed eqns.

The mixed equations are given in section 7.2.3. All you have are equations for the averaged NuL, and the averaged friction coefficient. These equations are also part of the summary in Table 7.9.

Group Exercise:

1)   Try to get into a different group than your usual. Choose the usual jobs. Pick your groups favorite HOLIDAY!

2)   Determine what happens to the heat transfer rate as the flow transitions to turbulence. (Does it go up or down or stay the same and why?)

3)   Draw a qualitative graph of hx vs. x. Include what happens to it as the flow transitions to turbulence.

4)   Draw a qualitative graph of d and dt for a fluid with a Prandtl no. of 5; include what happens to them at the transition to turbulence.

5)   Start working on Problem 7.33a from the text.