Question

Assume that we are working with an aluminum alloy (k = 180 W/moC) triangular fin with a length, L = 5 cm, base thickness, b = 1 cm, a very large width, w = 1 m. The base of the fin is maintained at a temperature of T0 = 200oC (at the left boundary node). The fin is losing heat to the surrounding air/medium at T? = 25oC with a heat transfer coefficient of h = 15 W/m2oC. Using the finite difference numerical method described previously, perform the following steps. 1- Rewrite the system of equations described by equations (4), (5), and (7) in the format AT = b where T is the temperature vector T(1:M). Start with 6 nodes which is the same number of nodes in Example 5-2 for comparison. 2- Solve this system using MATLAB and determine the temperature field T(1:6) and compare your results with that in example 5-2 of reference [1]. To check your answers, your resulting temperatures should match those seen in Example 5-2 in reference [1] provided in the supplementary background material on UBlearns. 3- Determine the fin rate of heat transfer ??? ?????? and the fin efficiency ???????? assuming a width, w = 1 m. 4- In order to determine a more precise temperature field you need to increase the number of nodes to M nodes, where M can be any integer number > 1. Rewrite the general system of equations for M nodes into the format AT = b, noting that equations (5) and (7) for boundary nodes will stay the same and equation (4) is M-2 equations. 5- Write a script file PP1P1.m that does the following a. Define all variables given in the statement above such as L, w, k, etc. with the same values given in the example. b. Preallocate matrix A and vector b using the zeros function. c. Generate the entries of matrix A and vector b for rows [2:M-1] using for loops. d. Entries for row 1 and row M can be entered manually. e. Solve the system AT = b for M = 11, 21, and 101. f. For M=101, plot the temperature T vs x where x is measured from the fin base, x(1) = 0. x can be determined using node location and should have corresponding units associated with it. Compare with the temperature calculated from analytical solution, equation (11), for the same x, and plot the analytical T on the same plot of the numerical T. Use different line styles, line width and Fully annotate your plot (titles, axis labels, legends, etc). Note: Use function besseli() in MATLAB to determine the modified Bessel function ??0 and ??1 (Hint: besseli(nu,Z) computes the modified Bessel function of the first kind, I?(z), for each element of the array Z. The order nu need not be an integer, but must be real. The argument Z can be complex. The result is real where Z is positive.) g. Find the rate of heat transfer ??? ?????? and the fin efficiency ???????? and compare with that of the analytical solution.

Answer #1

A pin fin, fabricated from an aluminum alloy (k = 185 W/m K),
has a diameter of D = 3 mm and a length of L = 15 mm. Its base
temperature is Tb = 100°C, and it is exposed to a fluid
for which T∞ = 20°C and h = 50 W/m2 K.
Provide a sketch and state your assumptions (1 point)
Use Table 3.5 in the book (grading is based on the use of
that particular table) to...

The extent to which the tip condition affects the thermal
performance of a fin depends on the fin geometry and thermal
conductivity, as well as the convection coefficient. Consider an
alloyed aluminum (k = 180 W/m*K) rectangular fin of length L = 10
mm, thickness t = 1 mm, and width w >> t. The base
temperature of the fin is Tb = 100°C, and the fin is exposed to a
fluid of temperature T∞ = 25°C. Assuming a uniform...

Consider an aluminum pin fin (k = 240 W/m·K) with a 2 mm by 2 mm
square cross-section and a length of 4 cm that is attached to a
surface at 100o C. The fin is exposed to air at 25o C with a
convection heat transfer coefficient of 20 W/m2 · o C. Determine
the rate of heat transfer and the tip temperature of the fin for
the following cases:
(a) Convection from the fin tip.
(b) Adiabatic tip...

It's a heat transfer question.
A stainless steel fin with a constant base temperature (900K)
and with an insulated end. Apply convection at all cylindrical
surfaces except the base and the tip. The convection coefficient, h
= 50 W/(m2·K), and fluid temperature of T∞ =
300K. Plot the temperature distribution along the center
axis line (T vs x). Include a contour plot across the
cross section of the fin. Assume zero contact resistance between
the sections.
K=19.8W/m-k Cp=557J/Kg-K Rho= 7900Kg/m^3...

Consider a large uranium plate of thickness 5 cm and thermal
conductivity k = 28 W/m K in which heat is generated uniformly at a
constant rate of q˙ = 6 × 10^5 W/m^3 . One side of the plate is
insulated while the other side is subjected to convection in an
environment at 30◦C with a heat transfer coefficient of h = 60 W/m2
K. Considering six equally spaced nodes with a nodal spacing of 1
cm,
(a) Sketch...

4-23 After heat treatment, the 2-cm thick metal
plates (k = 180 W/m·K, ρ = 2800 kg/m3, and cp
= 880 J/kg·K) are conveyed through a cooling chamber with a
length of 10 m. The plates enter the cooling
chamber at an initial temperature of 500°C. The cooling chamber
maintains a temperature of 10°C, and
the convection heat transfer coefficient is given as a function
of the air velocity blowing over the plates h
= 33V0.8, where h is in...

1. An oven chimney is
made of brick with a heat transmission coefficient 1.1 W/mK 10 cm
thick. Since the shaft exterior radiation beam coefficient is 0.8
and the flue gas temperature is 350°C, the external ambient
temperature is 25°C and the outer ambient heat transport
coefficient is 20 W/m2K;
a) Calculate the shaft exterior
temperature.
b) In order to reduce the risk of burn
injury that may occur in the body, the shaft is asked to be below
55°Cve...

Use Matlab to solve the following
(a) Create a plot with a sphere at the center of the graph
(origin) representing the sun with a radius of 6955000 km. Make
sure that the outside of the sphere is painted in ’autumn’ colors.
(Hint: look up the sphere() function, the colormap() function, and
the surf() function).
(b) Create a variable t ranging from 0 to 2? with increments of
0.01.
(c) The following Table gives you important values needed to
compute...

(1) Using a generator for a binomial distribution, we will test
the results of Example 3.8.2. Using software generate 500 random
deviates for X from a B(10, 0.3) distribution and 500 random
deviates for Y from a B(5, 0.3) distribution. Add corresponding
random deviates from each distribution to form an empirical W=X+Y.
Then use the theoretical result of Example 3.8.2 and directly
generate another 500 random deviates for W from a B(15, 0.3). Order
the result of the sum of...

Homework-9
Due:
Q) A fuel plate is fabricated from 0.3 cm thick 1.5% enriched
uranium. The cladding is 0.25 mm 304 stainless steel. The coolant
saturation temperature is 260 oC. The
average thermal neutron flux is 2.5 X
1014
neutrons/cm2 /s. The surface
temperature of the clad is 350 oC.
Assume any missing data to answer the following questions:.
1) Write an expression of the heat generated per unit volume
2 What is the heat flux at the surface of...

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