Answered: Consider the following one-dimensional,…

Engineering

Mechanical Engineering

Consider the following one-dimensional, steady-state heat con- duction problem d²T(x) 1 dx² +80=0 in 0

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Basic Thermodynamic Processes

The word 'thermodynamics' can be divided into two words, 'thermo' and 'dynamics'. The word thermo deals with the heat and thermal phenomenon, whereas dynamics deals with forces or external agent that drives the heat flow or aids in the motion of heat.

Question

Please solve clearly.

Consider the following one-dimensional, steady-state heat con-
duction problem
d²T(x) 1
dx²
80=0 in 0<x<L
dT (x)
dx
T=0 at x=L
-k.
= 90 in x=0
a. Write the finite difference formulation of this heat conduction
problem by dividing the region 0<x< L into four equal parts.
b. Compute the node temperatures for k = 12 W/(m°C),
L = 0.012 m, qo= 105 W/m², and go = 4 x 10² W/m³.
c.
Compare the numerical solution at the nodes with the exact
solution.

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