  In this work, we develop a posteriori error control for a generalized
Boussinesq model in which thermal conductivity and viscosity are
temperature-dependent. Therein, the stationary Navier-Stokes equations are
coupled with a stationary heat equation. The coupled problem is modeled and
solved in a monolithic fashion. The focus is on multigoal-oriented error
estimation with the dual-weighted residual method in which an adjoint problem
is utilized to obtain sensitivity measures with respect to several goal
functionals. The error localization is achieved with the help of a
partition-of-unity in a weak formulation, which is specifically convenient for
coupled problems as we have at hand. The error indicators are used to employ
adaptive algorithms, which are substantiated with several numerical tests such
as one benchmark and two further experiments that are motivated from laser
material processing. Therein, error reductions and effectivity indices are
consulted to establish the robustness and efficiency of our framework.
