dimensionless no in heat transfer

1. DIMENSIONLESS
NUMBER

2. GROUP
MEMBERS:
MUHAMMAD FEROZ
2017-CH-720
IHTASHAM MEHMOOD
2017-CH-719
ADEEL AKRAM
2017-CH-718
MUHAMMAD AKMAL
2017-CH-722

3. DIMENSIONAL ANALYSIS:
• Dimensional analysis is a topic that deal with dimension.
• There are two types of dimensions.
• Fundamental dimension
• Derived dimension
• Dimensional analysis is use wo check the correction of given formula.
• Two terms are add when the dimensions of both quantities is same.

4. DIMENSIONAL ANALYSIS

5. 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.

6. 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 flowingfluids.
• 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

7. 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 pipediameter.
• At a Nusselt number of around one means that convection and conduction areabout
equal.
Where,
h = Heat transfer coefficient
l = Characteristic length
k = Thermal conductivity

8. Grashof Number:
• The Grashof number is used to determine the heat
transfer coefficient under free convection conditions.
It is basically a ratio between the buoyancy forces and
viscous forces.

9. Biot Number (Bi)
• It the ratio of the heat transfer resistances inside of and at the
surface of abody.
• The Biot number (Bi) is used in heat transfer calculations.
Where,
h = Heat transfer coefficient
l = Characteristic length
kb = Thermal conductivity of the
body

10. 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 isused.
Where,
α = Thermal Diffusivity
t = Characteristic time
L = Length through which conduction occurs
D = Diffusivity

11. 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.

12. Mach Number (Ma)
• The Mach Number, Ma, is the ratio of the fluid velocity to the velocity
of sound inthat
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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