Boundary Value Problems of Heat Conduction

applying approximation boundary condition boundary surface boundary-value problem Btu/hr ft³ cartesian coordinate system conduction is given coordinate system cylindrical coordinate system defined derivatives determined eigenfunctions eigenvalues ẞm equation of heat evaluated finite region finite-difference given by Eq Green's function H₁ heat conduction heat flux heat source heat-conduction problems initial condition initially at temperature initially at zero integral transform inversion formula k₁ kernel layer method Monte Carlo method nodal point nonlinear obtain one-dimensional ordinary differential equation partial positive roots problem of heat radius random-walk semi-infinite region separation of variables side of Eq slab solid cylinder solution space variable spherical coordinate system ẞmx ẞx Substituting Eq T₁ temperature distribution temperature F(r thermal conductivity third kind tion transcendental equation unknown coefficients vector x₁ Xi+1 zero temperature Δι θμ ат әт дх дх² ᏊᎢ