Nusselt Number for Hypersonic Vehicle Calculator

✖The Local Heat Transfer Rate is the amount of heat transferred per unit area per unit time from the surface to the fluid in a hypersonic boundary layer.ⓘ Local Heat Transfer Rate [q_w]			+10% -10%
✖The Distance from Nose Tip to Required Base Diameter is the length from the nose tip to the base diameter of a hypersonic vehicle's boundary layer.ⓘ Distance from Nose Tip to Required Base Diameter [x_d]			+10% -10%
✖The Thermal Conductivity is a measure of the ability of a material to conduct heat in the hypersonic boundary layer, characterizing heat transfer properties.ⓘ Thermal Conductivity [k]			+10% -10%
✖The Adiabatic Wall Temperature is the temperature at the surface of an object in hypersonic flow, where the heat transfer is zero and the flow is in equilibrium.ⓘ Adiabatic Wall Temperature [T_wall]			+10% -10%
✖The Wall Temperature is the temperature at the surface of the wall in a hypersonic flow, which affects the flow's thermal and velocity boundary layers.ⓘ Wall Temperature [Tw]			+10% -10%

✖The Nusselt Number is a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid in hypersonic flow conditions.ⓘ Nusselt Number for Hypersonic Vehicle [N_u]

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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))
N_u = (q_w*x_d)/(k*(T_wall-Tw))
This formula uses 6 Variables

Variables Used

Nusselt Number - The Nusselt Number is a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid in hypersonic flow conditions.
Local Heat Transfer Rate - (Measured in Watt per Square Meter) - The Local Heat Transfer Rate is the amount of heat transferred per unit area per unit time from the surface to the fluid in a hypersonic boundary layer.
Distance from Nose Tip to Required Base Diameter - (Measured in Meter) - The Distance from Nose Tip to Required Base Diameter is the length from the nose tip to the base diameter of a hypersonic vehicle's boundary layer.
Thermal Conductivity - (Measured in Watt per Meter per K) - The Thermal Conductivity is a measure of the ability of a material to conduct heat in the hypersonic boundary layer, characterizing heat transfer properties.
Adiabatic Wall Temperature - (Measured in Kelvin) - The Adiabatic Wall Temperature is the temperature at the surface of an object in hypersonic flow, where the heat transfer is zero and the flow is in equilibrium.
Wall Temperature - (Measured in Kelvin) - The Wall Temperature is the temperature at the surface of the wall in a hypersonic flow, which affects the flow's thermal and velocity boundary layers.

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: 0.093 Watt per Meter per K --> 0.093 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

N_u = (q_w*x_d)/(k*(T_wall-Tw)) --> (12000*1.2)/(0.093*(125-15))

Evaluating ... ...

N_u = 1407.62463343108

STEP 3: Convert Result to Output's Unit

1407.62463343108 --> No Conversion Required

FINAL ANSWER

1407.62463343108 ≈ 1407.625 <-- Nusselt Number

(Calculation completed in 00.004 seconds)

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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Indian Institute of Technology (IIT), Bombay

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< Local Heat Transfer for Hypersonic Flow Calculators

Thermal Conductivity at Edge of Boundary Layer Equation using Nusselt's Number

LaTeX 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

LaTeX 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

LaTeX Go Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))

Stanton Number for Hypersonic Vehicle

LaTeX Go Stanton Number = Local Heat Transfer Rate/(Static Density*Static Velocity*(Adiabatic Wall Enthalpy-Wall Enthalpy))

Nusselt Number for Hypersonic Vehicle Formula

LaTeX Go

Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))
N_u = (q_w*x_d)/(k*(T_wall-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 formula is defined as a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid, typically used to analyze the thermal behavior of hypersonic vehicles during re-entry into the Earth's atmosphere. Nusselt Number is denoted by N_u 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 (q_w), Distance from Nose Tip to Required Base Diameter (x_d), Thermal Conductivity (k), Adiabatic Wall Temperature (T_wall) & 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)/(0.093*(125-15)).

FAQ

What is Nusselt Number for Hypersonic Vehicle?

Nusselt Number for Hypersonic Vehicle formula is defined as a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid, typically used to analyze the thermal behavior of hypersonic vehicles during re-entry into the Earth's atmosphere and is represented as N_u = (q_w*x_d)/(k*(T_wall-Tw)) or Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)). The Local Heat Transfer Rate is the amount of heat transferred per unit area per unit time from the surface to the fluid in a hypersonic boundary layer, The Distance from Nose Tip to Required Base Diameter is the length from the nose tip to the base diameter of a hypersonic vehicle's boundary layer, The Thermal Conductivity is a measure of the ability of a material to conduct heat in the hypersonic boundary layer, characterizing heat transfer properties, The Adiabatic Wall Temperature is the temperature at the surface of an object in hypersonic flow, where the heat transfer is zero and the flow is in equilibrium & The Wall Temperature is the temperature at the surface of the wall in a hypersonic flow, which affects the flow's thermal and velocity boundary layers.

How to calculate Nusselt Number for Hypersonic Vehicle?

Nusselt Number for Hypersonic Vehicle formula is defined as a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid, typically used to analyze the thermal behavior of hypersonic vehicles during re-entry into the Earth's atmosphere 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 (q_w), Distance from Nose Tip to Required Base Diameter (x_d), Thermal Conductivity (k), Adiabatic Wall Temperature (T_wall) & 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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