This article investigates the behavior of various viscosity models under conjugated natural convection in a square cavity with a conductive baffle at various angles of inclination and differential heating of the side walls. Numerical simulations were performed using the finite volume method for a fluid having viscous properties similar to those of a non-Newtonian fluid. The slope angle of the computational domain and the choice of the non-Newtonian fluid model were considered as the main parameters. The inclination of the hull took on the values 0°, 30°, 45°, 60° and 90°. The received data illustrate that the increase in the velocity of convection flows is strongly influenced by the angles of inclination of 30° and 60°. By analyzing various non-Newtonian fluid models, the power low viscosity model predicted velocities more than other viscosity models. Whereas in the Herschel-Bulkley viscosity model, only the heat transfer process mainly occurred. Analysis of the obtained local Nusselt number showed that the values were higher on the cold wall. This is explained by more intense heat transfer due to convection on this wall. It should also be noted from the data obtained that when the region is tilted at α = 90° for the Carreau viscosity model, one can notice the complete absence of the convection process, and when using the Herschel–Bulkley viscosity model, no flow mixing occurred, which led to heat exchange solely due to heat transfer for different tilt angles.