D = diameter of pipe
DH = 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
- 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.
- 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.
- 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.
- 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
- Heat transported by convection to Heat transported by conduction.
- Product of Re & Pr for Pe(HT) & product of Re & SC for Pe(MT)
- 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)
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)
- 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.
- 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.
- 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
- 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.
- 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.