The steady state heat conduction over a thin plate is governed by the partial differential equation: a'T a'T = 0 + a) Show the imaginary nodes over the plate necessary to solve this problem by the finite difference method for the 3x3 grid shown in the figure. b) Apply finite difference discretization and obtain the linear algebraic equation system to solve the temperature distribution (obtain the equations, present them in matrix form but do not solve them). T=10 °C T =0 for the insulated di Hint: -k 1m T=10 °C• Insulated edges where i is the direction normal to the edge. Insulated 1m-

The steady state heat conduction over a thin plate is governed by the partial differential equation: a'T a'T = 0 + a) Show the imaginary nodes over the plate necessary to solve this problem by the finite difference method for the 3x3 grid shown in the figure. b) Apply finite difference discretization and obtain the linear algebraic equation system to solve the temperature distribution (obtain the equations, present them in matrix form but do not solve them). T=10 °C T =0 for the insulated di Hint: -k 1m T=10 °C• Insulated edges where i is the direction normal to the edge. Insulated 1m-

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

3.
The steady state heat conduction over a thin plate is governed by the partial differential
equation:
(35Pts)
+
2
= 0
a) Show the imaginary nodes over the plate necessary to solve this problem by the
finite difference method for the 3x3 grid shown in the figure.
b) Apply finite difference discretization and obtain the linear algebraic equation
system to solve the temperature distribution (obtain the equations, present them
in matrix form but do not solve them).
T=10 °C
T
Hint: -k =0 for the insulated
1m
T=10 °C
* Insulated
ĉi
edges where i is the direction normal to
the edge.
Insulated
1m

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