In this paper, the fluid flow and heat transfer around a circular cylinder are studied under various conditions (Reynolds number 10 < Re < 200; Prandtl number, 0.1 ≤ Pr ≤ 2). To solve the governing equations, we use the simplified thermal lattice Boltzmann model based on double-distribution function approach, and present a corresponding boundary treatment for both velocity and temperature fields. Extensive numerical results have been obtained to the flow and heat transfer behaviors. The vortices and temperature evolution processes indicate that the flow and temperature fields change synchronously, and the vortex shedding plays a determinant role in the heat transfer. Furthermore, the effects of Reynolds and Prandtl number on the flow and isothermal patterns and local and averaged Nusselt numbers are discussed in detail. Our simulations show that the local and averaged Nusselt numbers increase with the Reynolds and Prandtl numbers, irrespective of the flow regime. However, the minimum value of the local Nusselt number can shift from the rear point at the back of the cylinder with higher Prandtl number even in the steady flow regime, and the distribution of the local Nusselt number is almost monotonous from front stagnation point to rear stagnation point with lower Prandtl number in the unsteady flow regime.

In this article the instabilities appearing in a liquid layer are studied numerically by means of the linear stability method. The fluid is confined in an annular pool and is heated from below with a linear decreasing temperature profile from the inner to the outer wall. The top surface is open to the atmosphere and both lateral walls are adiabatic. Using the Rayleigh number as the only control parameter, many kind of bifurcations appear at moderately low Prandtl numbers and depending on the Biot number. Several regions on the Prandtl-Biot plane are identified, their boundaries being formed from competing solutions at codimension-two bifurcation points.