Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or flat plate are for incompressible fluid. Here, fluid with viscosity proportional to a linear function of temperature is considered in the problem of an unaxisymmetric stagnation-point flow and heat transfer of an infinite stationary cylinder with non-uniform normal transpiration and constant heat flux. The impinging free-stream is steady and with a constant strain rate . 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 above are presented for Reynolds numbers, , ranging from 0.01 to 100 for different values of Prandtl number and viscosity-variation parameter and for selected values of transpiration rate function, , where is cylinder radius and is the reference kinematic viscosity of the fluid. Dimensionless shear-stresses corresponding to all the cases increase with the increase of Reynolds number and transpiration rate function while dimensionless shear stresses decrease with the increase of viscosity-variation parameter. The local coefficient of heat transfer (Nusselt number) increases with the increasing transpiration rate function and Prandtl number.

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