a²T (x,t) ƏT (x,t) at α 3x² 4. Consider the heat conduction equation: = Solve the above equation, subject to the followi

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a²T (x,t) ƏT (x,t) at α 3x² 4. Consider the heat conduction equation: = Solve the above equation, subject to the following boundary and initial conditions: for a one-dimensional rod of length “L”. (a) Both ends of the rod at T=0, with an initial temperature, i.e., T (x, 0) = 100. Given that the material of the rod is Silicon (with thermal conductivity, k = 130 W/mK, density (p) = 2330 kg/m³, and the specific heat (c) = 700 J/kgK), estimate the temperature at x=L/2, assuming L= 1 m, and t= 1000 seconds. π.χ. (b) Both ends of the rod at T=0, with an initial temperature, T (x, 0) = 6 sin( L +4 sin 2πχ. 5/~