__Nomenclature:__

D = diameter of pipe

D

_{H = }Hydraulic diameter

L = Length of the pipe

Lch = characteristic length

R = Length through which conduction occurs.

u = mean characteristic velocity of the object relative to the fluid.

Vch = Characteristic velocity

k = thermal conductivity

μ = dynamic viscosity of the fluid

= density of fluid.

h = heat transfer coefficient.

g = acceleration due to earths gravity.

t = characteristic time

ν = Kinematic viscosity of fluid.

α = Thermal diffusivity

β

*=*volumetric thermal expansion coefficient ( = 1/T for ideal fluids, T = absolute temperature)

Ts = surface temperature

T

_{∞ }= Bulk Temperature_{ }

__Significance:__- Ratio of
**Inertial forces to viscous forces.** - Primarily used
**to analyse different flow regimes**namely Laminar, Turbulent, or both. - When Viscous forces are dominant its a laminar flow & when Inertial forces are dominant it is a Turbulent flow.

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- Depends only on
**fluid & its properties.**It is also ratio of**velocity boundary layer to thermal boundary layer** - Pr = small, implies that rate of thermal diffusion (heat) is more than the rate of momentum diffusion (velocity).
- Also the
**thickness**of thermal boundary layer is much larger than the velocity boundary layer.

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__Significance:__**Analogous of Prandtl number**in Heat Transfer.- Used in fluid flows in which there is
**simultaneous momentum & mass diffusion**. - It is also ratio of
**fluid boundary layer to mass transfer boundary layer thickness.** - To find mass transfer coefficient using Sherwood number, we need Schmidt number.

__Significance:__- Ratio of
**t****hermal diffusivity to mass diffusivity**. - Fluid flow with
**simultaneous Heat & mass transfer**by convection. - It is also ratio of
**Schmidt number to Prandtl number**

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__Significance:__**Heat transported by convection to Heat transported by conduction.****Product of Re & Pr for Pe(HT) & product of Re & SC for Pe(MT)**

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__Significance:__- It is the ratio of
**heat transferred to the fluid to the heat transported by the fluid (ratio of****Nusselt number to Peclet number)** - Used to find
**heat transfer in forced convection flows.** **St(HT) = Nu/(Re.Pr) & St(MT) = Sh/(Re.Sc)**

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__Significance:__A)

__Sherwood Number:__- Ratio of
**Convective to diffusive mass transport.**Used in**mass transfer operations.** - Analogous of Nusselt number in Heat transfer OR Sherwood number is
**Nusselt number for mass transfer.**

B)

__Nusselt Number__- Ratio of
**convective to conductive heat transfer coefficient**across the boundary layer. **Low Nu**=> conduction is more =>**Laminar flow****High Nu**=> convection is more=>**Turbulent flow**.- It can also be viewed as
**conduction resistance to convection resistance**of the material. **Free convection:**Nu = f(Ra, Pr)__Forced Convection:__Nu = f(Re, Pr)

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__Significance:__- Ratio of
**Buoyancy force to viscous force**in natural convection. **Reynolds number**is**used in forced convection**of fluid flow, whereas**Grashof number is used in natural convection.**

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__Significance:__- used in
**unsteady state (transient) heat transfer conditions**. - ratio of
**heat transfer resistance inside**the body**to heat transfer resistance at the surface**of the body. OR ratio of**internal thermal resistance to external thermal resistance**. - Shows the
**variation of temperature inside the body w.r.t to time.** **Bi < 0.1**=> heat transfer**resistance inside**the body is**very low**=> inside the body**conduction**takes place**faster compared to convection**at the surface. => no temperature gradient inside the body (**uniformity in temperature**) vice versa implies that Temperature is not uniform throughout hte material volume.

__Significance:__- It shows the
**presence & strength of convection**in a fluid body. - Heat transfer by Conduction within fluid < Critical value for that fluid < Heat transfer by convection. (consequences of Ra values)
**Product of Gr.Pr**

__Significance:__- Characterizes
**laminar flow in a conduit**OR**transfer of heat by streamline fluid flow in a pipe** - In case of
**mass transfer, Pr is replaced by Sc**.

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__Significance:__- 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.
- It can also be understood as
**current time to the time taken to reach steady state.**

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