R olling noise levels from railways are strongly dependent on the roughness generated on the running surfaces of wheels and rails. As an initial effort concerning the wheels, a two-dimensional nite element (F E) model of the transient thermal convection-diffusion problem at block braking is developed. The streamline diffusion method is used to stabilize the solution. A constitutive law is adopted that describes the division of frictional heat between block and wheel. The model parameters are calibrated using available experimental data, and a sensitivity analysis is carried out. The results are in good agreement with experimentally obtained experience, especially regarding the division of frictional heat. Keywords: nite element model, transient convection-diffusion equation, streamline diffusion method, division of frictional heat, railway block braking NOTATION a nodal temperatures (8C) c p speci c heat capacity (J/kg 8C) · e e unit vector E objective function (8C) f force vector (W/m) h element size (m) I identity matrix J Bessel function of the rst kind k thermal conductivity (W/m 8C) k thermal conductivity matrix (W/m 8C) K stiffness matrix (W/m 8C) M mass matrix (J/m 8C) n unit normal vector N number of data points p pressure (N m 2 ) Pe Peclet number q heat ux (W m 2 ) q heat ux vector (W m 2 ) Q internally generated heat (W m 3 ) r thermal contact resistance constant (N 8C/W) R radius (m) R w outer wheel radius (mm) t time (s) T temperature (8C) T c calculated temperature (8C) T e measured temperature (8C) v velocity of material point (m/s) v velocity vector (m/s) V sliding speed (m/s) w test function (8C) W weights x , y spatial coordinates (m) Y Bessel function of the second kind a thermal diffusivity (m 2 s) a b coef cient of heat transfer for the block (W m 2¯C