What is a small enough temperature difference to make the boussinesq assumption?
Best insight from top research papers
The Boussinesq approximation is commonly used in natural convection problems, but its validity is limited to small temperature differences. The exact threshold for a "small enough" temperature difference varies depending on the specific problem being studied. However, some papers provide insights into this. Manela and Frankel suggest that for small temperature differences, the Boussinesq approximation holds when based on a modified Rayleigh number incorporating the potential-temperature gradient . El-Gendi and Aly mention that using the Boussinesq approximation, the temperature difference should be less than 28.6 K . Asai and Nakasuji indicate that the Boussinesq approximation is applicable when the Mach number, the relative range of the potential temperature, and the ratio of the depth of the layer to that of the isentropic atmosphere are much smaller than unity . Therefore, the specific temperature difference that qualifies as "small enough" depends on the context and the specific problem being analyzed.
Answers from top 4 papers
More filters
| Papers (4) | Insight |
|---|---|
Open access•Journal Article | The paper does not provide a specific value for the temperature difference that is considered small enough to make the Boussinesq assumption. |
Open access•Journal Article 7 Citations | The paper does not provide information about the specific temperature difference required to make the Boussinesq assumption. |
14 Citations | The paper states that the temperature difference should be less than 28.6 K to make the Boussinesq approximation. |
1 Citations | The paper does not provide a specific value for the temperature difference that is considered small enough to make the Boussinesq assumption. |
Related Questions
What is the assumption in barlaw formula?4 answersThe assumption in the Barcan formula pertains to modal metaphysics and the interpretation of possibility. The Barcan formula is often seen as challenging actualism, but it can be reinterpreted as a bridge principle connecting different modalities while maintaining a robust sense of reality in modal matters. In the context of a barb formula building pile, specific assumptions are made regarding the structure and components of the pile, such as the installation of protection hoops, clamp plates, connectors, spiral shell heads, main barbs, drilling rods, and vice barbs to enhance stability. Additionally, in a utility model related to building piles, assumptions are made about the design elements like extrusion pieces, springs, fluted inner walls, side stakes, stake holes, and inclined planes to prevent slippage and ensure proper functionality.
What are the specific temperature ranges that have been found to affect soil compaction?5 answersSpecific temperature ranges affecting soil compaction have been extensively studied. Research indicates that soil compaction properties are influenced by temperature variations within certain ranges. For instance, in the study by Lee et al., it was observed that soil compaction of cohesionless sand varied with temperatures ranging from -10°C to 17°C. Additionally, Xu et al. found that thermal conductivity of soil samples decreased linearly with decreasing temperatures in the positive range and increased exponentially in the negative range, impacting soil compaction. Moreover, Ali et al. highlighted that heating soil to temperatures of 50°C to 200°C improved its geotechnical properties, affecting collapse potential, maximum dry density, and optimum water content, all crucial factors in soil compaction. These findings collectively emphasize the significant impact of temperature on soil compaction across various temperature ranges.
Can the divergent part of a Feynman diagram be temperature dependant?5 answersThe divergent part of a Feynman diagram can be temperature dependent. In high-temperature QCD, the running coupling in the magnetic sector is strongly coupled even after renormalization group improvement. However, if the momentum scale is changed simultaneously with temperature in a specified manner, the coupling decreases. This indicates that the temperature can affect the behavior of the divergent part of the Feynman diagram. Additionally, the temperature dependence of the sum of the QCD up- and down-quark masses and the pion decay constant has been studied, showing that the quark mass increases sharply with increasing temperature near the critical temperature for deconfinement/chiral-symmetry restoration. Therefore, the temperature can have an impact on various aspects of QCD, including the divergent part of Feynman diagrams.
How does the Boussinesq dispersion model compare to other models of dispersion?4 answersThe Boussinesq dispersion model is not specifically mentioned in the provided abstracts. However, the abstracts do discuss various models of dispersion and their comparisons. Brolly et al. compare the Brownian and Langevin dynamics models for particle dispersion in turbulent flows, showing that the Langevin model outperforms the Brownian model on certain time scales. Gerbec et al. compare three different tools for simulating LNG dispersion during bunkering operations in a port, including the Unified Dispersion Model (UDM) and two CFD models. Labouriau presents a technique for constructing new proper dispersion models (PDMs) and non-standard dispersion models (NSDMs). Kehrig and Vincent discuss dispersion in marginal revenue products of inputs across plants and argue that dispersion can be "good" in certain contexts. Benintendi presents a method for modeling dispersion phenomena downstream of a containment outlet. While the Boussinesq dispersion model is not specifically addressed, these abstracts provide insights into the comparison and construction of different dispersion models.
How does temperature affect the volume change of sands?5 answersTemperature has a significant effect on the volume change of sands. When sands are subjected to high temperatures, they undergo expansion, resulting in negative axial and volumetric strains. The volume change behavior of sand is influenced by the differential thermal expansion between the pore water and sand particles, causing the pore water to flow out of the specimen during heating. The volume change of bentonite-sand mix is also affected by high temperature, with the initial hours of heating playing a significant role. Even a few degrees variation in ambient temperature can produce relatively large pore water pressures in saturated soil specimens during triaxial testing, particularly in sands. The influence of temperature on the volume change behavior of statically compacted kaolin clay was also investigated, showing that an increase in temperature increased the magnitude of volumetric strain. Alternative mechanisms of thermal volume change, such as thermally accelerated creep, may provide better predictions than thermal softening.
What assumptions is the Langmuir model based on?4 answersThe Langmuir model is not mentioned in any of the provided abstracts.