Nusselt Number by Sieder-Tate for Shorter Tubes Calculator

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✖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. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.ⓘ 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%
✖Diameter of tube is defined as the OUTSIDE DIAMETER (O.D.), specified in inches (e.g., 1.250) or fraction of an inch (eg. 1-1/4″).ⓘ Diameter of Tube [d]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l]			+10% -10%
✖Fluid Viscosity (at fluid bulk temperature) is the resistance offered by the fluid with respect to the fluid bulk temperature(in kelvin).ⓘ Fluid Viscosity (at fluid bulk temperature) [μ_b]			+10% -10%
✖Fluid Viscosity (At pipe wall temperature) is the resistance offered by the fluid with respect to the pipe wall temperature(in kelvin).ⓘ Fluid Viscosity (At pipe wall temperature) [μ_pw]			+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 by Sieder-Tate for Shorter Tubes [Nu]

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Formula

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Nusselt Number by Sieder-Tate for Shorter Tubes

Formula

`"Nu" = ((1.86)*(("Re")^(1/3))* (("Pr")^(1/3))* (("d"/"l")^(1/3))* (("μ"_{"b"}/"μ"_{"pw"})^(0.14))) `

Example

`"23.30876"= ((1.86)*(("5000")^(1/3))* (("0.7")^(1/3))* (("4m"/"6m")^(1/3))* (("8Pa*s"/"12Pa*s")^(0.14))) `

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Nusselt Number by Sieder-Tate for Shorter Tubes Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
Nu = ((1.86)*((Re)^(1/3))* ((Pr)^(1/3))* ((d/l)^(1/3))* ((μ_b/μ_pw)^(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 - 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. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
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.
Diameter of Tube - (Measured in Meter) - Diameter of tube is defined as the OUTSIDE DIAMETER (O.D.), specified in inches (e.g., 1.250) or fraction of an inch (eg. 1-1/4″).
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Fluid Viscosity (at fluid bulk temperature) - (Measured in Pascal Second) - Fluid Viscosity (at fluid bulk temperature) is the resistance offered by the fluid with respect to the fluid bulk temperature(in kelvin).
Fluid Viscosity (At pipe wall temperature) - (Measured in Pascal Second) - Fluid Viscosity (At pipe wall temperature) is the resistance offered by the fluid with respect to the pipe wall temperature(in kelvin).

STEP 1: Convert Input(s) to Base Unit

Reynolds Number: 5000 --> No Conversion Required
Prandtl Number: 0.7 --> No Conversion Required
Diameter of Tube: 4 Meter --> 4 Meter No Conversion Required
Length of Cylinder: 6 Meter --> 6 Meter No Conversion Required
Fluid Viscosity (at fluid bulk temperature): 8 Pascal Second --> 8 Pascal Second No Conversion Required
Fluid Viscosity (At pipe wall temperature): 12 Pascal Second --> 12 Pascal Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Nu = ((1.86)*((Re)^(1/3))* ((Pr)^(1/3))* ((d/l)^(1/3))* ((μ_b/μ_pw)^(0.14))) --> ((1.86)*((5000)^(1/3))* ((0.7)^(1/3))* ((4/6)^(1/3))* ((8/12)^(0.14)))

Evaluating ... ...

Nu = 23.3087560406245

STEP 3: Convert Result to Output's Unit

23.3087560406245 --> No Conversion Required

FINAL ANSWER

23.3087560406245 ≈ 23.30876 <-- Nusselt Number

(Calculation completed in 00.020 seconds)

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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 by Sieder-Tate for Shorter Tubes Formula

What is Sieder-Tate equation?

This equation validates tubes over a large Reynolds number range, including the transition region. The Darcy friction factor, f, is a dimensionless quantity used in the Darcy–Weisbach equation for the description of frictional losses in pipe or duct as well as for open-channel flow.

What is Nusselt Number?

The Nusselt number is defined as the ratio of convection heat transfer to fluid conduction heat transfer under the same conditions.

How to Calculate Nusselt Number by Sieder-Tate for Shorter Tubes?

Nusselt Number by Sieder-Tate for Shorter Tubes calculator uses 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))) to calculate the Nusselt Number, The Nusselt Number by Sieder-Tate for Shorter Tubes formula is used when the difference between the surface and the fluid temperatures is large, it may be necessary to account for the viscosity variation with temperature. Nusselt Number is denoted by Nu symbol.

How to calculate Nusselt Number by Sieder-Tate for Shorter Tubes using this online calculator? To use this online calculator for Nusselt Number by Sieder-Tate for Shorter Tubes, enter Reynolds Number (Re), Prandtl Number (Pr), Diameter of Tube (d), Length of Cylinder (l), Fluid Viscosity (at fluid bulk temperature) (μ_b) & Fluid Viscosity (At pipe wall temperature) (μ_pw) and hit the calculate button. Here is how the Nusselt Number by Sieder-Tate for Shorter Tubes calculation can be explained with given input values -> 23.30876 = ((1.86)*((5000)^(1/3))* ((0.7)^(1/3))* ((4/6)^(1/3))* ((8/12)^(0.14))) .

FAQ

What is Nusselt Number by Sieder-Tate for Shorter Tubes?

The Nusselt Number by Sieder-Tate for Shorter Tubes formula is used when the difference between the surface and the fluid temperatures is large, it may be necessary to account for the viscosity variation with temperature and is represented as Nu = ((1.86)*((Re)^(1/3))* ((Pr)^(1/3))* ((d/l)^(1/3))* ((μ_b/μ_pw)^(0.14))) or 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))). 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. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe, 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, Diameter of tube is defined as the OUTSIDE DIAMETER (O.D.), specified in inches (e.g., 1.250) or fraction of an inch (eg. 1-1/4″), Length of Cylinder is the vertical height of the Cylinder, Fluid Viscosity (at fluid bulk temperature) is the resistance offered by the fluid with respect to the fluid bulk temperature(in kelvin) & Fluid Viscosity (At pipe wall temperature) is the resistance offered by the fluid with respect to the pipe wall temperature(in kelvin).

How to calculate Nusselt Number by Sieder-Tate for Shorter Tubes?

The Nusselt Number by Sieder-Tate for Shorter Tubes formula is used when the difference between the surface and the fluid temperatures is large, it may be necessary to account for the viscosity variation with temperature is calculated using 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))). To calculate Nusselt Number by Sieder-Tate for Shorter Tubes, you need Reynolds Number (Re), Prandtl Number (Pr), Diameter of Tube (d), Length of Cylinder (l), Fluid Viscosity (at fluid bulk temperature) (μ_b) & Fluid Viscosity (At pipe wall temperature) (μ_pw). With our tool, you need to enter the respective value for Reynolds Number, Prandtl Number, Diameter of Tube, Length of Cylinder, Fluid Viscosity (at fluid bulk temperature) & Fluid Viscosity (At pipe 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, Diameter of Tube, Length of Cylinder, Fluid Viscosity (at fluid bulk temperature) & Fluid Viscosity (At pipe 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 = 1.86*(((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14
Nusselt Number = 1.30*((Reynolds Number Dia*Prandtl Number)/(Length/Diameter))^0.333

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