Effective thermal conductivity given Prandtl number Calculator

✖Thermal conductivity of liquid is defined as the transport of energy due to random molecular motion across a temperature gradient.ⓘ Thermal Conductivity of Liquid [kl]			+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%
✖Rayleigh Number Based on Turbulance is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom.ⓘ Rayleigh Number Based on Turbulance [Ra_c]			+10% -10%

✖Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.ⓘ Effective thermal conductivity given Prandtl number [k_Eff]

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Formula

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Effective thermal conductivity given Prandtl number

Formula

k Eff = 0.386 \cdot kl \cdot ({(\frac{Pr}{0.861 + Pr})}^{0.25}) \cdot {(Ra c)}^{0.25}

Example

0.268272 W/(m*K) = 0.386 \cdot 1.01 W/(m*K) \cdot ({(\frac{0.7}{0.861 + 0.7})}^{0.25}) \cdot {(0.5)}^{0.25}

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Effective thermal conductivity given Prandtl number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number Based on Turbulance)^0.25
k_Eff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(Ra_c)^0.25
This formula uses 4 Variables

Variables Used

Effective Thermal Conductivity - (Measured in Watt per Meter per K) - Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.
Thermal Conductivity of Liquid - (Measured in Watt per Meter per K) - Thermal conductivity of liquid is defined as the transport of energy due to random molecular motion across a temperature gradient.
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.
Rayleigh Number Based on Turbulance - Rayleigh Number Based on Turbulance is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom.

STEP 1: Convert Input(s) to Base Unit

Thermal Conductivity of Liquid: 1.01 Watt per Meter per K --> 1.01 Watt per Meter per K No Conversion Required
Prandtl Number: 0.7 --> No Conversion Required
Rayleigh Number Based on Turbulance: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_Eff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(Ra_c)^0.25 --> 0.386*1.01*(((0.7)/(0.861+0.7))^0.25)*(0.5)^0.25

Evaluating ... ...

k_Eff = 0.268271763280796

STEP 3: Convert Result to Output's Unit

0.268271763280796 Watt per Meter per K --> No Conversion Required

FINAL ANSWER

0.268271763280796 ≈ 0.268272 Watt per Meter per K <-- Effective Thermal Conductivity

(Calculation completed in 00.004 seconds)

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< Effective Thermal Conductivity and Heat Transfer Calculators

Heat transfer between concentric spheres given both diameters

Go Heat transfer Between Concentric Spheres = (Effective Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length)

Effective thermal conductivity for annular space between concentric cylinders

Go Effective Thermal Conductivity = Heat Transfer per Unit Length*((ln(Outside Diameter/Inside Diameter))/(2*pi)*(Inside Temperature-Outside Temperature))

Heat transfer per unit length for annular space between concentric cylinders

Go Heat Transfer per Unit Length = ((2*pi*Effective Thermal Conductivity)/(ln(Outside Diameter/Inside Diameter)))*(Inside Temperature-Outside Temperature)

Effective thermal conductivity given Prandtl number

Go Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number Based on Turbulance)^0.25

Effective thermal conductivity given Prandtl number Formula

What is convection?

Convection is the process of heat transfer by the bulk movement of molecules within fluids such as gases and liquids. The initial heat transfer between the object and the fluid takes place through conduction, but the bulk heat transfer happens due to the motion of the fluid.

Convection is the process of heat transfer in fluids by the actual motion of matter.
It happens in liquids and gases.
It may be natural or forced.
It involves a bulk transfer of portions of the fluid.

How to Calculate Effective thermal conductivity given Prandtl number?

Effective thermal conductivity given Prandtl number calculator uses Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number Based on Turbulance)^0.25 to calculate the Effective Thermal Conductivity, The Effective thermal conductivity given Prandtl number formula is defined as the transport of energy due to random molecular motion across a temperature gradient. Effective Thermal Conductivity is denoted by k_Eff symbol.

How to calculate Effective thermal conductivity given Prandtl number using this online calculator? To use this online calculator for Effective thermal conductivity given Prandtl number, enter Thermal Conductivity of Liquid (kl), Prandtl Number (Pr) & Rayleigh Number Based on Turbulance (Ra_c) and hit the calculate button. Here is how the Effective thermal conductivity given Prandtl number calculation can be explained with given input values -> 2.39054 = 0.386*1.01*(((0.7)/(0.861+0.7))^0.25)*(0.5)^0.25.

FAQ

What is Effective thermal conductivity given Prandtl number?

The Effective thermal conductivity given Prandtl number formula is defined as the transport of energy due to random molecular motion across a temperature gradient and is represented as k_Eff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(Ra_c)^0.25 or Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number Based on Turbulance)^0.25. Thermal conductivity of liquid is defined as the transport of energy due to random molecular motion across a temperature gradient, 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 & Rayleigh Number Based on Turbulance is a dimensionless parameter that is a measure of the instability of a layer of fluid due to differences of temperature and density at the top and bottom.

How to calculate Effective thermal conductivity given Prandtl number?

The Effective thermal conductivity given Prandtl number formula is defined as the transport of energy due to random molecular motion across a temperature gradient is calculated using Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number Based on Turbulance)^0.25. To calculate Effective thermal conductivity given Prandtl number, you need Thermal Conductivity of Liquid (kl), Prandtl Number (Pr) & Rayleigh Number Based on Turbulance (Ra_c). With our tool, you need to enter the respective value for Thermal Conductivity of Liquid, Prandtl Number & Rayleigh Number Based on Turbulance 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 Effective Thermal Conductivity?

In this formula, Effective Thermal Conductivity uses Thermal Conductivity of Liquid, Prandtl Number & Rayleigh Number Based on Turbulance. We can use 3 other way(s) to calculate the same, which is/are as follows -

Effective Thermal Conductivity = Heat Transfer per Unit Length*((ln(Outside Diameter/Inside Diameter))/(2*pi)*(Inside Temperature-Outside Temperature))
Effective Thermal Conductivity = Heat transfer Between Concentric Spheres/((pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length))
Effective Thermal Conductivity = (Heat transfer Between Concentric Spheres*(Outer Radius-Inside Radius))/(4*pi*Inside Radius*Outer Radius*Temperature Difference)

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