Heat Conduction and Laplace Transforms Quiz

$T(x, t) = T_0 + \sum_{n=1}^\infty \left(\frac{4T_0}{\pi n}\right) \sin\left(\frac{n\pi x}{L}\right) e^{-\alpha (n\pi/L)^2 t}$ (correct)

$T(x, t) = T_0 + \sum_{n=0}^\infty \left(\frac{4T_0}{\pi (2n+1)}\right) \cos\left(\frac{(2n+1)\pi x}{2L}\right) e^{-\alpha ((2n+1)\pi/2L)^2 t}$

$T(x, t) = T_0 + \sum_{n=1}^\infty \left(\frac{4T_0}{\pi n} \right) \cos\left(\frac{n\pi x}{L}\right) e^{-\alpha (n\pi/L)^2 t}$

$T(x, t) = T_0 + \sum_{n=0}^\infty \left(\frac{4T_0}{\pi (2n+1)}\right) \sin\left(\frac{(2n+1)\pi x}{2L}\right) e^{-\alpha ((2n+1)\pi/2L)^2 t}$

$0.88\times10^{-5} \,m^2/s$ (correct)

$6.3\times10^{-7} \,m^2/s$

$26 \,W/(mK)$

$50 \,W/(m^2K)$

$6.3\times10^{-7} \,m^2/s$

$26 \,W/(mK)$

$0.88\times10^{-5} \,m^2/s$

$50 \,W/(m^2K)$ (correct)

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