Mass/heat transfer through laminar boundary layer in axisymmetric microchannels with nonuniform cross section and fixed wall concentration/temperature

We present a similarity solution for mass/heat transfer in laminar forced convection at high Peclet numbers. The classical boundary layer solution of the Graetz–Nusselt problem, valid for straight channels or pipes, is generalized to an axisymmetric microchannel with circular cross-section, whose radius R(z) varies continuously along the axial coordinate z. The case of fixed wall concentration/temperature is analyzed.The advection/diffusion transport problem is solved by taking into account both the tangential and normal velocity components (and their scaling behaviours as a function of the wall normal distance), in order to obtain an accurate description of the concentration/temperature profile in the boundary layer.The analytical solution of the local Sherwood/Nusselt number is compared with finite elements numerical results for a truncated cone and a wavy sinusoidal channel.