In high Peclet number convection-diffusion flows, transport perpendicular to streamlines is governed exclusively by molecular diffusion near boundaries due to the absence of normal convective velocity components, creating a localized boundary layer where diffusive and convective effects balance despite global dominance of advection. This phenomenon necessitates an asymptotic analysis employing distinct length scales for cross-stream (boundary layer thickness scaling as Pe^-1/3) versus stream-wise directions, reducing the partial differential equation to a similarity solution in which temperature fields depend solely on a composite coordinate defined by local flow parameters and thermal diffusivity. The theoretical framework establishes that neglecting diffusion entirely renders boundary value problems incompatible at solid surfaces, whereas retaining cross-stream diffusion while ignoring streamwise diffusion yields an analytical description of heat transfer correlations valid for large Peclet numbers.
In high Peclet number convection-diffusion flows, transport perpendicular to streamlines is governed exclusively by molecular diffusion near boundaries due to the absence of normal convective velocit…