A numerical study of a plane wall jet with heat transfer

•A well resolved direct numerical simulation of wall jet is performed.•Turbulent Prandtl number for wall jets is not a constant value.•Heat transfer variables scale with inner, outer and thermal scales.•Temperature variance and heat flux budgets are presented.•Wall normal heat flux production is balanced by pressure diffusion.

A direct numerical simulation (DNS) of a wall jet is performed at Re=7500. To the authors' knowledge, this is the highest Reynolds number DNS study of a wall jet. The heat transfer process is studied with an iso-thermal boundary condition at the wall. The molecular Prandtl number is Pr=0.71. Mean flow and heat transfer parameters are contrasted with available measurements and Nusselt number coefficient correlations. The scaling parameters for heat transfer variables are investigated. The mean temperature ⟨T⟩, temperature root mean square Trms, streamwise ⟨u′T′⟩ and wall normal 〈v′T′〉 heat flux profiles show collapse in the streamwise direction, with the inner scaling, the outer scaling and the thermal scaling parameters. The complete budgets for temperature variance ⟨T′T′⟩ and turbulent heat fluxes are also presented.