A rod of length a is fully insulated along it sides. Assuming the initial temperature is defined by, 0 4, sin nxe't n=1 where 4, are an arbitrary constant. (b) Solve the particular solution for the general solution obtained from the Q1 (a).
A rod of length a is fully insulated along it sides. Assuming the initial temperature is defined by, 0 4, sin nxe't n=1 where 4, are an arbitrary constant. (b) Solve the particular solution for the general solution obtained from the Q1 (a).
Related questions
Question
Transcribed Image Text:A rod of length a is fully insulated along it sides. Assuming the initial temperature is
defined by,
0<x<-
2
х,
f(x) ={
T- x,
-<x<T
2
and at t= 0, the ends are dipped into cold water and held at temperature of 0°C. The heat
equation given as,
ôt ôx
(a) Analyze the given partial differential equation by using the method of separation
of variables and prove that the solution of the heat transfer problem above gives
as,
u(x,t) =4, sin nxe
-n't
n=1
where 4, are an arbitrary constant.
(b) Solve the particular solution for the general solution obtained from the Q1 (a).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
