Chapter 6 Empirical and Practical Relations for Forced-Convection Heat Transfer

Empirical relations for pipe and tube flow Turbulent flow in smooth tube: Dittus and Boelter

0.8

5

0.023Re Pr0.40.3

0.6 Pr 1002500 Re 1.25 10

nd dNu

for heating of the fluidn

for cooling of the fluid

=

⎧= ⎨⎩< <

< < ×

Gnielinske

0.8 0.4

4 6

0.0214(Re 100) Pr0.5 Pr 1.510 Re 5 10

dNu = −< <

< < ×

, or

0.87 0.4

6

0.012(Re 280) Pr1.5 Pr 5003000 Re 10

dNu = −< <

< <

To take into account the property variations Sieder and Tate

0.14

0.8 1/30.027 Re Prd dw

Nu μμ

⎛ ⎞= ⎜ ⎟

⎝ ⎠ for turbulent fully developed flow

More accurate relations, Petukhov

1/ 2 2/3

210

4 6

( / 8) Re Pr1.07 12.7( / 8) (Pr 1)

0.110.250 .

(1.82log Re 1.64)0.5 Pr 200 6%0.5 Pr 2000 10%10 Re 5 100.8 / 40

n

d bd

w

w b

w b

d

d

b w

fNuf

for T Tn for T T

const heat flux

faccuracy withinaccuracy within

μμ

μ μ

−

⎛ ⎞= ⎜ ⎟+ − ⎝ ⎠

>⎧⎪= >⎨⎪⎩

= −

< << <

< < ×< <

For fully developed, laminar tube flow at const. wall temp. Hausen

2/3

0.0668( / ) Re Pr3.661 0.04[( / ) Re Pr]

dd

d

d LNud L

= ++

Laminar tube flow Sieder and Tate :

0.141/31/31.86(Re Pr)

Re Pr 10

d dw

d

dNuL

dL

μμ

⎛ ⎞⎛ ⎞= ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠

>

For rough tube,

2/3

2

Pr8

2

b f

m

fSt

Pf friction coefficientu L

dρ

=

Δ= =

In the entrance region, Nusselt

0.055

0.8 1/30.036Re Pr 10 400d dd LNu forL d

⎛ ⎞= < <⎜ ⎟⎝ ⎠

Turbulent flow

Or

Fig 6-5 & 6-6. Re Pr dGz Graetz numberx

= =

Noncircular pipe, Hydraulic diameter

4

::

HAD

PA cross section area of the flowP wetted perimeter

=

Flow across cylinder Hilpert for gases & Knudsen and Katz for liquids

1/3Re Prnf dfNu C=

Redf C N 0.4-4 0.989 0.330 4-40 0.911 0.385

40-4000 0.683 0.466 4000-40,000 0.193 0.618

40,000-400,000 0.0266 0.805