Nusselt Number (Nu)

Physical Significance of Nusselt Number

# Consider a layer of fluid of thickness L, difference in temperature  ΔT = T₂-T₁. 

Heat Transfer through a fluid layer

# Heat transfer through the fluid layer is convection when the fluid involves some motion.

# Heat transfer for this case is Q_Conv = h . A . ΔT ---------1.

# On the contrary, heat transfer through the fluid layer is conduction when the fluid is not in motion.

# Heat transfer for this case is Q_Cond = k . A.  ΔT / (L ) --------2.

# By taking their ratio of equation 1. & 2.,

Q_Conv / Q_Cond = (h .  ΔT .  L) / (k .  ΔT)

                         = (h .  L) / (k )

                         = Nu, Nusselt number.

# Nusselt number represents the improvement of heat transfer through a fluid layer as a result of convection relative to conduction across the same fluid.

# The larger the Nusselt number, the more efficient the convection.

# Nusselt number, Nu is unity for fluid layer represents heat flux across the layer by pure conduction.

Note;

k - Thermal Conductivity, W/m K
h - Convection heat transfer coefficient , W/m² K