Page 123 - Modelling in Transport Phenomena A Conceptual Approach

4.5. FLOW IN CIRCULAR PIPES 103

Solution
Assumptions

1. Steady-state conditions prevail.
2. Physical properties remain constant.

3. Changes in kinetic and potential energies are negligible.
Analysis

System: Oil an the pipe
The inventory rate equation for mass becomes
Rate of mass in = Rate of mass out = m = p(v)(sD2/4) (1)

On the other hand, the inventory rate equation for energy reduces to

Rate of energy in = Rate of energy out (2)
The terms in Eq. (2) are expressed by
Rate of energy in = m &(Tbi, - Tref) + sDL(h)ATLM (3)
Rate of energy out = m&p(Tbo,, - Tref) (4)

Since the wall temperature is constant, the expression for ATLM, Eq. (4.5-30),
becomes

Substitution of Eqs. (l), (3), (4) and (5) into Eq. (2) gives
-=-- 1 (~>P&P In ( Tw -Thin )
L
D 4 (h) Tw - Tbout (6)
Noting that StH = (h)/((v)p&p) = Nu/(RePr), Eq. (6) becomes
Tw - Tbi, )=1Reprln( Tw - Tbd, )
L
1
-=--In( 1 (7)
D 4 StH Tw -TbeUt 4 Nu Tw - Tbo,,t
To determine Nu (or, (h)), first the Reynolds number mmt be calculated. The
mean bulk temperature is (40 + 60)/2 = 50 "C and the Reynolds number is

D(4
Re = -
v
- (65 10-3)(1) = 1519 + Laminar flow
-
4.28 x 10-5