Download Examination Heat Transfer

Examination Heat Transfer
code: 4B680
date: June 13, 2008
time: 14.00 - 17.00
Note:
There are 4 questions in total. The first one consists of independent subquestions. If possible and necessary, guide numbers are given for the
answers.
Good luck
Question 1 (all sub-questions can be solved independently)
a) Consider a long cylinder submerged in a flowing fluid with a constant heat transfer
coefficient hc (no variations in length and circumferential direction). At time t = 0 the
cylinder temperature equals T = Ti and an internal heat source q’’’ is switched on.
1) Give the describing differential equation and accompanying boundary and initial
conditions for the temperature in the cylinder as function of time t and position r.
2) Which dimensionless numbers determine the solution.
3) Give an expression for the temperature at t → ∞.
hc
0,4
b) If the heat transfer of a flow over a flat plate can be described by Nu x = 0.4 Re0,6
,
x Pr
calculate then Nu L and express Nu L in Nu L (Nusselt at position x = L).
c) Water at the rate of 68 kg/min is heated from 35 to 75 0C by an oil having a specific heat
of 1.9 kJ/kg.0C. The oil enters the exchanger at 110 0C and leaves at 75 0C. The overall
heat transfer coefficient is 320 W/m2.K. The fluids are used in a shell-and-tube heat
exchanger with the oil making one shell pass and the water making two tube passes.
Calculate the heat exchanger area using the figure below.
Question 2 (all sub-questions can be solved independently)
A small ball of steel (diameter 4 cm) falls into a constant temperature bath. The initial
temperature of the ball is 400 0C and the material properties of steel can be taken as: k =10
W/m⋅K, ρ = 8000 kg/m3 and c = 500 J/kg⋅K
The cooling medium is oil or water, the bath temperature is 20 0C and the accompanying
heat transfer coefficients are:
Oil
Water
a)
h = 100 W/m2⋅K
h = 1 000 W/m2⋅K
Determine for both situations the Biot-number. Take the radius as characteristic length
scale. Based on the value of the Biot-number determine whether a lumped capacity
analysis is valid or not.
Using the lumped capacity analysis determine for both situations:
b)
the contact time needed till the ball reaches a temperature of 100 0C;
c)
the amount of heat that is transferred to the environment when reaching this temperature
of 100 0C.
Using the full analysis (using the figures on the next page) determine for both situations:
d)
the contact time needed till the maximum temperature in the ball is dropped to 100 0C;
e)
the maximum occurring temperature difference in the ball at that time level. Based on the
value of this maximum temperature difference determine again whether a lumped
capacity analysis is valid or not.
Question 3 (all sub-questions can be solved independently)
A system for heating water from an inlet temperature of Tm,i = 20 0C to an outlet temperature
of Tm,o = 60 0C involves passing the water through a thick-walled bronze tube (k = 50 W/m.K)
having inner and outer diameters of 20 and 40 mm, respectively. The outer surface of the
tube is well insulated, and electrical heating within the wall provides for a uniform generation
rate of q’’’ = 106 W/m3. It is assumed that this uniform heat source results in a constant
= 0,1 kg/s.
heating rate q” from the wall to the water. The water flow rate equals to m
a)
b)
c)
d)
e)
How long must the tube be to achieve the desired temperature?
(L = 20 m)
Determine whether the flow is hydrodynamically and thermally fully developed at tube
outlet.
What is the local convection heat transfer coefficient at tube outlet?
(hx=L = 1500 W/m2⋅K)
What is the inner surface temperature at tube outlet?
What is the outer surface temperature at tube outlet?
Question 4 (all sub-questions can be solved independently)
Two concentric cylinders with diameters D1 = 10 cm and D2 = 20 cm are situated in a large
room with a temperature T3 = 300 K. The cylinders are long L = 20 cm. Cylinder 1 is massive
and has a temperature T1 = 1000 K. Cylinder 2 is thin-walled. Furthermore the emissivities
are equal to ε1 = 0.8 and ε2 = 0.2. The whole system is in thermal equilibrium..
Cylinder 1
Cylinder 2
L= 20 cm
T3= 300K
D1= 10 cm
Room 3
D2= 20 cm
a)
b)
Calculate the view factors F12, F13, F23,i en F23,o, with F23,i the view factor from the inner
side of cylinder 2 to the surrounding room 3 and F23,o from the outer side of cylinder 2 to
the surrounding room 3. Make use of the figures on the next page.
(F12=0.8, F13=0,15, F23,i = 0,23 en F23,o = 0.9)
Below the thermal network of the problem is presented. It concerns a 4-surface
enclosure because cylinder 2 is radiating in 2 directions, indicated in the network with the
radiosities J2i for the inner surface and J2o for the outer surface. Fill out the missing
thermal resistances (first reproduce the thermal network) and determine all the values of
the thermal resistances in the network.
(R13 = 150; R12 = 20; R23i = 30; R23o = 8; r1 = 5; r2 = 35; all values in 1/m2)
= r2
= r2
=
c)
Set up the equations with which the radiosities J1, J2i, J2o en J3 can be calculated.
Take for the values of the radiosities: J1 = 50 000 W/m2, J2i = 25 000 W/m2, J2o = 3 000 W/m2,
J3 = 500 W/m2.
d)
e)
Determine the temperature T2 of cyinder 2.
Calculate the total radiation rate of cylinder 1 to cylinder 2 and the environment.
Zichtsfactoren voor twee concentrische cilinders van eindige lengte. Boven: buiten
cilinder naar binnen cilinder; Beneden: buiten cilinder naar zichzelf.