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  3. 2 effect of a source consider the equilibrium temperature distribution...

Question: 2 effect of a source consider the equilibrium temperature distribution...

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2. Effect of a source Consider the equilibrium temperature distribution u(x) inside a uniform one-dimensional rod (with cross-sectional area A, length L-1, and ther mal conductivity Ko -1) with a source of thermal energy Q(x)- π sin(nx) (a) Write down the ODE satisfied by u(z) (b) Solve the ODE subject to the boundary conditions u(0 and (c) Find the thermal energy generated by the source per unit time inside the rod. The specific heat is c and the density p, both constants. (d) Find the thermal energy flux leaving the rod at x = 0 and x = 1. (e) What is the relationship between your answers to parts (c) and (d)? Explain this relationship in physical terms.
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