TThis article investigates the influence of radiation and temperature-dependent viscosity on the problem of unsteady MHD flow and heat transfer of an electrically conducting fluid past an infinite vertical porous plate taking into account the effect of viscous dissipation. The governing equations are converted into a system of nonlinear ordinary differential equations via a local similarity parameter which is taken as a function of time. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the fourth order Runge–Kutta integration scheme with the shooting method. The numerical results for the velocity and the temperature are displayed graphically showing the effects of various parameters. The results show that increasing the Eckert number and decreasing the viscosity of air leads to a rise in the velocity, while increasing in the magnetic or the radiation parameters is associated with a decrease in the velocity. Also, an increase in the Eckert number leads to an increase in the temperature, whereas an increase in radiation parameter leads to a decrease in the temperature. This article investigates the influence of radiation and temperature-dependent viscosity on the problem of unsteady MHD flow and heat transfer of an electrically conducting fluid past an infinite vertical porous plate taking into account the effect of viscous dissipation. The governing equations are converted into a system of nonlinear ordinary differential equations via a local similarity parameter which is taken as a function of time. The resulting system of coupled nonlinear ordinary differential equations is solved numerically using the fourth order Runge–Kutta integration scheme with the shooting method. The numerical results for the velocity and the temperature are displayed graphically showing the effects of various parameters. The results show that increasing the Eckert number and decreasing the viscosity of air leads to a rise in the velocity, while increasing in the magnetic or the radiation parameters is associated with a decrease in the velocity. Also, an increase in the Eckert number leads to an increase in the temperature, whereas an increase in radiation parameter leads to a decrease in the temperature.