Discrete-velocity models and lattice Boltzmann methods are presented for solving
convection-radiation effects in thermal fluid flows. The discrete-velocity equations are
derived from the continuous Boltzmann equation with appropriate scaling suitable for incompressible
flows. The radiative heat flux in the energy equation is obtained using the
discrete-ordinates solution of the radiative transfer equation. This chapter is structured in
two parts. In the first part we investigate the derivation of the discrete-velocity models and
we perform an asymptotic analysis to show at the leading order, the macroscopic models
are recovered from these discrete-velocity models. In this part we also formulate the lattice
Boltzmann method for solving the convection-radiation problems. The second part
of this chapter is devoted to the computational aspects of the considered models. Consistent
boundary and initial conditions in the lattice Boltzmann models are also discussed in
this part. Numerical results are presented for several test examples on coupled convectionradiation
flows in two dimensional enclosures. Detailed simulation results at different flow
and radiative regimes, as well as benchmark solutions, are also presented and discussed.
The obtained results show that the developed models are competitive tools for convectionradiation
problems.
Keywords: Discrete-velocity models, forced convection, heat transfer, implicit-explicit schemes, incompressible
Navier-Stokes equations, large-eddy simulation, Lattice-Boltzmann method, natural convection,
radiative heat transfer, relaxation scheme.
