Project ForgeIn the following two-dimensional momentum equation for natural convection over a surface immersed in a quiescent fluid at temperature T∞ (g is the gravitational acceleration, β is the volumetric thermal expansion coefficient, ν is the kinematic viscosity, u and v are the velocities in x and y directions, respectively, and T is the temperature): u(∂u/∂x)+v(∂u/∂y) = gβ(T−T∞) + ν(∂²u/∂y²), the term gβ(T−T∞) represents
- ARatio of inertial force to viscous force.
- BRatio of buoyancy force to viscous force.
- CViscous force per unit mass.
- Buoyancy force per unit mass.
Explanation
In the natural-convection momentum equation (Boussinesq approximation), each term has units of acceleration (force per unit mass). Comparing with ν(∂²u/∂y²) which is viscous force per unit mass, gβ(T−T∞) is analogously the buoyancy force per unit mass, driving the flow due to density differences from thermal expansion.
Source: GATE ME 2022 Session 1 (ME-1) (2022)
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