Unit Operation(II)
2nd Exam.
12/9/2003
Prob.1 (16 %)
(a)Explain why the local heat transfer coefficient in a boundary layer decreases
progressively along the flow direction.
(b) Under what conditions would you expect the temperature profile of a flat plat at
steady state appears as in the following figure to be reasonable?
T
1
T
2
Prob.2 (20%)
A cold fluid of temperature Tca is introduced at a mass flow rate m into a long
tube of length L maintained at a constant wall temperature Ts> Tca. The tube diameter
is not uniform but varied with an increases linearly from D1 at the inlet to D2 at the
outlet. The turbulent convective heat transfer coefficient was correlated
experimentally by the relation
h x  D2 
 
h2  D 
9/5
where hx is the local heat transfer coefficient in the region having a diameter D and h2
is the heat transfer coefficient at the outlet. Find an expression for the fluid outlet
temperature, Tb, in terms of the tube parameters(D1, D2, L), the mass flow rate(m), the
wall temperature(Ts), the fluid inlet temperature(Ta) and the heat transfer coefficient
at the outlet (h2).
Ts
m, Tb
m, Ta
x
L
Prob.3 (20%)
A plate comprised of two materials is well insulated on its sides and the top
surface, while the bottom surface is exposed to a fluid at T∞ with a heat transfer
coefficient h∞. The material 2 in the middle layer of the plate has an uniform heat
generation rate q (per unit volume) and a thermal conductivity varied with
temperature as k2=aT, where a is a constant. The material 1 has a constant thermal
conductivity that is k1. Show the maximum temperature within the middle layer 2.
L
L
L
1
2
1
T∞
well insulated
Prob.4 (20%)
A long cylindrical rod of diameter d having an uniform heat generation rate, q, is
placed in a square solid of dimension ten times the rod diameter, i.e. a= 10d. The
square solid has a thermal conductivity of ks and is exposed to an ambient fluid of
temperature T∞ with a heat transfer coefficient of h∞. If each surface temperature both
of the rod and the square solid are assumed to be uniform, determine
(1) the temperatures at rod surface and solid surface, respectively,
(2) the maximum temperature in the rod ( constant thermal conductivity; kr).
T2
d
T1
a
ks
T∞
q=kS(T1-T2)
S=2πL/ln(1.08 a/d)
S: conduction shape factor
L: length of the rod
ΔT: temperature difference
between the rod surface
and that of the square
surface
a =10d
T∞
Prob.5 (25%)
A heater containing thin-walled pipe which surface is maintained at a constant
temperature of 100oC is used to heat a given rate of water for bath. When the water
entering the pipe is at 20.0 oC, the water outlet temperature obtained is 60oC.
Estimate the outlet water temperature under the same feed rate and pipe surface
temperature if the inlet temperature drops to 10.0oC,. The water flow through the pipe
is turbulent and the physical properties of water in a temperature range of 10 to 50 oC
are given as
μ(cp)=1.662－0.04T＋0.0004T2
Npr=12.64－0.3313T＋0.0032T2
where T is in oC. For water at 100 oC,μ=0.278 cp and Npr=1.72. The heat capacity of
water is assumed to be independent of temperature.
Given Eq.:
For turbulent flow inside a pipe

hD
0.8
 0.027 N Re
N 1pr/ 3  b
k
 w



0.14
All the physical properties are evaluated at the bulk fluid temperature except μw .