Unsteady1D heat conduction,steady:,unsteady: (transient),Integration,integrate with respect to x:,integrate with respect to t:,Time integration,repeat for points E and W:,Explicit vs implicit,f=0 explicit scheme f=0.5 semi-implicit (Crank- Nicolson) scheme f=1 fully implicit scheme,Explicit scheme,for:,in order to give realistic solutions,Crank-Nicolson scheme,can give unrealistic solutions,Implicit scheme,always gives realistic solutions,Unsteady2-D heat conduction,Discretized unsteady 2-D heat conduction equation,Unsteady 3-D heat conduction equation,Discretized unsteady 3-D heat conduction equation,Solution of the equations,direct method Gauss-Seidel method line-by-line method alternating-direction implicit strongly implicit procedure,Relaxation,overrelaxation underrelaxation,Relaxation,relaxation through inertia:,