Many thermal boundary conditions are available in OpenFOAM. I will upload some basic cases that explain the usage of these boundary conditions.

**Source Code**

**src/TurbulenceModels/compressible/turbulentFluidThermoModels/derivedFvPatchFields/**

**convectiveHeatTransfer**It calculates the heat transfer coefficients from the following empirical correlations for forced convection heat transfer:

\begin{eqnarray}

\left\{

\begin{array}{l}

Nu = 0.664 Re^{\frac{1}{2}} Pr^{\frac{1}{3}} \left( Re \lt 5 \times 10^5 \right) \\

Nu = 0.037 Re^{\frac{4}{5}} Pr^{\frac{1}{3}} \left( Re \ge 5 \times 10^5 \right) \tag{1} \label{eq:NuPlate}

\end{array}

\right.

\end{eqnarray}

where \(Nu\) is the**Nusselt number**, \(Re\) is the**Reynolds number**and \(Pr\) is the**Prandtl number**.**externalCoupledTemperature****externalWallHeatFluxTemperature**This boundary condition can operate in the following two modes:

**Mode#1**Specify the heat flux \(q\)

\begin{equation}

-k \frac{T_p – T_b}{\vert \boldsymbol{d} \vert} = q + q_r \tag{2} \label{eq:fixedHeatFlux}

\end{equation}

* \(k\): thermal conductivity

* \(q_r\): radiative heat flux

* \(T_b\): temperature on the boundary**Mode#2**Specify the heat transfer coefficient \(h\) and the ambient temperature \(T_a\) (Fig. 1)

\begin{equation}

-k \frac{T_p – T_b}{\vert \boldsymbol{d} \vert} = \frac{T_a – T_b}{R_{th}} + q_r \tag{3} \label{eq:fixedHeatTransferCoeff}

\end{equation}

* \(R_{th}\): total thermal resistance of convective and conductive heat transfer

\begin{equation}

R_{th} = \frac{1}{h} + \sum_{i=1}^{n} \frac{l_i}{k_i} \tag{4} \label{eq:Rth}

\end{equation}**fixedIncidentRadiation****lumpedMassWallTemperature**There is a dimensionless quantity called the

**Biot number**, which is defined as

\begin{equation}

Bi = \frac{l/k}{1/h} = \frac{hl}{k}, \tag{5} \label{eq:Biot}

\end{equation}

where \(h\) is the heat transfer coefficient, \(k\) is the thermal conductivity of a solid and \(l\) is the characteristic length of the solid. As the definition in Eq. \eqref{eq:Biot} indicates, it represents the ratio of the internal conduction resistance \(l/k\) and the external convection resistance \(1/h\). If the Biot number is small (\(Bi \ll 1\)), the solid may be treated as a simple lumped mass system of an uniform temperature. This boundary condition calculates the uniform temperature variation \(\Delta T\) on the boundary from the following equation:

\begin{equation}

m c_p \Delta T = Q \Delta t. \tag{6} \label{eq:lumpedmass}

\end{equation}

* \(m\): total mass [kg]

* \(c_p\): specific heat capacity [J/(kg.K)]

* \(Q\): net heat flux on the boundary [W]

* \(\Delta t\): time step [s]**outletMappedUniformInletHeatAddition****totalFlowRateAdvectiveDiffusive****wallHeatTransfer****compressible::thermalBaffle1D****compressible::turbulentHeatFluxTemperature****compressible::turbulentTemperatureCoupledBaffleMixed****compressible::turbulentTemperatureRadCoupledMixed****compressible::alphatJayatillekeWallFunction****compressible::alphatPhaseChangeWallFunction****compressible::alphatWallFunction**