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(t))^0.25
kEff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(RaC)^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(t) - Rayleigh number(t) 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: 9 Watt per Meter per K --> 9 Watt per Meter per K No Conversion Required
Prandtl Number: 0.7 --> No Conversion Required
Rayleigh Number(t): 0.5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
kEff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(RaC)^0.25 --> 0.386*9*(((0.7)/(0.861+0.7))^0.25)*(0.5)^0.25
Evaluating ... ...
kEff = 2.39054046487838
STEP 3: Convert Result to Output's Unit
2.39054046487838 Watt per Meter per K --> No Conversion Required
FINAL ANSWER
2.39054046487838 2.39054 Watt per Meter per K <-- Effective Thermal Conductivity
(Calculation completed in 00.004 seconds)

Credits

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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8 Effective Thermal Conductivity and Heat Transfer Calculators

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 for space between two concentric spheres
Go Effective Thermal Conductivity = Heat transfer/((pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length))
Heat transfer between concentric spheres given both diameters
Go Heat transfer = (Effective Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length)
Effective thermal conductivity
Go Effective Thermal Conductivity = (Heat transfer*(Outer Radius-Inside Radius))/(4*pi*Inside Radius*Outer Radius*Temperature Difference)
Heat transfer between concentric spheres given both radii
Go Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius)
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(t))^0.25
Effective Thermal Conductivity given Rayleigh Number based on Turbulence
Go Effective Thermal Conductivity = Thermal Conductivity of Liquid*0.74*((Prandtl Number/(0.861+Prandtl Number))^0.25)*Rayleigh Number(t)^0.25

Effective thermal conductivity given Prandtl number Formula

Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number(t))^0.25
kEff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(RaC)^0.25

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(t))^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 kEff 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(t) (RaC) 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*9*(((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 kEff = 0.386*kl*(((Pr)/(0.861+Pr))^0.25)*(RaC)^0.25 or Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number(t))^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(t) 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(t))^0.25. To calculate Effective thermal conductivity given Prandtl number, you need Thermal Conductivity of Liquid (kl), Prandtl Number (Pr) & Rayleigh Number(t) (RaC). With our tool, you need to enter the respective value for Thermal Conductivity of Liquid, Prandtl Number & Rayleigh Number(t) 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(t). We can use 4 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/((pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length))
  • Effective Thermal Conductivity = (Heat transfer*(Outer Radius-Inside Radius))/(4*pi*Inside Radius*Outer Radius*Temperature Difference)
  • Effective Thermal Conductivity = Thermal Conductivity of Liquid*0.74*((Prandtl Number/(0.861+Prandtl Number))^0.25)*Rayleigh Number(t)^0.25
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