Question

By means of a dimensional analysis, verifies that the dimensionless numbers corresponding to mass, energy and moment have no dimensions.

Answer 1

dimensionless numbers in mass transfer

Schmidt number = momentum diffusivity / mass diffusivity

= /D

= (cm2/s) /(cm2/s)

It is dimensionless

Sherwood number = interface flux / molecular flux

= mass transfer coefficient x diameter / diffusivity

= kd/D

= (cm/s) * (cm) / (cm2/s)

= (cm2/s) /(cm2/s)

It is dimensionless

dimensionless numbers in heat transfer

Prandtl number = momentum diffusivity / thermal diffusivity

=

= (cm2/s) /(cm2/s)

It is dimensionless

Nusselt number = heat transfer by convection / heat transfer by conduction

= h L /k

= Heat transfer coefficient x characteristic length /thermal conductivity

= (W/m2-K) *(m) /(W/m-K)

= (W/m-K) /(W/m-K)

It is dimensionless

dimensionless numbers in momentum transfer

Grashof Number = Buoyancy force*inertia force/viscous force

?=Volumetric Thermal Expansion

= (m/s2) *(K-1) *(K) *(m3) /(m4/s2)

= (m4/s2)/(m4/s2)

It is dimensionless

Reynolds number = inertial force/viscous force

= Dv/

= m x m/s / m2/s

= m2/s / m2/s

It is dimensionless