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Local Heat Transfer Rate using Nusselt's Number Formula

GoLocal Heat Transfer Rate Calculation using Stanton Number Formula

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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. Check FAQs

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

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

Local Heat Transfer Rate using Nusselt's Number Example

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Here is how the Local Heat Transfer Rate using Nusselt's Number equation looks like with Values.

Here is how the Local Heat Transfer Rate using Nusselt's Number equation looks like with Units.

Here is how the Local Heat Transfer Rate using Nusselt's Number equation looks like.

11935 = \frac{1400 \cdot 0.093 \cdot (125 - 15)}{1.2}

11935W/m² = \frac{1400 \cdot 0.093W/(m*K) \cdot (125K - 15K)}{1.2m}

11935 = \frac{1400 \cdot 0.093 \cdot (125 - 15)}{1.2}

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Local Heat Transfer Rate using Nusselt's Number Solution

Follow our step by step solution on how to calculate Local Heat Transfer Rate using Nusselt's Number?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

q w = \frac{1400 \cdot 0.093W/(m*K) \cdot (125K - 15K)}{1.2m}

Next Step Prepare to Evaluate

∴

q w = \frac{1400 \cdot 0.093 \cdot (125 - 15)}{1.2}

LAST Step Evaluate

∴

q w = 11935W/m²

Local Heat Transfer Rate using Nusselt's Number Formula Elements

Variables

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

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

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

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

Other Formulas to find Local Heat Transfer Rate

Go Local Heat Transfer Rate Calculation using Stanton Number

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

Other formulas in Local Heat Transfer for Hypersonic Flow category

Go Nusselt Number for Hypersonic Vehicle

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

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 Static Density Equation using Stanton Number

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

How to Evaluate Local Heat Transfer Rate using Nusselt's Number?

Local Heat Transfer Rate using Nusselt's Number evaluator uses Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter) to evaluate the Local Heat Transfer Rate, Local Heat Transfer Rate using Nusselt's Number formula is defined as a measure of the convective heat transfer between a surface and a fluid, typically used in hypersonic flow applications to determine the heat transfer rate at the wall. Local Heat Transfer Rate is denoted by q_w symbol.

How to evaluate Local Heat Transfer Rate using Nusselt's Number using this online evaluator? To use this online evaluator for Local Heat Transfer Rate using Nusselt's Number, enter Nusselt Number (N_u), Thermal Conductivity (k), Adiabatic Wall Temperature (T_wall), Wall Temperature (Tw) & Distance from Nose Tip to Required Base Diameter (x_d) and hit the calculate button.

FAQs on Local Heat Transfer Rate using Nusselt's Number

What is the formula to find Local Heat Transfer Rate using Nusselt's Number?

The formula of Local Heat Transfer Rate using Nusselt's Number is expressed as Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter). Here is an example- 16041.67 = (1400*0.093*(125-15))/(1.2).

How to calculate Local Heat Transfer Rate using Nusselt's Number?

With Nusselt Number (N_u), Thermal Conductivity (k), Adiabatic Wall Temperature (T_wall), Wall Temperature (Tw) & Distance from Nose Tip to Required Base Diameter (x_d) we can find Local Heat Transfer Rate using Nusselt's Number using the formula - Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter).

What are the other ways to Calculate Local Heat Transfer Rate?

Here are the different ways to Calculate Local Heat Transfer Rate-

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

Can the Local Heat Transfer Rate using Nusselt's Number be negative?

No, the Local Heat Transfer Rate using Nusselt's Number, measured in Heat Flux Density cannot be negative.

Which unit is used to measure Local Heat Transfer Rate using Nusselt's Number?

Local Heat Transfer Rate using Nusselt's Number is usually measured using the Watt per Square Meter[W/m²] for Heat Flux Density. Kilowatt per Square Meter[W/m²], Watt per Square Centimeter[W/m²], Watt per Square Inch[W/m²] are the few other units in which Local Heat Transfer Rate using Nusselt's Number can be measured.

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Local Heat Transfer Rate using Nusselt's Number Formula

​GoLocal Heat Transfer Rate Calculation using Stanton Number Formula

Local Heat Transfer Rate using Nusselt's Number Example

Local Heat Transfer Rate using Nusselt's Number Solution

Local Heat Transfer Rate using Nusselt's Number Formula Elements

Other Formulas to find Local Heat Transfer Rate

Other formulas in Local Heat Transfer for Hypersonic Flow category

How to Evaluate Local Heat Transfer Rate using Nusselt's Number?

FAQs on Local Heat Transfer Rate using Nusselt's Number

Variable Name

GoLocal Heat Transfer Rate Calculation using Stanton Number Formula