Question

3) In steady state condition derive the solution of the one dimensional heat flow equation.
A. u(x) = ax
B. u(x) = ax + b
C. u(x)=b
D. None of the above​

Answer 1

Answer:

in this conditions our equations will be option b u (x) + is equals to a x + b

Answer 2

Answer:

OPtion (B) u(x) = ax + b

Step-by-step explanation:

To find steady state solution that is

$= \lim_{t \to \infty} u(x,t)$

Suppose, partially differentiating the above equation we get the heat equation

$\frac{du}{dt}= c^{2} . \frac{d^{2}u }{dx^{2} }$    0 ≤ x ≤ L,

The solution is said to be steady-state if it is independent of time

Therefore we can write heat solution by u(x)

Therefore $u_{xx} = 0$ because the solution is independent of time

$\frac{d^{2}u }{dx^{2} }= 0$

Therefore u(x) = ax + b

Therfore in steady state condition the one dimensional heat flow equation is u(x) = ax + b