Question

An infinitely long plane uniform plate is bounded by two parallel edges and an end at right
angles to them. The breadth is tt; this end is maintained at a temperature up at all points and
other edges are at zero temperature then which of the following is not true in the steady
state?​

Answer 1

Answer:

pls mark brainlist and follow

Answer 2

We need to use LAPLACE's Two-Dimensional Heat Equation here.

Explanation:

• Laplace eqn.'s basic form is $\frac{\delta^2 u}{\delta x^2} + \frac {\delta^2 u}{\delta y^2} = 0$
• Let u = X(x) . Y(y) be a solution of laplace eqn.
• we get

                           $\frac{\delta^2 u}{\delta x^2} = X''Y\\\\\\frac {\delta^2 u}{\delta y^2} =XY''\\\\\\\therefore X''Y + XY'' = 0\\\\\implies \frac{X''}{X} = -(\frac{Y''}{Y})$

• let us say both sides are equal to some "k"

                            $when\ k \ is \ positive \ and k = \lambda^2\\ \\X = c_1 e^l^x + c_2 e ^- ^l^x\\\\Y= c_3 cos(ly) + c_4 sin (ly)\\\\\\when\ k \ is \ negative \ and k = -\lambda^2 \\\\X= c_3 cos(ly) + c_4 sin (ly)\ \\\\Y = c_1 e^l^x + c_2 e ^- ^l^x \\\ \\\\when\ k \ is \ zero\\\\X = c_1 x + c_2\\\\Y = c_3 x + c_4$