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The solution manual provides detailed steps and explanations for obtaining this solution, including the use of the heat generation term and the application of the boundary conditions.

The general heat conduction equation in one dimension is:

ρ * c_p * (∂T/∂t) = k * (∂^2T/∂x^2) + Q

where ρ is the density, c_p is the specific heat capacity, T is the temperature, t is time, and Q is the heat source term.

The solution manual provides numerous examples and solutions to problems in heat conduction. For instance, consider a problem involving one-dimensional steady-state heat conduction in a slab: