Consider the fuel element of Example 5.11, which operates at a uniform volumetric generation rate of q ˙ = 10 7 W / m 3 , until the generation rate suddenly changes to q ˙ = 2 × 10 7 W / m 3 . Use the Finite-Difference Equations, One-Dimensional, Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the 6 nodes, with 2 mm, as shown in the example. (a) Calculate the temperature distribution 1.5 s after the change in operating power, and compare your results with those tabulated in the example. (b) Use the Explore and Graph opt ions of IHT to calculate and plot temperature histories at the midplane (00) and surface (05) nodes for 0 ≤ t ≤ 400 s . What are the steady-state temperatures, and approximately how long does it take to reach the new equilibrium condition after the step change in operating power?
Consider the fuel element of Example 5.11, which operates at a uniform volumetric generation rate of q ˙ = 10 7 W / m 3 , until the generation rate suddenly changes to q ˙ = 2 × 10 7 W / m 3 . Use the Finite-Difference Equations, One-Dimensional, Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the 6 nodes, with 2 mm, as shown in the example. (a) Calculate the temperature distribution 1.5 s after the change in operating power, and compare your results with those tabulated in the example. (b) Use the Explore and Graph opt ions of IHT to calculate and plot temperature histories at the midplane (00) and surface (05) nodes for 0 ≤ t ≤ 400 s . What are the steady-state temperatures, and approximately how long does it take to reach the new equilibrium condition after the step change in operating power?
Solution Summary: The author calculates the energy balance to the center of the rod using one dimensional conduction with uniform heat generation.
Consider the fuel element of Example 5.11, which operates at a uniform volumetric generation rate of
q
˙
=
10
7
W
/
m
3
, until the generation rate suddenly changes to
q
˙
=
2
×
10
7
W
/
m
3
. Use the Finite-Difference Equations, One-Dimensional, Transient conduction model builder of IHT to obtain the implicit form of the finite-difference equations for the 6 nodes, with 2 mm, as shown in the example.
(a) Calculate the temperature distribution 1.5 s after the change in operating power, and compare your results with those tabulated in the example.
(b) Use the Explore and Graph opt ions of IHT to calculate and plot temperature histories at the midplane (00) and surface (05) nodes for
0
≤
t
≤
400
s
. What are the steady-state temperatures, and approximately how long does it take to reach the new equilibrium condition after the step change in operating power?
A 1-D conduction heat transfer problem with internal energy generation is governed by the following equation:
+-=
dx2 =0
W
where è = 5E5 and k = 32 If you are given the following node diagram with a spacing of Ax = .02m and know that
m-K
T = 611K and T, = 600K, write the general equation for these internal nodes in finite difference form and determine the
temperature at nodes 3 and 4.
Insulated
Ar
, T
For the answer window, enter the temperature at node 4 in Kelvin (K).
Your Answer:
EN
SORN
Answer
units
Pri
qu) 232 PM
4/27/2022
99+
66°F Sunny a .
20
ENLARGED
oW TEXTURE
PRT SCR
IOS
DEL
F8
F10
F12
BACKSPACE
num
-
%3D
LOCK
HOME
PGUP
170
Please solve clearly.
Write the finite difference form of the two dimensional steady state heat conduction equation with internal heat generation at a constant rate ‘g’ for a region 0.03m X 0.03m by using a mesh size ∆x=∆y= 0.01 m for a material having thermal conductivity 25 W/m.K and heat generation rate, 107 W/m3 . All the boundary surfaces are maintained at 10°C. Express the finite difference equations in matrix form for the unknown node temperatures.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.