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Nusselt Number for Hypersonic Vehicle Formula

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The Nusselt Number is a dimensionless quantity that characterizes the convective heat transfer between a surface and a fluid in hypersonic flow conditions. Check FAQs

N u = \frac{q w \cdot x d}{k \cdot (T wall - Tw)}

N_u - Nusselt Number?q_w - Local Heat Transfer Rate?x_d - Distance from Nose Tip to Required Base Diameter?k - Thermal Conductivity?T_wall - Adiabatic Wall Temperature?Tw - Wall Temperature?

Nusselt Number for Hypersonic Vehicle Example

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Here is how the Nusselt Number for Hypersonic Vehicle equation looks like with Values.

Here is how the Nusselt Number for Hypersonic Vehicle equation looks like with Units.

Here is how the Nusselt Number for Hypersonic Vehicle equation looks like.

1407.6246 = \frac{12000 \cdot 1.2}{0.093 \cdot (125 - 15)}

1407.6246 = \frac{12000W/m² \cdot 1.2m}{0.093W/(m*K) \cdot (125K - 15K)}

1407.6246 = \frac{12000 \cdot 1.2}{0.093 \cdot (125 - 15)}

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Nusselt Number for Hypersonic Vehicle Solution

Follow our step by step solution on how to calculate Nusselt Number for Hypersonic Vehicle?

FIRST Step Consider the formula

N u = \frac{q w \cdot x d}{k \cdot (T wall - Tw)}

Next Step Substitute values of Variables

∴

N u = \frac{12000W/m² \cdot 1.2m}{0.093W/(m*K) \cdot (125K - 15K)}

Next Step Prepare to Evaluate

∴

N u = \frac{12000 \cdot 1.2}{0.093 \cdot (125 - 15)}

Next Step Evaluate

∴

N u = 1407.62463343108

LAST Step Rounding Answer

∴

N u = 1407.6246

Nusselt Number for Hypersonic Vehicle Formula Elements

Variables

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.

Symbol: N_u

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Nusselt Number

Local Heat Transfer Rate

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.

Symbol: q_w

Measurement: Heat Flux DensityUnit: W/m²

Note: Value should be greater than 0.

Formulas to find Local Heat Transfer Rate

Distance from Nose Tip to Required Base Diameter

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.

Symbol: x_d

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Distance from Nose Tip to Required Base Diameter

Thermal Conductivity

The Thermal Conductivity is a measure of the ability of a material to conduct heat in the hypersonic boundary layer, characterizing heat transfer properties.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity

Adiabatic Wall Temperature

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.

Symbol: T_wall

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Adiabatic Wall Temperature

Wall Temperature

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.

Symbol: Tw

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Wall Temperature

Other formulas in Local Heat Transfer for Hypersonic Flow category

Go Local Heat Transfer Rate using Nusselt's Number

q w = \frac{N u \cdot k \cdot (T wall - Tw)}{x d}

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

k = \frac{q w \cdot x d}{N u \cdot (T wall - Tw)}

Go Stanton Number for Hypersonic Vehicle

St = \frac{q w}{ρ e \cdot u e \cdot (h aw - h w)}

Go Local Heat Transfer Rate Calculation using Stanton Number

q w = St \cdot ρ e \cdot u e \cdot (h aw - h w)

How to Evaluate Nusselt Number for Hypersonic Vehicle?

Nusselt Number for Hypersonic Vehicle evaluator uses Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)) to evaluate 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 evaluate Nusselt Number for Hypersonic Vehicle using this online evaluator? To use this online evaluator 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.

FAQs on Nusselt Number for Hypersonic Vehicle

What is the formula to find Nusselt Number for Hypersonic Vehicle?

The formula of Nusselt Number for Hypersonic Vehicle is expressed as Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)). Here is an example- 1047.273 = (12000*1.2)/(0.093*(125-15)).

How to calculate Nusselt Number for Hypersonic Vehicle?

With 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) we can find Nusselt Number for Hypersonic Vehicle using the formula - Nusselt Number = (Local Heat Transfer Rate*Distance from Nose Tip to Required Base Diameter)/(Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature)).

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Nusselt Number for Hypersonic Vehicle Formula

Nusselt Number for Hypersonic Vehicle Example

Nusselt Number for Hypersonic Vehicle Solution

Nusselt Number for Hypersonic Vehicle Formula Elements

Other formulas in Local Heat Transfer for Hypersonic Flow category

How to Evaluate Nusselt Number for Hypersonic Vehicle?

FAQs on Nusselt Number for Hypersonic Vehicle

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