DEPARTMENT OF CHEMICAL ENGINEERING PRESENTED BY AQIB JAH TEMURI (D-14-CH-33)
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DEPARTMENT OF CHEMICAL ENGINEERING
PRESENTED BYAQIB JAH TEMURI (D-14-CH-33)
DIMENSIONLESS NUMBER
Reynold’s Number (Re)It gives a measure of the ratio of inertial and viscous forces in fluid flow. It is often used to determine if the flow is either laminar or turbulent:
• In laminar flow, viscous forces dominate. The flow paths are smooth, streamline and constant.
• In turbulent flow, inertial forces dominate. The flow regime is unstable, generating eddies and vortices.
The Kind of flow depends on value of Re
• If Re < 2000 the flow is Laminar
• If Re > 4000 the flow is turbulent
• If 2000 < Re < 4000 it is called transition flow.
Prandtl Number (Pr)• The Prandtl number, Pr, is the ratio of kinematic viscosity to the thermal diffusivity.
• It is used in many calculations involving heat transfer in flowing fluids.
• it gives a measure of the relative thickness of the thermal and momentum boundary layers.
Where,
Cp = Fluid specific heat capacity
μ = Dynamic viscosity
k = Thermal conductivity
Nusselt Number (Nu)• The Nusselt Number, Nu, is the ratio of convective to conductive heat transfer in a fluid
over a given length, l:
• For heat transfer in pipes, the characteristic length is the pipe diameter.
• At a Nusselt number of around one means that convection and conduction are about equal.
Where,
h = Heat transfer coefficient
l = Characteristic length
k = Thermal conductivity
Sherwood Number (Sh)The Sherwood Number, Sh, is a measure of the ratio of convective and diffusive mass transfer in a fluid. It is analogous to the Nusselt Number in heat transfer:
Where,
hD = Mass transfer coefficient
l = Characteristic length
k = Molecular diffusivity
Froude Number (Fr)• The Froude Number, Fr, is a measure of the ratio of the inertial and gravitational forces.
• It is often used to analyse fluid flow problems where there is a free surface. For example, in agitated vessels, Fr governs the formation of free surface vortices.
Where,
v = Velocity
l = Characteristic length
g = Acceleration due to gravity
Schmidt Number (Sc)• Schmidt Number, Sc, is the ratio of kinematic viscosity to the diffusivity. It can be expressed as:
• It characterises mass transfer in a flowing fluid
Where,
D = Diffusivity
μ = Dynamic viscosity
p = Fluid density
Biot Number (Bi)• It the ratio of the heat transfer resistances inside of and at the surface of a body.
• The Biot number (Bi) is used in heat transfer calculations.
Where,
h = Heat transfer coefficient
l = Characteristic length
kb = Thermal conductivity of the body
Fourier Number (Fo)• Ratio of rate of heat conduction to the rate of heat storage.
• Used along with Biot number to solve transient state heat transfer problems.
• For mass transfer by diffusion, Fourier number for MT is used.
Where,
α = Thermal Diffusivity
t = Characteristic time
L = Length through which conduction occurs
D = Diffusivity
Lewis Number (Le)• Ratio of thermal diffusivity to mass diffusivity.
• Fluid flow with simultaneous Heat & mass transfer by convection.
• It is also ratio of Schmidt number to Prandtl number.
Mach Number (Ma)• The Mach Number, Ma, is the ratio of the fluid velocity to the velocity of sound in that
medium.
• In Chemical Engineering, the Mach Number is commonly used in calculations involving high velocity gas flow.
Where,
u = Velocity of fluid
a = Speed of sound in fluid medium
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