Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids Calculator

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✖Reynolds Number Dia is the ratio of inertial forces to viscous forces.ⓘ Reynolds Number Dia [Re_D]			+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%
✖Length is the measurement or extent of something from end to end.ⓘ Length [L]			+10% -10%
✖Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.ⓘ Diameter [D]			+10% -10%
✖Dynamic Viscosity at Bulk Temperature is the measurement of the fluid's internal resistance to flow at the bulk temperature.ⓘ Dynamic Viscosity at Bulk Temperature [μ_bt]			+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 simultaneous development of hydrodynamic and thermal layers for liquids [Nu]

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Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids

Formula

`"Nu" = 1.86*((("Re"_{"D"}*"Pr")/("L"/"D"))^0.333)*("μ"_{"bt"}/"μ"_{"w"})^0.14`

Example

`"29.20298"=1.86*((("1600"*"0.7")/("3m"/"10m"))^0.333)*("0.002"/"0.0018")^0.14`

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Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids Solution

STEP 0: Pre-Calculation Summary

Formula Used

Nusselt Number = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14
Nu = 1.86*(((Re_D*Pr)/(L/D))^0.333)*(μ_bt/μ_w)^0.14
This formula uses 7 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 Dia - Reynolds Number Dia is the ratio of inertial forces to viscous forces.
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.
Length - (Measured in Meter) - Length is the measurement or extent of something from end to end.
Diameter - (Measured in Meter) - Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.
Dynamic Viscosity at Bulk Temperature - Dynamic Viscosity at Bulk Temperature is the measurement of the fluid's internal resistance to flow at the bulk temperature.
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 Dia: 1600 --> No Conversion Required
Prandtl Number: 0.7 --> No Conversion Required
Length: 3 Meter --> 3 Meter No Conversion Required
Diameter: 10 Meter --> 10 Meter No Conversion Required
Dynamic Viscosity at Bulk Temperature: 0.002 --> No Conversion Required
Dynamic Viscosity at Wall Temperature: 0.0018 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Nu = 1.86*(((Re_D*Pr)/(L/D))^0.333)*(μ_bt/μ_w)^0.14 --> 1.86*(((1600*0.7)/(3/10))^0.333)*(0.002/0.0018)^0.14

Evaluating ... ...

Nu = 29.2029830664446

STEP 3: Convert Result to Output's Unit

29.2029830664446 --> No Conversion Required

FINAL ANSWER

29.2029830664446 ≈ 29.20298 <-- Nusselt Number

(Calculation completed in 00.020 seconds)

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< 15 Laminar Flow Calculators

Nusselt Number by Sieder-Tate for Shorter Tubes

Go Nusselt Number = ((1.86)*((Reynolds Number)^(1/3))* ((Prandtl Number)^(1/3))* ((Diameter of Tube/Length of Cylinder)^(1/3))* ((Fluid Viscosity (at fluid bulk temperature)/Fluid Viscosity (At pipe wall temperature))^(0.14)))

Nusselt number for hydrodynamic length fully developed and thermal length still developing

Go Nusselt Number = 3.66+((0.0668*(Diameter/Length)*Reynolds Number Dia*Prandtl Number)/(1+0.04*((Diameter/Length)*Reynolds Number Dia*Prandtl Number)^0.67))

Nusselt number for simultaneous development of hydrodynamic and thermal layers

Go Nusselt Number = 3.66+((0.104*(Reynolds Number Dia*Prandtl Number*(Diameter/Length)))/(1+0.16*(Reynolds Number Dia*Prandtl Number*(Diameter/Length))^0.8))

Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids

Go Nusselt Number = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14

Nusselt number for short tube thermal development

Go Nusselt Number = 1.30*((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333

Nusselt number for short lengths

Go Nusselt Number = 1.67*(Reynolds Number Dia*Prandtl Number*Diameter/Length)^0.333

Diameter of thermal entry tube

Go Diameter = Length/(0.04*Reynolds Number Dia*Prandtl Number)

