Flow and heat transfer at a stagnation-point over an exponentially shrinking vertical sheet with suction

• Similarity solutions for the flow at stagnation point can be obtained either with or without the presence of suction.
• Skin friction and heat transfer rate would increase with the addition of suction.
• The presence of buoyancy force would contribute towards the occurrence of triple similarity solutions.
• When the buoyancy force is absent, the problem admits only dual solutions.

This paper investigate theoretically the problem of steady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid at a stagnation point over an exponentially shrinking vertical sheet with suction. In this study, we assume that the shrinking velocity and wall temperature have specific exponential function form. An appropriate similarity transformation is employed to transform the governing equations in partial differential equations form to similarity equations in ordinary differential equations form. The resulting equations are then solved numerically using shooting technique with Maple implementation. The influence of mixed convection/buoyancy parameter λ, suction parameter s and shrinking variable c/a on the flow and heat transfer characteristics is examined and discussed. Numerical results indicate that the presence of buoyancy force would contribute to the presence of triple solutions to the flow and heat transfer for particular value of pertinent parameters.