LAUSR

The current problem is performed to analyze the heatline visualization of the mixed convection mechanism and heat transfer in a double lid-driven square cavity having a heated wavy bottom surface. The moving vertical surfaces are under adiabatic conditions, and the top surface is at a cold temperature. The finite element method is employed to determine the dimensionless governing equations controlled by specific boundary conditions. The implications of the Reynolds number ( $$10 \le {\mathrm{Re}} \le 500$$ 10 ≤ Re ≤ 500 ), the directions of the constant moving wall ( $$\lambda _{\mathrm{l}}= \pm 1, \lambda _{\mathrm{r}}= \pm 1$$ λ l = ± 1 , λ r = ± 1 ), Richardson number ( $$0.01 \le {\mathrm{Ri}} \le 100$$ 0.01 ≤ Ri ≤ 100 ), Prandtl number ( $$0.015 \le \Pr \le 10$$ 0.015 ≤ Pr ≤ 10 ) and the number of oscillations ( $$1 \le {\mathrm{N}} \le 4$$ 1 ≤ N ≤ 4 ) are visualized by the streamlines, isotherms and the heatlines. The same direction of lid-driven cases leads to two primary circulation cells. The Richardson number increases as it imposes the increment of the vertical temperature gradient. At a high Prandtl number, the convection mode of heat transfer is fully established, and heat conduction occurs at a low Prandtl number. Moreover, the number of oscillations has the most significant direct impact on the streamlines and the temperature distributions compared to the flat surface. Higher Reynolds and Prandtl numbers result in an increment in the local and average Nusselt numbers. The result shows that one oscillation of the wavy surface with a low Richardson number yields to have an optimum heat transfer in the cavity.