# Grashof Number

on . Posted in Dimensionless Numbers

Grashof number, abbreviated as Gr, a dimensionless number, is used in fluid dynamics and heat transfer to characterize the relative importance of buoyancy forces to viscous forces in a fluid flow or heat transfer process.  It is particularly relevant in natural convection, where fluid motion is driven by temperature differences, and buoyancy plays a significant role.  The Grashof number helps determine the dominant mode of heat transfer within a fluid system.

### Grashof number Interpretation

• Gr < 1  -  Viscous forces dominate over buoyancy forces.  In this case, the fluid flow or heat transfer is primarily driven by the viscous properties of the fluid, and buoyancy effects are negligible.
• Gr > 1  -  Buoyancy forces dominate over viscous forces.  This indicates that the fluid motion or heat transfer is significantly influenced by buoyancy, and natural convection becomes important.

The Grashof number is commonly used in the analysis and design of heat exchangers, cooling systems, and other situations where fluid motion is driven by temperature differences.  It helps engineers and scientists predict when natural convection will be a significant factor in a given system and how it will affect heat transfer or fluid flow.

### Grashof Number for vertical flat places formula

$$Gr = g \; l^3 \; \alpha_c \; ( T_s - T_{\infty}) \;/\; \nu^2$$
Symbol English Metric
$$\large{ Gr }$$ = Grashof number $$dimensionless$$
$$\large{ T_{\infty} }$$ = bulk temperature $$F$$ $$C$$
$$\large{ g }$$ = gravitational acceleration $$ft \;/\; sec^2$$ $$m \;/\; s^2$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity of fluid $$ft^2 \;/\; sec$$ $$m^2 \;/\; s$$
$$\large{ l }$$ = vertical length $$ft$$ $$m$$
$$\large{ T_s }$$ = temperature of surface $$F$$ $$C$$
$$\large{ \alpha_c }$$  (Greek symbol alpha) = thermal expansion coefficient of fluid $$in \;/\; in\;F$$ $$mm \;/\; mm\;C$$

### Grashof Number for bulk bodies and pipes formula

$$Gr = g \; l^3 \; \alpha_c \; ( T_s^{\nu^2} - T_{\infty} ) \;/\; \nu^2$$
Symbol English Metric
$$\large{ Gr }$$ = Grashof number $$dimensionless$$
$$\large{ T_{\infty} }$$ = bulk temperature $$F$$ $$C$$
$$\large{ g }$$ = gravitational acceleration $$ft \;/\; sec^2$$ $$m \;/\; s^2$$
$$\large{ \nu }$$  (Greek symbol nu) = kinematic viscosity of fluid $$ft^2 \;/\; sec$$ $$m^2 \;/\; s$$
$$\large{ l }$$ = vertical length $$ft$$ $$m$$
$$\large{ T_s }$$ = temperature of surface $$F$$ $$C$$
$$\large{ \alpha_c }$$  (Greek symbol alpha) = thermal expansion coefficient of fluid $$in \;/\; in\;F$$ $$mm \;/\; mm\;C$$