Nusselt number for gases and liquids Calculator

✖The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.ⓘ Reynolds Number [Re]			+10% -10%
✖The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.ⓘ Prandtl Number [Pr]			+10% -10%
✖Dynamic Viscosity at Free Stream Temperature is the resisting force offered by the adjacent layers of the fluid flowing with freestream velocity.ⓘ Dynamic Viscosity at Free Stream Temperature [μ_∞]			+10% -10%
✖Dynamic Viscosity at Wall Temperature is the external force offered by the fluid to the wall of the object at the temperature of its surface.ⓘ Dynamic Viscosity at Wall Temperature [μ_w]			+10% -10%

✖The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion.ⓘ Nusselt number for gases and liquids [Nu]

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Nusselt number for gases and liquids Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nusselt Number = 2+(0.4*(Reynolds Number^0.5)+0.06*(Reynolds Number^0.67))*(Prandtl Number^0.4)*(Dynamic Viscosity at Free Stream Temperature/Dynamic Viscosity at Wall Temperature)^0.25
Nu = 2+(0.4*(Re^0.5)+0.06*(Re^0.67))*(Pr^0.4)*(μ_∞/μ_w)^0.25
This formula uses 5 Variables

Variables Used

Nusselt Number - The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion.
Reynolds Number - The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities.
Prandtl Number - The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.
Dynamic Viscosity at Free Stream Temperature - Dynamic Viscosity at Free Stream Temperature is the resisting force offered by the adjacent layers of the fluid flowing with freestream velocity.
Dynamic Viscosity at Wall Temperature - Dynamic Viscosity at Wall Temperature is the external force offered by the fluid to the wall of the object at the temperature of its surface.

STEP 1: Convert Input(s) to Base Unit

Reynolds Number: 50000 --> No Conversion Required
Prandtl Number: 19 --> No Conversion Required
Dynamic Viscosity at Free Stream Temperature: 0.0015 --> No Conversion Required
Dynamic Viscosity at Wall Temperature: 0.0018 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Nu = 2+(0.4*(Re^0.5)+0.06*(Re^0.67))*(Pr^0.4)*(μ_∞/μ_w)^0.25 --> 2+(0.4*(50000^0.5)+0.06*(50000^0.67))*(19^0.4)*(0.0015/0.0018)^0.25

Evaluating ... ...

Nu = 541.411586483276

STEP 3: Convert Result to Output's Unit

541.411586483276 --> No Conversion Required

FINAL ANSWER

541.411586483276 ≈ 541.4116 <-- Nusselt Number

(Calculation completed in 00.005 seconds)

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< Flow over Sphere Calculators

Nusselt number for air

LaTeX Go Nusselt Number = 430+((5*(10^-3))*(Reynolds Number))+((0.025*(10^-9))*(Reynolds Number^2))-((3.1*(10^-17))*(Reynolds Number^3))

Nusselt number for gases

LaTeX Go Nusselt Number = 2+(0.25*Reynolds Number+(3*10^-4)*(Reynolds Number^1.6))^0.5

Nusselt number for liquids for external flow

LaTeX Go Nusselt Number = (0.97+0.68*(Reynolds Number^0.5))/(Prandtl Number^-0.3)

Nusselt number

LaTeX Go Nusselt Number = 0.37*Reynolds Number^0.6

Nusselt number for gases and liquids Formula

LaTeX Go

What is external flow

In fluid mechanics, external flow is such a flow that boundary layers develop freely, without constraints imposed by adjacent surfaces. Accordingly, there will always exist a region of the flow outside the boundary layer in which velocity, temperature, and/or concentration gradients are negligible. It can be defined as the flow of a fluid around a body that is completely submerged in it.

An example includes fluid motion over a flat plate (inclined or parallel to the free stream velocity) and flow over curved surfaces such as a sphere, cylinder, airfoil, or turbine blade, air flowing around an airplane and water flowing around the submarines.

How to Calculate Nusselt number for gases and liquids?

Nusselt number for gases and liquids calculator uses Nusselt Number = 2+(0.4*(Reynolds Number^0.5)+0.06*(Reynolds Number^0.67))*(Prandtl Number^0.4)*(Dynamic Viscosity at Free Stream Temperature/Dynamic Viscosity at Wall Temperature)^0.25 to calculate the Nusselt Number, Nusselt number for gases and liquids formula is defined as a dimensionless quantity that characterizes convective heat transfer between a fluid and a solid sphere, providing a measure of the ratio of convective to conductive heat transfer. Nusselt Number is denoted by Nu symbol.

How to calculate Nusselt number for gases and liquids using this online calculator? To use this online calculator for Nusselt number for gases and liquids, enter Reynolds Number (Re), Prandtl Number (Pr), Dynamic Viscosity at Free Stream Temperature (μ_∞) & Dynamic Viscosity at Wall Temperature (μ_w) and hit the calculate button. Here is how the Nusselt number for gases and liquids calculation can be explained with given input values -> 541.4116 = 2+(0.4*(50000^0.5)+0.06*(50000^0.67))*(19^0.4)*(0.0015/0.0018)^0.25.

FAQ

What is Nusselt number for gases and liquids?

Nusselt number for gases and liquids formula is defined as a dimensionless quantity that characterizes convective heat transfer between a fluid and a solid sphere, providing a measure of the ratio of convective to conductive heat transfer and is represented as Nu = 2+(0.4*(Re^0.5)+0.06*(Re^0.67))*(Pr^0.4)*(μ_∞/μ_w)^0.25 or Nusselt Number = 2+(0.4*(Reynolds Number^0.5)+0.06*(Reynolds Number^0.67))*(Prandtl Number^0.4)*(Dynamic Viscosity at Free Stream Temperature/Dynamic Viscosity at Wall Temperature)^0.25. The Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity, Dynamic Viscosity at Free Stream Temperature is the resisting force offered by the adjacent layers of the fluid flowing with freestream velocity & Dynamic Viscosity at Wall Temperature is the external force offered by the fluid to the wall of the object at the temperature of its surface.

How to calculate Nusselt number for gases and liquids?

Nusselt number for gases and liquids formula is defined as a dimensionless quantity that characterizes convective heat transfer between a fluid and a solid sphere, providing a measure of the ratio of convective to conductive heat transfer is calculated using Nusselt Number = 2+(0.4*(Reynolds Number^0.5)+0.06*(Reynolds Number^0.67))*(Prandtl Number^0.4)*(Dynamic Viscosity at Free Stream Temperature/Dynamic Viscosity at Wall Temperature)^0.25. To calculate Nusselt number for gases and liquids, you need Reynolds Number (Re), Prandtl Number (Pr), Dynamic Viscosity at Free Stream Temperature (μ_∞) & Dynamic Viscosity at Wall Temperature (μ_w). With our tool, you need to enter the respective value for Reynolds Number, Prandtl Number, Dynamic Viscosity at Free Stream Temperature & Dynamic Viscosity at Wall Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Nusselt Number?

In this formula, Nusselt Number uses Reynolds Number, Prandtl Number, Dynamic Viscosity at Free Stream Temperature & Dynamic Viscosity at Wall Temperature. We can use 3 other way(s) to calculate the same, which is/are as follows -

Nusselt Number = 0.37*Reynolds Number^0.6
Nusselt Number = 2+(0.25*Reynolds Number+(3*10^-4)*(Reynolds Number^1.6))^0.5
Nusselt Number = 430+((5*(10^-3))*(Reynolds Number))+((0.025*(10^-9))*(Reynolds Number^2))-((3.1*(10^-17))*(Reynolds Number^3))

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