Nusselt Number for Hypersonic Vehicle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))
Nu = (qw*xd)/(k*(Twall-Tw))
This formula uses 6 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.
Local Heat Transfer Rate - (Measured in Watt per Square Meter) - Local Heat Transfer Rate, is that energy per second per unit area.
Distance from Nose Tip to Required Base Diameter - (Measured in Meter) - Distance from Nose Tip to Required Base Diameter, used for studying the leading edge of the hypersonic vehicles.
Thermal Conductivity - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Adiabatic Wall Temperature - (Measured in Kelvin) - Adiabatic wall temperature, is the temperature acquired by a wall in liquid or gas flow if the condition of thermal insulation is observed on it.
Wall Temperature - (Measured in Kelvin) - Wall Temperature is the temperature at the wall.
STEP 1: Convert Input(s) to Base Unit
Local Heat Transfer Rate: 12000 Watt per Square Meter --> 12000 Watt per Square Meter No Conversion Required
Distance from Nose Tip to Required Base Diameter: 1.2 Meter --> 1.2 Meter No Conversion Required
Thermal Conductivity: 0.125 Watt per Meter per K --> 0.125 Watt per Meter per K No Conversion Required
Adiabatic Wall Temperature: 125 Kelvin --> 125 Kelvin No Conversion Required
Wall Temperature: 15 Kelvin --> 15 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Nu = (qw*xd)/(k*(Twall-Tw)) --> (12000*1.2)/(0.125*(125-15))
Evaluating ... ...
Nu = 1047.27272727273
STEP 3: Convert Result to Output's Unit
1047.27272727273 --> No Conversion Required
FINAL ANSWER
1047.27272727273 1047.273 <-- Nusselt Number
(Calculation completed in 00.004 seconds)

Credits

Created by Sanjay Krishna
Amrita School of Engineering (ASE), Vallikavu
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Indian Institute of Technology (IIT), Bombay
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9 Local Heat Transfer for Hypersonic Flow Calculators

Thermal Conductivity at Edge of Boundary Layer Equation using Nusselt's Number
Go Thermal Conductivity = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Nusselt Number*(Adiabatic Wall Temperature-Wall Temperature))
Local Heat Transfer Rate using Nusselt's Number
Go Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter)
Nusselt Number for Hypersonic Vehicle
Go Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))
Static Density Equation using Stanton Number
Go Static Density = Local Heat Transfer Rate/(Stanton Number*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy))
Stanton Number for Hypersonic Vehicle
Go Stanton Number = Local Heat Transfer Rate/(Static Density*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy))
Static Velocity using Stanton Number
Go Static Velocity = Local Heat Transfer Rate/(Stanton Number*Static Density*(Adiabatic Wall Enthalpy-Wall Enthalpy))
Local Heat Transfer Rate Calculation using Stanton Number
Go Local Heat Transfer Rate = Stanton Number*Static Density*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy)
Adiabatic Wall Enthalpy using Stanton Number
Go Adiabatic Wall Enthalpy = Local Heat Transfer Rate/(Static Density*Static Velocity*Stanton Number)+Wall Enthalpy
Enthalpy of Wall using Stanton Number
Go Wall Enthalpy = Adiabatic Wall Enthalpy-Local Heat Transfer Rate/(Static Density*Static Velocity*Stanton Number)

Nusselt Number for Hypersonic Vehicle Formula

Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))
Nu = (qw*xd)/(k*(Twall-Tw))

What is Nusselt's number?

The Nusselt number is the ratio of convective to conductive heat transfer across a boundary. The convection and conduction heat flows are parallel to each other and to the surface normal of the boundary surface, and are all perpendicular to the mean fluid flow in the simple case.

How to Calculate Nusselt Number for Hypersonic Vehicle?

Nusselt Number for Hypersonic Vehicle calculator uses Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)) to calculate the Nusselt Number, Nusselt Number for Hypersonic Vehicle is defined as the ratio of product of local heat-transfer rat and distance along the wall measured from the leading edge to the product of thermal conductivity at the edge of the boundary layer and difference of adiabatic wall temperature and wall temperature. Nusselt Number is denoted by Nu symbol.

How to calculate Nusselt Number for Hypersonic Vehicle using this online calculator? To use this online calculator for Nusselt Number for Hypersonic Vehicle, enter Local Heat Transfer Rate (qw), Distance from Nose Tip to Required Base Diameter (xd), Thermal Conductivity (k), Adiabatic Wall Temperature (Twall) & Wall Temperature (Tw) and hit the calculate button. Here is how the Nusselt Number for Hypersonic Vehicle calculation can be explained with given input values -> 1047.273 = (12000*1.2)/(0.125*(125-15)).

FAQ

What is Nusselt Number for Hypersonic Vehicle?
Nusselt Number for Hypersonic Vehicle is defined as the ratio of product of local heat-transfer rat and distance along the wall measured from the leading edge to the product of thermal conductivity at the edge of the boundary layer and difference of adiabatic wall temperature and wall temperature and is represented as Nu = (qw*xd)/(k*(Twall-Tw)) or Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)). Local Heat Transfer Rate, is that energy per second per unit area, Distance from Nose Tip to Required Base Diameter, used for studying the leading edge of the hypersonic vehicles, Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, Adiabatic wall temperature, is the temperature acquired by a wall in liquid or gas flow if the condition of thermal insulation is observed on it & Wall Temperature is the temperature at the wall.
How to calculate Nusselt Number for Hypersonic Vehicle?
Nusselt Number for Hypersonic Vehicle is defined as the ratio of product of local heat-transfer rat and distance along the wall measured from the leading edge to the product of thermal conductivity at the edge of the boundary layer and difference of adiabatic wall temperature and wall temperature is calculated using Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)). To calculate Nusselt Number for Hypersonic Vehicle, you need Local Heat Transfer Rate (qw), Distance from Nose Tip to Required Base Diameter (xd), Thermal Conductivity (k), Adiabatic Wall Temperature (Twall) & Wall Temperature (Tw). With our tool, you need to enter the respective value for Local Heat Transfer Rate, Distance from Nose Tip to Required Base Diameter, Thermal Conductivity, Adiabatic Wall Temperature & Wall Temperature and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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