Boundary layer flow and heat transfer over an exponentially shrinking vertical sheet with suction

In this paper, we investigate theoretically the problem of steady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid in the presence of buoyancy force over an exponentially shrinking vertical sheet with suction. The shrinking velocity and wall temperature are assumed to have specific exponential function forms. The governing equations are first transformed to similarity equations using an appropriate similarity transformation. The resulting equations were then solved numerically using shooting technique involving fourth-order Runge–Kutta method and Newton–Raphson method. The influence of mixed convection/buoyancy parameter λ, suction parameter s and Prandtl number Pr on the flow and heat transfer characteristics is examined and discussed. Numerical results indicate that the presence of buoyancy force would contribute to the existence of triple solutions to the flow and heat transfer for particular value of pertinent parameters. It is different for the non-buoyant flow case i.e. when the buoyancy force is absent, the problem admits only dual solutions. Further, this study also reveals that the features of flow and heat transfer characteristics are significantly affected by buoyancy parameter λ, suction parameter s and Prandtl number Pr.

► The presence of buoyancy forces contribute towards the existence of triple solutions of skin friction coefficient f″(0) and heat transfer rate −θ′(0).
► For assisting flow, f″(0) and −θ′(0) increase with s and λ but decrease with Pr for the first solution.
► For opposing flow, f″(0) and −θ′(0) increase with s and Pr but decrease with λ for the first solution.