A direct numerical simulation of turbulent heat transfer in a channel flow has been conducted for a Reynolds number of $5000$ and the Prandtl number of air, $0.71$. The mixed boundary condition has been used as the boundary condition of the thermal field. The computational domain has been set to $3.2 {\rm \pi}h$, $2h$ and $1.6 {\rm \pi}h$ in the $x$, $y$ and $z$ directions, respectively. This domain is large enough to accurately compute the statistics of the flow. Mean values and intensities of the temperature have been obtained. Derived parameters from the average thermal field, such as the von Kármán constant and the Nusselt number have been calculated. An asymptotic behaviour of the von Kármán constant is observed when ${\textit {Re}}_\tau$ is increased. A correlation for the Nusselt number is proposed. Also, the turbulent Prandtl number has been calculated and it does not present significant changes when ${\textit {Re}}_\tau$ is increased. Finally, the turbulent budgets are presented. A relation between the increment of the inner peak of the temperature intensities and the scaling failure of the dissipation and viscous diffusion terms is provided. The statistics of all simulations can be downloaded from the web page of our group: http://personales.upv.es/serhocal/....

Direct numerical simulation of thermal channel flow for ${\textit {Re}}_\tau =5000$ and ${\textit {Pr}} = 0.71

10.1017/jfm.2021.231