SEMI-ANALYTIC NUMERICAL SOLUTION OF HEAT CONDUCTION PROBLEMS USING GREEN'S FUNCTIONS
A semi-analytic numerical solution using Green's functions (GFs) is developed and demonstrated. The X22B10T0 solution for 1 − D transient conduction is used as a kernel to govern the dynamics of energy over discrete elements in the computational domain. Assembly of the elemental equations results in an explicit time marching scheme to compute new temperatures at the nodes at each time steps. An assumption regarding the temperature variation over each element is necessary in order to account for the "initial condition" term in the GF at each time step. Piecewise constant and linear variations in temperature over each element are examined. The semi-analytic method is benchmarked against a standard Crank − Nicolson scheme. Test cases evaluated include the temperature responses due to step, triangular, quadratic, and quartic heat flux pulses. The effect of element size and time step on each case is studied, and the results are compared to the exact solution.