This research explores the combined effects of magnetic field and viscous dissipation on the heat field and discusses the second law study (generation of entropy) in an electrically conducting fluid under the influence of wall mass transfer over a continuous, variable viscosity spread non-isothermal surface. It is considered that the viscosity of the fluid is an inverse linear temperature property. The theory of approximation of boundary layers is used to model the governing equations of momentum, energy and concentration. To transfer the governing partial differential equations into ordinary ones, appropriate similarity transformations are used and numerical results are obtained by using the shooting technique. To measure the entropy generation and the Bejan number in the flow region, velocity, temperature and concentration distribution are obtained and used. The effect on velocity, temperature, concentration, entropy production, and Bejan number of the vector viscosity, Schmidt number, Hartman and Reynolds number are are studied and discussed. It is found that presences of the variable viscosity parameter reduces the fluid friction in the region close to the surface. This in turn results in low irreversibility (i.e. entropy) with increasing Schmidt number Sc and viscous dissipation parameter Ec inside the boundary layer. Further, the Bejan number for the variable viscosity case is lower than that for uniform viscosity when there is a variation in the values of group parameter and Hartman number Ha