The steady state heat conduction over a thin plate is governed by the partial differentialequation:- = 0ôx² ' ôy²a) Obtain the temperature distribution for the given boundary conditions in thefigure using finite difference approximation and a 3x3 grid.Tb) Calculate the temperature gradientsÔxand-at the plate mid-point usingдуan appropriate numerical differentiation approximation.TT=10 °CHint: -k = 0 for the insulatedôiedges where i is the directionnormal to the edge.1m InsulatedInsulatedT=100 °C1m-

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The steady state heat conduction over a thin plate is governed by the partial diffe equation: ôx² ' ôy² a) Obtain the temperature distribution for the given boundary conditions in figure using finite difference approximation and a 3x3 grid. T and at the plate mid-point us ôy b) Calculate the temperature gradients ôx an appropriate numerical differentiation approximation. Hint: -k=0 for the insula ôi T=10 °C edges where i is the direction normal to the edge. 1m Insulated Insulated T=100 °C 1m-

The steady state heat conduction over a thin plate is governed by the partial diffe equation: ôx² ' ôy² a) Obtain the temperature distribution for the given boundary conditions in figure using finite difference approximation and a 3x3 grid. T and at the plate mid-point us ôy b) Calculate the temperature gradients ôx an appropriate numerical differentiation approximation. Hint: -k=0 for the insula ôi T=10 °C edges where i is the direction normal to the edge. 1m Insulated Insulated T=100 °C 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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

100%

The steady state heat conduction over a thin plate is governed by the partial differential
equation:
- = 0
ôx² ' ôy²
a) Obtain the temperature distribution for the given boundary conditions in the
figure using finite difference approximation and a 3x3 grid.
T
b) Calculate the temperature gradients
Ôx
and
-at the plate mid-point using
ду
an appropriate numerical differentiation approximation.
T
T=10 °C
Hint: -k = 0 for the insulated
ôi
edges where i is the direction
normal to the edge.
1m Insulated
Insulated
T=100 °C
1m-

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