09. Heat and Mass Transfer

Conventionally, when a natural convection is numerically calculated, we usually assume an incompressible fluid with applying the Boussinesq approximation. However, this approximation is not likely to be applied for a thermal phenomenon with large temperature difference. The thermal phenomena with large temperature difference exist in many scenes from our daily life to various engineering fields. These phenomena are often accompanied by compressible effects. Therefore, it is important to consider the compressible effects caused by the large temperature difference in numerical analyses. In the present analyses, we focused on the compressible effects, and conducted a low Mach compressible thermal fluid analysis without the Boussinesq approximation. We used an equation of state of the ideal gas and assumed constant physical properties such as viscosity coefficient and thermal conductivity. In addition, we ignored viscosity dissipation. A numerical model is a natural convection with vertical heating and cooling in a closed container. Important parameters are a dimensionless temperature difference and a Mach number. The dimensionless temperature difference is defined as (Th - Tc) / T0. Regarding the Mach number, we set it to a small value of 3×10^-4 because small Mach number flow behaves like as an incompressible fluid flow. Concerning an evaluation of the compressible effect caused by large temperature difference, we conducted both the low Mach compressible analysis and the incompressible analysis for the same numerical conditions, and we regarded differences between these analyses as the compressible effects. We conducted analyses for Pr = 1.0, 0.71 and 0.025 when the dimensionless temperature difference is ranged from 10^-4 to 1.2. According to these numerical results, we found that the thermal flow field was spatially asymmetry when the dimensionless temperature difference was large.