Thermal Conductivity using Prandtl Number Calculator

✖The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.ⓘ Dynamic Viscosity [μ_viscosity]			+10% -10%
✖Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.ⓘ Specific Heat Capacity at Constant Pressure [C_p]			+10% -10%
✖The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.ⓘ Prandtl Number [Pr]			+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 using Prandtl Number [k]

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Formula

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Thermal Conductivity using Prandtl Number

Formula

`"k" = ("μ"_{"viscosity"}*"C"_{"p"})/"Pr"`

Example

`"1464.429W/(m*K)"=("10.2P"*"1.005kJ/kg*K")/"0.7"`

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Thermal Conductivity using Prandtl Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number
k = (μ_viscosity*C_p)/Pr
This formula uses 4 Variables

Variables Used

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.
Dynamic Viscosity - (Measured in Pascal Second) - The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied.
Specific Heat Capacity at Constant Pressure - (Measured in Joule per Kilogram per K) - Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure.
Prandtl Number - The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.

STEP 1: Convert Input(s) to Base Unit

Dynamic Viscosity: 10.2 Poise --> 1.02 Pascal Second (Check conversion here)
Specific Heat Capacity at Constant Pressure: 1.005 Kilojoule per Kilogram per K --> 1005 Joule per Kilogram per K (Check conversion here)
Prandtl Number: 0.7 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k = (μ_viscosity*C_p)/Pr --> (1.02*1005)/0.7

Evaluating ... ...

k = 1464.42857142857

STEP 3: Convert Result to Output's Unit

1464.42857142857 Watt per Meter per K --> No Conversion Required

FINAL ANSWER

1464.42857142857 ≈ 1464.429 Watt per Meter per K <-- Thermal Conductivity

(Calculation completed in 00.020 seconds)

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Home » Engineering » Mechanical » Fluid Mechanics » Hypersonic Flow » Viscous Flow Fundamentals » Aero-Thermal Dynamics » Thermal Conductivity using Prandtl Number

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Created by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

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PSG College of Technology (PSGCT), Coimbatore

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< 16 Aero-Thermal Dynamics Calculators

Aerodynamic Heating to Surface

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

Static Viscosity Calculation using Chapman-Rubesin Factor

Go Static Viscosity = (Density*Kinematic Viscosity)/(Chapman–Rubesin factor*Static Density)

Static Density Calculation using Chapman-Rubesin Factor

Go Static Density = (Density*Kinematic Viscosity)/(Chapman–Rubesin factor*Static Viscosity)

Chapman-Rubesin Factor

Go Chapman–Rubesin factor = (Density*Kinematic Viscosity)/(Static Density*Static Viscosity)

Viscosity Calculation using Chapman-Rubesin Factor

Go Kinematic Viscosity = Chapman–Rubesin factor*Static Density*Static Viscosity/(Density)

Density Calculation using Chapman-Rubesin Factor

Go Density = Chapman–Rubesin factor*Static Density*Static Viscosity/(Kinematic Viscosity)

Thermal Conductivity using Prandtl Number

Go Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number

Non Dimensional Internal Energy Parameter

Go Non-Dimensional Internal Energy = Internal Energy/(Specific Heat Capacity*Temperature)

Stanton Number for Incompressible Flow

Go Stanton Number = 0.332*(Prandtl Number^(-2/3))/sqrt(Reynolds Number)

Wall Temperature Calculation using Internal Energy Change

Go Temperature of wall in Kelvin = Non-Dimensional Internal Energy*Free Stream Temperature

Stanton Equation using Overall Skin Friction Coefficient for Incompressible Flow

Go Stanton Number = Overall Skin-friction Drag Coefficient*0.5*Prandtl Number^(-2/3)

Non Dimensional Internal Energy Parameter using Wall-to-Freestream Temperature Ratio

Go Non-Dimensional Internal Energy = Wall Temperature/Free Stream Temperature

Internal Energy for Hypersonic Flow

Go Internal Energy = Enthalpy+Pressure/Density

Non Dimensional Static Enthalpy

Go Non Dimensional Static Enthalpy = Stagnation Enthalpy/Static Enthalpy

Coefficient of Friction using Stanton Equation for Incompressible Flow

Go Coefficient of Friction = Stanton Number/(0.5*Prandtl Number^(-2/3))

Static Enthalpy

Go Static Enthalpy = Enthalpy/Non Dimensional Static Enthalpy

Thermal Conductivity using Prandtl Number Formula

Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number
k = (μ_viscosity*C_p)/Pr

What is Prandtl number?

The Prandtl number is a dimensionless quantity that puts the viscosity of a fluid in correlation with the thermal conductivity. It therefore, assesses the relation between momentum transport and thermal transport capacity of the fluid.

How to Calculate Thermal Conductivity using Prandtl Number?

Thermal Conductivity using Prandtl Number calculator uses Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number to calculate the Thermal Conductivity, The Thermal conductivity using Prandtl number formula is defined as the ratio of the product of dynamic viscosity and specific heat for constant pressure to the Prandtl number. Thermal Conductivity is denoted by k symbol.

How to calculate Thermal Conductivity using Prandtl Number using this online calculator? To use this online calculator for Thermal Conductivity using Prandtl Number, enter Dynamic Viscosity (μ_viscosity), Specific Heat Capacity at Constant Pressure (C_p) & Prandtl Number (Pr) and hit the calculate button. Here is how the Thermal Conductivity using Prandtl Number calculation can be explained with given input values -> 1464.429 = (1.02*1005)/0.7.

FAQ

What is Thermal Conductivity using Prandtl Number?

The Thermal conductivity using Prandtl number formula is defined as the ratio of the product of dynamic viscosity and specific heat for constant pressure to the Prandtl number and is represented as k = (μ_viscosity*C_p)/Pr or Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number. The Dynamic Viscosity of a fluid is the measure of its resistance to flow when an external force is applied, Specific Heat Capacity at Constant Pressure means the amount of heat that is required to raise the temperature of a unit mass of gas by 1 degree at constant pressure & The Prandtl number (Pr) or Prandtl group is a dimensionless number, named after the German physicist Ludwig Prandtl, defined as the ratio of momentum diffusivity to thermal diffusivity.

How to calculate Thermal Conductivity using Prandtl Number?

The Thermal conductivity using Prandtl number formula is defined as the ratio of the product of dynamic viscosity and specific heat for constant pressure to the Prandtl number is calculated using Thermal Conductivity = (Dynamic Viscosity*Specific Heat Capacity at Constant Pressure)/Prandtl Number. To calculate Thermal Conductivity using Prandtl Number, you need Dynamic Viscosity (μ_viscosity), Specific Heat Capacity at Constant Pressure (C_p) & Prandtl Number (Pr). With our tool, you need to enter the respective value for Dynamic Viscosity, Specific Heat Capacity at Constant Pressure & Prandtl Number 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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