Question

Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where ?(?,?) represents the temperature. 9??? = ?? ; 0 < ? < 6; ? > 0; B. C. : ?? (0,?) = 0; ?? (6,?) = 0; ? > 0; I. C. : ?(?, 0) = 12 + 5??? ( ? 6 ?) − 4???(2??); 0 < ? < 6 (a) When ? = 0, what would be the temperature at ? = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed Dirichlet-Neumann. Then, state the general solution for ?(?,?). (Note: you don’t need to derive the general solution ?(?,?).) (7 marks) (c) Find the particular solution of this initial-boundary value problem making use of your general solution in Q2(b). (10 marks)

Х + X Let F(x) = 4 - XO < X < 2 (a) Exp с X Test 2_202005.pdf 5 X (5) WhatsApp ... C:/Users/User/Downloads/Test%202_202005.pdf lo o Q2 Given the following heat conduction initial-boundary value problem of a thin homogeneous rod, where u(x, t) represents the temperature. 9uxx = ut; 0 < x < 6; t> 0; B.C.: Uz(0,t) = 0; Ux(6,t) = 0; t> 0; 1. C.: u(x,0) = 12 + Scos 6 x) – 4cos(2x); 0 < x < 6 (a) When t = 0, what would be the temperature at x = 3? (Use the initial condition.) (3 marks) (b) Determine whether the boundary conditions in this case is Dirichlet, Neumann, or mixed Dirichlet-Neumann. Then, state the general solution for u(x,t). (Note: you don't need to derive the general solution u(x, t).) (7 marks) (c) Find the particular solution of this initial-boundary value problem making use of your general solution in Q2(b). (10 marks) [Total: 20 marks] TNT OOITATION DATED X عرض الكل WhatsApp Image....jpeg H Type here to search 1 14) ENG 9:42 AM 30/7/2020 5

Answer 1

In this question to evaluate the first part use initial condition as t=0 given and just put x=3.

now for the second part the conditions are Neumann Conditions and then write the solution.

i have written the derivation but you can also skip this part.

For the last part do the comparing as in u(x,0) there are cosine terms in both the general solution and in the initial conditions.

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