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The steady-state viscous flow and heat transfer in the vicinity of an unaxisymmetric stagnation-point of an infinite stationary cylinder with non-uniform normal transpiration U0φ and uniform transverse magnetic field and constant wall temperature are investigated. The impinging free-stream is steady and with a constant strain rate k¯. A reduction of Navier–Stokes and energy equations is obtained by use of appropriate similarity transformations. The semi-similar solution of the Navier–Stokes equations and energy equation has been obtained numerically using an implicit finite-difference scheme. All the solutions aforesaid are presented for Reynolds numbers, Re=k¯a2/2υ, ranging from 0.01 to 100 for different values of Prandtl number and magnetic parameter and for selected values of transpiration rate function, S(φ)=U0(φ)/k¯a, where a is cylinder radius and υ is kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase in Reynolds number and transpiration rate function while dimensionless shear-stresses decrease with the increase in magnetic parameter. The local coefficient of heat transfer (Nusselt number) increases with the increasing transpiration rate function and Prandtl number.