Table Q1 shows the initial temperature distribution of a 1 cm long steel bar at equal distance Table Q1: The initial temperature distribution of a 1 cm long steel bar Point B Point D 85 55 Point A A +90 Point C 70 Temperature The initial point A is maintained at (A +90) °C, while the last point E is convectively cooled by a coolant at (B + 10) °C for 0.1 seconds. The unsteady state heating equation follows a heat equation, given as (b) Point E B + 10 where K is thermal diffusivity of material, x is the longitudinal coordinate of the bar, I' is temperature and t is time. The thermal diffusivity of the material is given as K = 2.5 cm²/s. O Note that A is the first 2 digits of your matrix number, while B is the last two digits of your matrix number. For example, a student with matrix number DD201026 will have the value of A = 20 and B=26 (a) Based on the stability requirement, show that the explicit finite difference method is not suitable to be used to find the unknown temperature of each point from 0 second to 0.1 seconds, with Ar=0.05 seconds. Draw finite-difference grid to predict the temperature at all points up to 0.1 seconds. Use At = 0.05 seconds. Label all the unknown temperature in the grid. Determine the unknown temperatures of point A, B, C, D and E at 0.05 seconds.
Table Q1 shows the initial temperature distribution of a 1 cm long steel bar at equal distance Table Q1: The initial temperature distribution of a 1 cm long steel bar Point B Point D 85 55 Point A A +90 Point C 70 Temperature The initial point A is maintained at (A +90) °C, while the last point E is convectively cooled by a coolant at (B + 10) °C for 0.1 seconds. The unsteady state heating equation follows a heat equation, given as (b) Point E B + 10 where K is thermal diffusivity of material, x is the longitudinal coordinate of the bar, I' is temperature and t is time. The thermal diffusivity of the material is given as K = 2.5 cm²/s. O Note that A is the first 2 digits of your matrix number, while B is the last two digits of your matrix number. For example, a student with matrix number DD201026 will have the value of A = 20 and B=26 (a) Based on the stability requirement, show that the explicit finite difference method is not suitable to be used to find the unknown temperature of each point from 0 second to 0.1 seconds, with Ar=0.05 seconds. Draw finite-difference grid to predict the temperature at all points up to 0.1 seconds. Use At = 0.05 seconds. Label all the unknown temperature in the grid. Determine the unknown temperatures of point A, B, C, D and E at 0.05 seconds.
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter5: Analysis Of Convection Heat Transfer
Section: Chapter Questions
Problem 5.12P
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Question
sub: numerical method
value A=20
value B = 7
point A=20+90=110
point E=7+10+17
Transcribed Image Text:Table Q1 shows the initial temperature distribution of a 1 cm long steel bar at equal distance
Table Q1: The initial temperature distribution of a 1 cm long steel bar
Point B
Point D
85
55
Point A
A +90
Temperature
The initial point A is maintained at (A +90) °C, while the last point E is convectively cooled by
a coolant at (B + 10) °C for 0.1 seconds. The unsteady state heating equation follows a heat
equation, given as
(b)
OT
ôt
(c)
K
Point C
70
ax
Point E
B+10
where K is thermal diffusivity of material, x is the longitudinal coordinate of the bar, I is
temperature and t is time. The thermal diffusivity of the material is given as K = 2.5 cm² /s.
Note that A is the first 2 digits of your matrix number, while B is the last two digits of your
matrix number. For example, a student with matrix number DD201026 will have the value of
A = 20 and B=26
(a)
Based on the stability requirement, show that the explicit finite difference method is not
suitable to be used to find the unknown temperature of each point from 0 second to 0.1
seconds, with At = 0.05 seconds.
Draw finite-difference grid to predict the temperature at all points up to 0.1 seconds.
Use At = 0.05 seconds. Label all the unknown temperature in the grid.
Determine the unknown temperatures of point A, B, C, D and E at 0.05 seconds.
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