Consider a concentric tube annulus for which the inner and outer diameters are 25 and 5 0 mm . Water enters the annular region at 0.0. 4kg / s and 25 ° C . If the inner tube wall is heated electrically at a rate (per unit length) of q ' = 4000 W/m , while the outer tube wall is insulated how long must the tubes be (or the water to achieve an outlet temperature of 85 ° C ? What is the inner tube surface temperature at the outlet, where fully developed conditions may be assumed?
Consider a concentric tube annulus for which the inner and outer diameters are 25 and 5 0 mm . Water enters the annular region at 0.0. 4kg / s and 25 ° C . If the inner tube wall is heated electrically at a rate (per unit length) of q ' = 4000 W/m , while the outer tube wall is insulated how long must the tubes be (or the water to achieve an outlet temperature of 85 ° C ? What is the inner tube surface temperature at the outlet, where fully developed conditions may be assumed?
Consider a concentric tube annulus for which the inner and outer diameters are 25 and
5
0
mm
. Water enters the annular region at
0.0.
4kg
/
s
and
25
°
C
. If the inner tube wall is heated electrically at a rate (per unit length) of
q
'
=
4000
W/m
, while the outer tube wall is insulated how long must the tubes be (or the water to achieve an outlet temperature of
85
°
C
? What is the inner tube surface temperature at the outlet, where fully developed conditions may be assumed?
(I) [40 Points] Using centered finite difference approximations as done in class, solve the equation for O:
d20
dx²
+ 0.010+ Q=0
subject to the boundary conditions shown in the stencil below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q= √(0.5 + 2x)e-sinx (cos(5x)+x-0.5√1.006-x| + e −43*|1+.001+x* | * sin (1.5 − x) +
(cosx+0.001 + ex-1250+ sin (1-0.9x)|) * x - 4.68x4. For Case (a) (that is, Q = 0.3), use the stencil in Fig.
1. For Case (b), calculate with both the stencils in Fig. 1 and Fig 2. For all the three cases, show a table as
well as a plot of O versus x. Discuss your results. Use MATLAB and hand in the MATLAB codes.
1
0=0
x=0
2
3
4
0=1
x=1
Fig 1
1 2 3 4 5 6 7 8 9 10
11
0=0
x=0
0=1
x=1
Fig 2
Fig 2
(II) [60 Points] Using centered finite difference approximation as done in class, solve the equation:
020 020
+
მx2 მy2
+0.0150+Q=0
subject to the boundary conditions shown in the stencils below. Do this for two values of Q: (a) Q = 0.3,
and (b) Q = 10.5x² + 1.26 * 1.5 x 0.002 0.008. For Case (a) (that is, Q = 0.3) use Fig 3. For Case (b),
use both Fig. 3 and Fig 4. For all the three cases, show a table as well as the contour plots of versus
(x, y), and the (x, y) heat flux values at all the nodes on the boundaries x = 1 and y = 1. Discuss your
results. Use MATLAB and hand in the MATLAB codes. (Note that the domain is (x, y)e[0,1] x [0,1].)
0=0
0=0
4
8
12
16
10
Ꮎ0
15
25
9
14
19
24
3
11
15
0=0
8-0
0=0
3
8
13
18
23
2
6
сл
5
0=0
10
14
6
12
17
22
1
6
11
16
21
13
e=0
Fig 3
Fig 4
Textbook: Numerical Methods for Engineers, Steven C. Chapra and Raymond P. Canale, McGraw-Hill, Eighth
Edition (2021).
Ship construction question. Sketch and describe the forward arrangements of a ship. Include componets of the structure and a explanation of each part/ term.
Ive attached a general fore end arrangement. Simplfy construction and give a brief describion of the terms.
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