Smoothed particle hydrodynamics (SPH) is a particle method for analyzing physical problems. But this method has numerical problems when treating multilayer problems and free surface. In this report we propose equations to treat multilayer heat conduction problems and normalized equations to avoid the edge effect which is caused by the lack of particles at the free surface. Numerical results, in the case of 1 layer heat conduction model has good agreement with results of difference method. Numerical results in the case of 2 layer heat conduction model, where the ratio of heat conductivity of 2 layer is changed from 5 to 50 shows that normalized equations are effective to treat multilayer heat conduction problems.
