An investigation of variable thermo-electrical field, viscosity, and thermal conductivity influence on blood rheological (Casson) fluid flow through micro annular channel subjected to suction/injection, slip, jump, and the nonlinear convective process is presented. The assumed steady, fully developed, and magnetized flow through the annular cylinder is modeled and non-dimensionalized under; Slip, jump, suction/injection conditions. Employing the Chebyshev collocation method, an approximate solution of the flow distributions is obtained. Parameters of interest indicate a declination of the flow field to a hike in variable thermal and electrical field parameters, appreciation to the risen value of viscosity parameter. Meanwhile, both momentum and energy distributions were promoted to a wider curvature radius.