Question

A rod AB of length 10 cm has the ends A and B kept at temperature 40^{\circ}c and 100°c respectively, until the steady state is reached. At some time thereafter the temperatures at A and B are lowered to 10^{\circ}c and 50°c and they are maintained thereafter, Find the subsequent temperature distribution.​

Answer 1

Answer:

The heat equation is

Let u = X(x) . T(t) be the solution of (1), where „X‟ is a function of „x‟ alone and „T‟ is a function of „t‟ alone.

Substituting these in (1), we get

Now the left side of (2) is a function of „x‟ alone and the right side is a function of „t‟ alone. Since „x‟ and „t‟ are independent variables, (2) can be true only if each side is equal to a constant.

Step-by-step explanation: