External Flow – Cylinders and Spheres

Sections 7.4-7.5

CH EN 3453 – Heat Transfer

Reminders…• No school next week

• Project outline due today– Can turn in to basket in ChE office as late as 4:30 pm– See Oct 3 lecture slides for suggestion...

• Homework #6 due Friday by 4:00 pm– Help session today at 4:30 pm in MEB 2325

• Homework #7 due Friday Oct. 24– Help session Wednesday, Oct. 22 4:30 pm

• Heat exchanger lab day Friday Oct. 24

• Bethany teaches Mon and Wed after fall break

Flow Correlation Summary(Table 7.7 in 7th edition of book)

Flow Correlation Summary

Example – Book Problem 7.13Consider a flat plate subject to parallel flow (top and bottom) characterized by u∞ = 5 m/s and T∞ = 20°C. Determine the average convective heat transfer coefficient and convective heat transfer rate associated with a L = 2 m long, w = 2 m plate for surface temperatures of 50 and 80°C.

Example – Book Problem 7.43A flat solar collector is at 15°C, while ambient air at 10°C is in parallel flow over the plate with u∞ = 2 m/s.

(a) What is the rate of convective heat loss from the plate?(b) Same as (a), but the plate is 2 m from the leading edge

Boundary Layer over Cylinder

Figure 7.5 Boundary layer formation and separation on a circular cylinder in cross flow.

Boundary Layer Separation

Figure 7.6 Velocity profile associated with separation on a circular cylinder in cross flow.

Laminar vs. Turbulent Flow

Figure 7.7 The effect of turbulence on separation.

Convective Heat Transfer

Figure 7.9 Local Nusselt number for airflow normal to a circular cylinder.

Turbulent

TransitionLaminar

Heat Transfer Correlations for Cylinders

Local heat transfer at stagnation point ONLY Properties evaluated at Tfilm

(Eq. 7.51)

Kays

Heat Transfer Correlations for Cylinders

Properties evaluated at Tfilm C and m from Table 7.2 Also can be used for non-circular cylinders using Table 7.3

(Eq. 7.52)

Hilpert

More Correlations for Cylinders…

Properties evaluated at T∞ except Prs

C and m from Table 7.4 n = 0.37 if Pr < 10, otherwise n = 0.36

(Eq. 7.53)

Properties evaluated at Tfilm

Does not require looking up in any table

(Eq. 7.54)

NuD =hDk

= CReDm Prn Pr

Prs

⎛⎝⎜

⎞⎠⎟

1/4

NuD = 0.3+ 0.62ReD1/2 Pr1/3

1+ 0.4 / Pr( )2 /3⎡⎣ ⎤⎦1/4 1+

ReD282,000

⎛⎝⎜

⎞⎠⎟5 /8⎡

⎣⎢⎢

⎤

⎦⎥⎥

4 /5

Churchill and Bernstein:

Zukauskas:

A Few Notes…

• All these expressions are empirical. No single expression is "correct"

• Best accuracy is ~20%

• Book focuses on 7.53 and 7.54

• For all expressions, check the ranges of Pr, Re, etc. for which the expression is valid

Heat Transfer Correlations for Spheres

For falling liquid droplets ONLY Properties evaluated at Tfilm

(Eq. 7.57)

Properties evaluated at T∞ except for µS

(Eq. 7.56)NuD = 2 + 0.4ReD1/2+ 0.06ReD

2 /3( )Pr0.4 µµs

⎛⎝⎜

⎞⎠⎟

1/4Whitaker

Ranz and Marshall (for falling liquid droplets)