Complex Variables and Partial Differential Equations (3130005)

Modeling and solution of the Heat equations

BE | Semester3 Topic : Modeling and solution of the Heat equations

Q4 (c) Winter-2019
Solve : $\frac{\partial u}{\partial t} = k \frac{\partial^{2} u}{\partial x^{2}}$ for the condition of heat along rod without radiation subject to the conditions $(i) \frac{\partial u}{\partial t} = 0$ for $x = 0$ and $x = L$ & $(ii) u = Lx - x^{2}$ at $t = 0$ for all $x$ .

7 Marks

Unit : HIgher order partial differential equations and applications

Q5 (b) Winter-2019
Find the temperature in the thin metal rod of length $L$ with both the ends insulated and initial temperature is $\sin \frac{πx}{L}$ .

4 Marks

Unit : HIgher order partial differential equations and applications

Q5 (c) Summer-2020
Find the solution of $u_{t} = c^{2} u_{tt}$ together with the initial and boundary conditions $u (0, t) = u (2, t) = 0; t \geq 0, u (x, 0) = 10; 0 \leq x \leq 2 .$

7 Marks

Unit : HIgher order partial differential equations and applications