A thin plate is initially at a uniform temperature of 200°C. At a certain time t = 0 the temperature of the east side of the plate is suddenly reduced to 0°C. The other surface is insulated. Use the explicit finite volume method in conjunction with a suitable time step size to calculate the transient temperature distribution of the slab and compare it with the analytical solution at the time (i) t = 40 s, (ii) t = 80 s, and (iii) t = 120 s. Recalculate the numerical solution using a time step size equal to the limit given by (8.13) for t = 40 s and compare the results with the analytical solution. The data are: plate thickness L = 2 cm, thermal conductivity k = 10 W/m.K and ρc = 10 × 106 J/m3 .K

Solve the problem using the Crank-Nicolson scheme (θ = 1/2). - Write the discretized equations for the interior nodes.

Modify the Eq. 8.9

and obtain the discretized equations for the boundary nodes

- Substitute the values and recast them in a matrix form (only for the 1 st time step)

- Obtain a solution at a time of 10 s with a time step of 2 s.
 

Transcribed Image Text:

pc Tp-T;) ΔΙ Δι ΔΙ +0 |Δx = 0 which may be rearranged to give ;)]T EXPE Re SN PE k(T-T)_kT-T] διάρκει δωρ +(1-0) + a k(T-T)_k(Tp-T) δυνα διάρ -[0T + (1 - 0T]+ διερε -[0T + (1 - 0)T] δωρ + SAY (8.9) pc Tp-T;) ΔΙ Δι ΔΙ +0 |Δx = 0 which may be rearranged to give ;)]T EXPE Re SN PE k(T-T)_kT-T] διάρκει δωρ +(1-0) + a k(T-T)_k(Tp-T) δυνα διάρ -[0T + (1 - 0T]+ διερε -[0T + (1 - 0)T] δωρ + SAY (8.9)

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The onedimensional transient heat conduction equation is ar a pc 817 dt dx dx and the initial condit... View the full answer