Local Variation of Heat Transfer for Laminar Flow Over a Finite Width Flat Plate

Lateral variation of wall heat transfer in laminar boundary layer flow is investigated for geometries where both the heated and cooled/adiabatic surfaces are finite in lateral extent. Two dimensional conduction models are compared to three dimensional thermal numerical simulations for a variety of Prandtl numbers, boundary conditions, unheated starting lengths, and widths. It is found that the conduction model works remarkably well at predicting wall heat transfer and the most relevant length scale for describing the problem is the conduction thickness. Three dimensionless spanwise variables that fully characterize the heat transfer are defined using the conduction thickness: the lateral location and the widths of the heated and cooled/adiabatic region normalized by the conduction thickness. The lateral variation of the Nusselt number is described for various widths and boundary conditions, with only the isoflux-adiabatic set of boundary conditions not resulting power law behavior for the Nusselt number near the lateral edge. Furthermore, it is found the spanwise extent of the region affected by the lateral edge is of the same order of magnitude as the conduction thickness. Effects of the finite lateral width and various boundary conditions on the heat flux at the center of a finite strip, convection from infinitesimally small strips, and lateral spacing of heated components are explored and presented. Finally, the accuracy and computational simplicity of the conduction model allows for impressive savings in numerical modeling of conjugate heat transfer where lateral variation in heat transfer is important.