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))* ((μb/μw)^(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: 3 Meter --> 3 Meter No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Fluid Viscosity ( at fluid bulk temperature): 10 Pascal Second --> 10 Pascal Second No Conversion Required
Fluid Viscosity ( At pipe wall temperature): 10 Pascal Second --> 10 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))* ((μbw)^(0.14))) --> ((1.86)*((5000)^(1/3))* ((0.7)^(1/3))* ((3/0.4)^(1/3))* ((10/10)^(0.14)))
Evaluating ... ...
Nu = 55.2784741606971
STEP 3: Convert Result to Output's Unit
55.2784741606971 --> No Conversion Required
FINAL ANSWER
55.2784741606971 <-- Nusselt Number
(Calculation completed in 00.016 seconds)

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Created by Prasana Kannan
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10+ Laminar flow Calculators

Nusselt number for hydrodynamic length fully developed and thermal length still developing
Nusselt Number = 3.66+((0.0668*(Diameter/Length)*Reynolds Number*Prandtl Number)/(1+0.04*((Diameter/Length)*Reynolds Number*Prandtl Number)^0.67)) Go
Nusselt number for simultaneous development of hydrodynamic and thermal layers
Nusselt Number = 3.66+((0.104*(Reynolds Number*Prandtl Number*(Diameter/Length)))/(1+0.16*(Reynolds Number*Prandtl Number*(Diameter/Length))^0.8)) Go
Nusselt number for simultaneous development of hydrodynamic and thermal layers for liquids
Nusselt Number = 1.86*(((Reynolds Number*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14 Go
Nusselt number for short lengths
Nusselt Number = 1.67*(Reynolds Number*Prandtl Number*Diameter/Length)^0.333 Go
Diameter of thermal entry tube
Diameter = Length/(0.04*Reynolds Number*Prandtl Number) Go
Thermal entry length
Length = 0.04*Reynolds Number*Diameter*Prandtl Number Go
Diameter of hydrodynamic entry tube
Diameter = Length/(0.04*Reynolds Number) Go
Hydrodynamic entry length
Length = 0.04*Diameter*Reynolds Number Go
Reynolds Number given Darcy Friction Factor
Reynolds Number = 64/Darcy Friction Factor Go
Darcy friction factor
Darcy Friction Factor = 64/Reynolds Number Go

Nusselt Number by Sieder-Tate for Shorter Tubes Formula

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))* ((μb/μw)^(0.14)))

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) b) & Fluid Viscosity ( At pipe wall temperature) w) 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 -> 55.27847 = ((1.86)*((5000)^(1/3))* ((0.7)^(1/3))* ((3/0.4)^(1/3))* ((10/10)^(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))* ((μb/μw)^(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) b) & Fluid Viscosity ( At pipe wall temperature) w). 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*Prandtl Number)/(1+0.04*((Diameter/Length)*Reynolds Number*Prandtl Number)^0.67))
  • Nusselt Number = 1.67*(Reynolds Number*Prandtl Number*Diameter/Length)^0.333
  • Nusselt Number = 3.66+((0.104*(Reynolds Number*Prandtl Number*(Diameter/Length)))/(1+0.16*(Reynolds Number*Prandtl Number*(Diameter/Length))^0.8))
  • Nusselt Number = 1.86*(((Reynolds Number*Prandtl Number)/(Length/Diameter))^0.333)*(Dynamic Viscosity at Bulk Temperature/Dynamic Viscosity at Wall Temperature)^0.14
  • Nusselt Number = 1.30*((Reynolds Number*Prandtl Number)/(Length/Diameter))^0.333
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