A new class of exact solutions of the Oberbeck–Boussinesq equations is constructed to describe diffusion convective flows of incompressible media taking into account mass forces, concentration sources (sinks), and Joule’s dissipation. The velocity field is described by quadratic forms with respect to two spatial coordinates. The announced exact solution generalizes the class of Lin–Sidorov–Aristov exact solutions. The solute concentration, pressure, and mass force field are described by nonlinear fourth-degree forms. © 2023, Allerton Press, Inc.