Application of Steady-State Heat Transfer

1
Application of Steady-State Heat Transfer
2
Steady-state heat transfer

• Temperature in a system remains constant with
  time.
• Temperature varies with location.

3
Conductive heat transfer in a rectangular slab


4
Example

• For the stainless steel plate 1 cm thick is
  maintained at 110?C, while the other face is at
  90 ?C. Calculate temperature at 0.5 cm from the
  110?C-temperature face.
• Given
• heat flux 34,000 W/m2
• thermal conductivity of stainless steel 17 W/m
  ?C

5
Conductive Heat Transfer through a Tubular
Pipe

• Consider a long hollow cylinder

6
Conductive Heat Transfer through a Tubular
Pipe

• Consider a long hollow cylinder

7
Example

• A 2 cm thick steel pipe (k 43 W/m?C) with 6 cm
  inside diameter is being used to convey steam
  from a boiler to process equipment for a distance
  of 40 m. The inside pipe surface temperature is
  115?C, and the outside pipe surface temperature
  is 90?C. Under steady state conditions, calculate
  total heat loss to the surrounding.

8
Heat conduction in multilayered systems
9
Composite rectangular wall (in series)
10
(No Transcript)
11
composite thermal resistance
12
(No Transcript)
13
Composite rectangular wall (in parallel)
q A ?T k / x A ?T / (x/k) ? T1
?T2 ?T3 ?T R Resistance x/k
1/C 1/RT 1/R11/ R21/ R3
(1/(x1 / k 1)) (1/(x2 / k 2)) (1/(x3
/ k 3))
14
and it is resistance which is additive when
several conducting layers lie between the hot and
cool regions, because A and Q are the same for
all layers. In a multilayer partition, the total
conductance is related to the conductance of its
layers by
So, when dealing with a multilayer partition, the
following formula is usually used
15
Example

• A cold storage wall (3m X 6m) is constructed of a
  15 cm thick concrete (k 1.37 W/m?C). Insulation
  must be provided to maintain a heat transfer rate
  through the wall at or below 500 W. If k of
  insulation is 0.04 W/m?C. The outside surface
  temperature of the wall is 38?C and the inside
  wall temperature is 5?C.

16
Example
How many joules of thermal energy flow through
the wall per second? ----------------------------
--------------- Heat is like a fluid  whatever
flows through the insulation must also flow
through the wood. 
17
Across insulationHins (0.20)(40)(25 -
T)/0.076         2631.6 -105.3 T          
Across woodHwood (0.80)(40)(T - 4)/0.019   
   1684.2 T - 6736.8Heat is like a fluid
 whatever flows through the insulation must also
flow through the woodHwood    Hins   1684.2
T - 6736.8 2631.6 -105.3 T     1789.5 T
9368.4                                          
      T 5.235 C       HHwoodHins           
                          H 1684.2 (5.235) -
6736.8 2080 J/s     H 2631.6 - 105.3 (5.235)
  2080 J/s    
                     k
(insulation) 0.20 J/(s-m-C)k (wood)     
0.80 J/(s-m-C)
18
Series and parallel one-dimensional heat transfer
through a composite wall and electrical analog
19
Composite cylindrical tube(in series)
r1
r3
r2
20
(No Transcript)
21
Example

• A stainless steel pipe (k 17 W/m?C) is being
  used to convey heated oil. The inside surface
  temperature is 130?C. The pipe is 2 cm thick with
  an inside diameter of 8 cm. The pipe is insulated
  with 0.04 m thick insulation (k 0.035 W/m?C).
  The outer insulation temperature is 25?C.
  Calculate the temperature of interface between
  steel and isulation. Assume steady-state
  conditions.

22
(No Transcript)
23
THERMAL CONDUCTIVITY CHANGE WITH TEMPERATURE
Heat transfer through a slab
?
24
THERMAL CONDUCTIVITY CHANGE WITH TEMPERATURE
Heat transfer through a cylindrical tube
25
Problem

• 1. Find the heat transfer per unit area through
  the composite wall. Assume one-dimensional heat
  flow.

Given kA 150 W/m?C kB 30 W/m?C kC 50
W/m?C kD 70 W/m?C AB AD
26
Problem

• 2. One side of a copper block 5 cm thick is
  maintained at 260?C. The other side is covered
  with a layer of fiber glass 2.5 cm thick. The
  outside of the fiber glass is maintained at 38?C,
  and the total heat flow through the
  copper-fiber-glass combination is 44 kW. What is
  the area of the slab?
• 3. A wall is constructed of 2.0 cm of copper, 3.0
  mm of asbestos, and 6.0 cm of fiber glass.
  Calculate the heat flow per unit area for an
  overall temperature difference of 500?C.

27
Problem

• 4. A certain material has a thickness of 30 cm
  and a thermal conductivity of 0.04 W/m?C. At a
  particular instant in time the temperature
  distribution with x, the distance from the left
  face, is T 150x2 - 30x, where x is in meters.
  Calculate the heat flow rates at x 0 and x 30
  cm. Is the solid heating up or cooling down?
• 5. A certain material 2.5 cm thick, with a
  cross-sectional area of 0.1 m2, has one side
  maintained at 35?C and the other at 95?C. The
  temperature at the center plane of the material
  is 62?C, and the heat flow through the material
  is 1 kW. Obtain an expression for the thermal
  conductivity of the material as a function of
  temperature.