AN ANALYSIS OF TRANSIENT HEAT CONDUCTION FOR FUNCTIONALLY GRADED SPHERES BASED ON STATE SPACE THEORY¹⁾

Based on the state space theory, the spherically symmetric transient heat conduction is analyzed for functionally graded spheres. According to the heat conduction equation and the heat flux definition, the temperature field and the heat flux are taken as the state vector for the system. By dividing the sphere into spherical subshells and using the finite difference scheme in the time domain to discretize the governing equations, the state equation is established and a semi-analytical solution is obtained for the transient heat conduction problem of functionally graded spheres. The numerical examples show that the present solution is not only correct and efficient, but also can be applied to the transient heat conduction analysis for arbitrarily graded spheres.