[en] This work is devoted to study a magnetohydrodynamic flow of the Casson fluid over a stretching surface in the presence of Hall effect. Cattaneo–Christov heat flux model is executed to explore the characteristics of heat transfer. The model is an adjustment of the classical Fourier’s law through thermal relaxation time. Convective boundary condition is used on the boundary for heat transfer. The boundary layer partial differential equations are reduced into a system of nonlinear ordinary differential equations through similarity transformations. An efficient computational procedure based on rational Legendre collocation method is formulated and implemented to simulate the resulting problem, numerically. Influences of the physical parameters on the velocity and temperature profiles are analyzed and discussed. Also, impacts of different values of Casson fluid parameter, Hall parameter, Hartman number and Biot numbers on local Nusselt number are computed and examined. (author)