Question

A nuclear fuel element consists of a solid cylindrical pin of radius, r1 and thermal conductivity, kf. The fuel pin is in good contact with a cladding material of radius, r2 and thermal conductivity, kc. Consider steady state condition for which uniform heat generation occurs within the fuel at a volumetric rate, g (w/m3 ) and the outer surface of the cladding is exposed to a coolant that is characterized by temperature, Tsur and convection coefficient, h.

a) Obtain equations for the temperature distribution Tf(r) and Tc(r) in the fuel and cladding, respectively.

b) Consider a uranium oxide fuel pin for which kf = 2 W/m.K and r1 = 6 mm and cladding for which kc = 25 W/m.K and r2 = 9 mm. If g = 2×108 W/m3 , h = 2000 W/m2 .K and Tsur = 300 K, what is the maximum temperature in the fuel element?

Answer #1

Steam at an average temperature of ?∞= 400°C flows through a
steel pipe. The inner and outer radii of the pipe are r1 = 4 cm and
r2 = 4.5 cm, respectively, and the outer surface of the pipe is
insulated with a layer of 50 mm thick-calcium silicate of thermal
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The fuel element of a nuclear reactor is in the shape of a plane
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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...

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 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...

Consider a cube of density, specific heat, and thermal
conductivity of 2700 kg/m3, 0.896 kJ/kg-K, and 204 W/m-K,
respectively. The cube is 5 cm in length, and is initially at a
temperature of 20 oC. For t>0, two of the boundary surfaces are
insulated, two are subjected to uniform heating at a rate of 10,000
W/m2, and two dissipate heat by convection to an ambient
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Assuming lumped capacitance...

71 mm thick horizontal plate made of an opaque material of
thermal conductivity k= 25 W/m-K. At the bottom, water flows at a
temperature of T∞,w = 25C, whereas air flows at the top of the
plate at T∞,a = 710 C having convection coefficient of ha= 71
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irradiated flux of 7100W/m2, of which 30% is reflected back. The
top and bottom surface temperatures are maintained at 43 C...

A 1-shell-2-tube pass heat exchanger
is made of a steel alloy (thermal conductivity 45.4 W/(m K). It is
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29oC using water which flows inside tubes with an outer
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tubes in the shell is 160 (80 per pass). The mass flow rate of
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A thin metallic wall may be constructed using copper (properties
are given in the table). The piping is required
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Properties
Copper
Insulation material
Thermal Conductivity (W/m per ˚C)
385
0.071
Density (kg/m3)
8940
453
i. If the external...

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