The problem was solved tp verify the performance by doing the calculations in the image. Redo the same problem, but by changing the design either to a Cylinder or Cube from Spherical.

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Chapter10: Heat Exchangers
Section: Chapter Questions
Problem 10.51P
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The problem was solved tp verify the performance by doing the calculations in the image. Redo the same problem, but by changing the design either to a Cylinder or Cube from Spherical.

The existing thermocouple has the following design data:
• Material: AISI 304 Stainless Steel
• Shape: Spherical (2 mm diameter)
• Heat transfer coefficient: h =
2.2(V/D)0.5
• Time to 0.99 A T: 18 seconds
• Minimum flow velocity: 43 m/s
Verify the performance of the existing thermocouple
• Check that for a minimum velocity of 43 m/s you can reach 99% of the T value at the center of the
thermocouple in 18 seconds
Transcribed Image Text:The existing thermocouple has the following design data: • Material: AISI 304 Stainless Steel • Shape: Spherical (2 mm diameter) • Heat transfer coefficient: h = 2.2(V/D)0.5 • Time to 0.99 A T: 18 seconds • Minimum flow velocity: 43 m/s Verify the performance of the existing thermocouple • Check that for a minimum velocity of 43 m/s you can reach 99% of the T value at the center of the thermocouple in 18 seconds
Step 1
SOL:>, For
AISI 304 stainless steel.
density , P = 8000 kg mo
Cppacity,
Thermal Conductivity
Specific heat
C = 500 J
=K= 16.2 W
Given.
h= 2,2X
V 10'5
0.5
= 2 2 x / 43
2x10-3
ニ
322. 583
m² K.
= h Lc
K.
Biot mum ber
; where Le-charactenistic leng th.
iLe= V
%3D
=322 583 x 1X10-3
16.2 X 3
= 0.0066
So, Lumped System approximalion applicable
Step 2
T- Too
hA
て、
= e Pev
T; - To
Ln (too)
て.
pev
99 % of Too .;
or,
4.60517 xP xex v
h x A
4. 60517X 8 000 × 500 X IX 10"
322.583 × 3
or,
t= 19.03 sec.
or,
+ 5% eror, the time o in limit.
with an approximation of
So, Hrermocouple vis comect,
Transcribed Image Text:Step 1 SOL:>, For AISI 304 stainless steel. density , P = 8000 kg mo Cppacity, Thermal Conductivity Specific heat C = 500 J =K= 16.2 W Given. h= 2,2X V 10'5 0.5 = 2 2 x / 43 2x10-3 ニ 322. 583 m² K. = h Lc K. Biot mum ber ; where Le-charactenistic leng th. iLe= V %3D =322 583 x 1X10-3 16.2 X 3 = 0.0066 So, Lumped System approximalion applicable Step 2 T- Too hA て、 = e Pev T; - To Ln (too) て. pev 99 % of Too .; or, 4.60517 xP xex v h x A 4. 60517X 8 000 × 500 X IX 10" 322.583 × 3 or, t= 19.03 sec. or, + 5% eror, the time o in limit. with an approximation of So, Hrermocouple vis comect,
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