The Grashof number (Gr)– It is a dimensionless number used in fluid dynamics and heat transfer which gives the ratio of the buoyancy force to viscous force acting on a fluid. It is used in situations involving natural convection and is analogous to the Reynolds number. Mathematical Representation of Grashof Number is given as–
Where: g = gravitational acceleration, β = coefficient of thermal expansion, Ts = surface temperature, T∞ = bulk temperature, L = vertical length, ν = kinematic viscosity= dynamics viscosity / density= μ / ρ
Physical Significance of Grashof Number-
- Grashof number is used to check the fluid flow behavior around a new prototype. Most of the times scaled models of the desired prototype are tested under similar environment. Grashof numbers uses when buoyancy and viscous forces are very important.
- It shows, how dominant is the buoyancy force which is responsible for the convection comparing to the viscous forces.
- It is very similar to the Reynolds’s number. Only difference is that Reynolds Number is used for forced convection while Grashof number is used for natural convection phenomenon.
- Nusselt Number is a function of Prandtle Number and Grashof Number.
- Reynolds number shows the flow as laminar, Transition and turbulent flow in forced convection cases. Grashof number does the same in natural convection.
- It is a function of buoyancy force, inertia force and viscous force.