Local Heat Transfer Rate using Nusselt's Number Calculator

✖The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion.ⓘ Nusselt Number [N_u]			+10% -10%
✖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.ⓘ Thermal Conductivity [k]			+10% -10%
✖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.ⓘ Adiabatic Wall Temperature [T_wall]			+10% -10%
✖Wall Temperature is the temperature at the wall.ⓘ Wall Temperature [Tw]			+10% -10%
✖Distance from Nose Tip to Required Base Diameter, used for studying the leading edge of the hypersonic vehicles.ⓘ Distance from Nose Tip to Required Base Diameter [x_d]			+10% -10%

✖Local Heat Transfer Rate, is that energy per second per unit area.ⓘ Local Heat Transfer Rate using Nusselt's Number [q_w]

⎘ Copy

👎

Formula

✖

Local Heat Transfer Rate using Nusselt's Number

Formula

`"q"_{"w"} = ("N"_{"u"}*"k"*("T"_{"wall"}-"Tw"))/("x"_{"d"})`

Example

`"16041.67W/m²"=("1400"*"0.125W/(m*K)"*("125K"-"15K"))/("1.2m")`

Calculator

LaTeX

Reset

👍

Download Boundary Layer Equations for Hypersonic Flow Formulas PDF

Local Heat Transfer Rate using Nusselt's Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter)
q_w = (N_u*k*(T_wall-Tw))/(x_d)
This formula uses 6 Variables

Variables Used

Local Heat Transfer Rate - (Measured in Watt per Square Meter) - Local Heat Transfer Rate, is that energy per second per unit area.
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.
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.
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.

STEP 1: Convert Input(s) to Base Unit

Nusselt Number: 1400 --> 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
Distance from Nose Tip to Required Base Diameter: 1.2 Meter --> 1.2 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q_w = (N_u*k*(T_wall-Tw))/(x_d) --> (1400*0.125*(125-15))/(1.2)

Evaluating ... ...

q_w = 16041.6666666667

STEP 3: Convert Result to Output's Unit

16041.6666666667 Watt per Square Meter --> No Conversion Required

FINAL ANSWER

16041.6666666667 ≈ 16041.67 Watt per Square Meter <-- Local Heat Transfer Rate

(Calculation completed in 00.004 seconds)

You are here -

Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Boundary Layer Equations for Hypersonic Flow » Local Heat Transfer for Hypersonic Flow » Local Heat Transfer Rate using Nusselt's Number

Credits

Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has created this Calculator and 300+ more calculators!

Verified by Maiarutselvan V

PSG College of Technology (PSGCT), Coimbatore

Maiarutselvan V has verified this Calculator and 300+ more calculators!

< 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)

Local Heat Transfer Rate using Nusselt's Number Formula

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

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 Local Heat Transfer Rate using Nusselt's Number?

Local Heat Transfer Rate using Nusselt's Number calculator uses Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter) to calculate the Local Heat Transfer Rate, Local Heat Transfer Rate using Nusselt's Number is defined as the ratio of the product of Nusselt's number, thermal conductivity at the edge of the boundary layer, and difference between adiabatic wall temperature and wall temperature to the distance along the wall measured from the leading edge. Local Heat Transfer Rate is denoted by q_w symbol.

How to calculate Local Heat Transfer Rate using Nusselt's Number using this online calculator? To use this online calculator 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. Here is how the Local Heat Transfer Rate using Nusselt's Number calculation can be explained with given input values -> 57.29167 = (1400*0.125*(125-15))/(1.2).

FAQ

What is Local Heat Transfer Rate using Nusselt's Number?

Local Heat Transfer Rate using Nusselt's Number is defined as the ratio of the product of Nusselt's number, thermal conductivity at the edge of the boundary layer, and difference between adiabatic wall temperature and wall temperature to the distance along the wall measured from the leading edge and is represented as q_w = (N_u*k*(T_wall-Tw))/(x_d) or Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter). The Nusselt Number is the ratio of convective to conductive heat transfer at a boundary in a fluid. Convection includes both advection and diffusion, 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 & Distance from Nose Tip to Required Base Diameter, used for studying the leading edge of the hypersonic vehicles.

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

Local Heat Transfer Rate using Nusselt's Number is defined as the ratio of the product of Nusselt's number, thermal conductivity at the edge of the boundary layer, and difference between adiabatic wall temperature and wall temperature to the distance along the wall measured from the leading edge is calculated using Local Heat Transfer Rate = (Nusselt Number*Thermal Conductivity*(Adiabatic Wall Temperature-Wall Temperature))/(Distance from Nose Tip to Required Base Diameter). To calculate Local Heat Transfer Rate using Nusselt's Number, you need 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). With our tool, you need to enter the respective value for Nusselt Number, Thermal Conductivity, Adiabatic Wall Temperature, Wall Temperature & Distance from Nose Tip to Required Base Diameter 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 Local Heat Transfer Rate?

In this formula, Local Heat Transfer Rate uses Nusselt Number, Thermal Conductivity, Adiabatic Wall Temperature, Wall Temperature & Distance from Nose Tip to Required Base Diameter. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search