Thermal entry length

Go Length = 0.04*Reynolds Number Dia*Diameter*Prandtl Number

Stanton number for Colburn analogy

Go Stanton Number = Darcy Friction Factor/(8*(Prandtl Number^0.67))

Darcy friction factor for Colburn analogy

Go Darcy Friction Factor = 8*Stanton Number*Prandtl Number^0.67

Colburn's j-factor

Go Colburn's j-factor = Stanton Number*(Prandtl Number)^(2/3)

Diameter of hydrodynamic entry tube

Go Diameter = Length/(0.04*Reynolds Number Dia)

Hydrodynamic entry length

Go Length = 0.04*Diameter*Reynolds Number Dia

Darcy friction factor

Go Darcy Friction Factor = 64/Reynolds Number Dia

Reynolds Number given Darcy Friction Factor

Go Reynolds Number = 64/Darcy Friction Factor

Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids Formula

What is internal flow?

internal flow is a flow for which the fluid is confined by a surface. Hence the boundary layer is unable to develop without eventually being constrained. The internal flow configuration represents a convenient geometry for heating and cooling fluids used in chemical processing, environmental control, and energy conversion technologies.

An example includes flow in a pipe.

How to Calculate Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids?

Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids calculator uses Nusselt Number = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14 to calculate the Nusselt Number, The Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone. Nusselt Number is denoted by Nu symbol.

How to calculate Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids using this online calculator? To use this online calculator for Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids, enter Reynolds Number Dia (Re_D), Prandtl Number (Pr), Length (L), Diameter (D), Dynamic Viscosity at Bulk Temperature (μ_bt) & Dynamic Viscosity at Wall Temperature (μ_w) and hit the calculate button. Here is how the Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids calculation can be explained with given input values -> 29.20298 = 1.86*(((1600*0.7)/(3/10))^0.333)*(0.002/0.0018)^0.14.

FAQ

What is Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids?

The Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone and is represented as Nu = 1.86*(((Re_D*Pr)/(L/D))^0.333)*(μ_bt/μ_w)^0.14 or Nusselt Number = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14. Reynolds Number Dia is the ratio of inertial forces to viscous forces, 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, Length is the measurement or extent of something from end to end, Diameter is a straight line passing from side to side through the center of a body or figure, especially a circle or sphere, Dynamic Viscosity at Bulk Temperature is the measurement of the fluid's internal resistance to flow at the bulk 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.

How to calculate Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids?

The Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids formula is defined as the ratio between heat transfer by convection (α) and heat transfer by conduction alone is calculated using Nusselt Number = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14. To calculate Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids, you need Reynolds Number Dia (Re_D), Prandtl Number (Pr), Length (L), Diameter (D), Dynamic Viscosity at Bulk Temperature (μ_bt) & Dynamic Viscosity at Wall Temperature (μ_w). With our tool, you need to enter the respective value for Reynolds Number Dia, Prandtl Number, Length, Diameter, Dynamic Viscosity at Bulk 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 Dia, Prandtl Number, Length, Diameter, Dynamic Viscosity at Bulk Temperature & Dynamic Viscosity at Wall Temperature. We can use 5 other way(s) to calculate the same, which is/are as follows -

Nusselt Number = 3.66+((0.0668*(Diameter/Length)*Reynolds Number Dia*Prandtl Number)/(1+0.04*((Diameter/Length)*Reynolds Number Dia*Prandtl Number)^0.67))
Nusselt Number = 1.67*(Reynolds Number Dia*Prandtl Number*Diameter/Length)^0.333
Nusselt Number = 3.66+((0.104*(Reynolds Number Dia*Prandtl Number*(Diameter/Length)))/(1+0.16*(Reynolds Number Dia*Prandtl Number*(Diameter/Length))^0.8))
Nusselt Number = 1.30*((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333
Nusselt Number = ((1.86)*((Reynolds Number)^(1/3))* ((Prandtl Number)^(1/3))* ((Diameter of Tube/Length of Cylinder)^(1/3))* ((Fluid Viscosity (at fluid bulk temperature)/Fluid Viscosity (At pipe wall temperature))^(0.14)))

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