The solution for the temperature in a plane wall, initially at t(0), whose surface temperatures at...

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The solution for the temperature in a plane wall, initially at t(0), whose surface temperatures at x=0 and x-L are each suddenly lowered to too is given by t(x,0) - too 4sin [(2n-1)n] exp[-(2n-1)²x² L² αθ t (0) - too π 2n - 1 n=1 (a) Verify that the given solution satisfies the differential equation and boundary conditions by direct substitution. (b) Verify that the initial condition is also satisfied. (c) Determine an analytical expression for the total amount of energy (per unit wall area) that has been given off to the surroundings from the beginning of 0 = 0 to time of 0 = T. Thermal conductivity is k. (Hint: heat is losing from both left x=0 and right x-L wall surfaces) The solution for the temperature in a plane wall, initially at t(0), whose surface temperatures at x=0 and x-L are each suddenly lowered to too is given by t(x,0) - too 4sin [(2n-1)n] exp[-(2n-1)²x² L² αθ t (0) - too π 2n - 1 n=1 (a) Verify that the given solution satisfies the differential equation and boundary conditions by direct substitution. (b) Verify that the initial condition is also satisfied. (c) Determine an analytical expression for the total amount of energy (per unit wall area) that has been given off to the surroundings from the beginning of 0 = 0 to time of 0 = T. Thermal conductivity is k. (Hint: heat is losing from both left x=0 and right x-L wall surfaces)

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Soluton a To verify that the given solution satisfies the differential equation and boundary conditions we first write the equation for the temperatur... View the full answer