Fourier Number Calculator

✖Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.ⓘ Thermal Diffusivity [α]			+10% -10%
✖Characteristic Time is an estimate of the order of magnitude of the reaction time scale of a system.ⓘ Characteristic Time [𝜏_c]			+10% -10%
✖Characteristic Dimension is the ratio of volume and the area.ⓘ Characteristic Dimension [s]			+10% -10%

✖Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.ⓘ Fourier Number [F_o]

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Formula

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Fourier Number

Formula

`"F"_{"o"} = ("α"*"𝜏"_{"c"})/("s"^2)`

Example

`"0.293006"=("5.58m²/s"*"2.5s")/(("6.9m")^2)`

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Download Unsteady State Heat Conduction Formulas PDF

Fourier Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)
F_o = (α*𝜏_c)/(s^2)
This formula uses 4 Variables

Variables Used

Fourier Number - Fourier Number is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat or matter.
Thermal Diffusivity - (Measured in Square Meter Per Second) - Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.
Characteristic Time - (Measured in Second) - Characteristic Time is an estimate of the order of magnitude of the reaction time scale of a system.
Characteristic Dimension - (Measured in Meter) - Characteristic Dimension is the ratio of volume and the area.

STEP 1: Convert Input(s) to Base Unit

Thermal Diffusivity: 5.58 Square Meter Per Second --> 5.58 Square Meter Per Second No Conversion Required
Characteristic Time: 2.5 Second --> 2.5 Second No Conversion Required
Characteristic Dimension: 6.9 Meter --> 6.9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_o = (α*𝜏_c)/(s^2) --> (5.58*2.5)/(6.9^2)

Evaluating ... ...

F_o = 0.293005671077505

STEP 3: Convert Result to Output's Unit

0.293005671077505 --> No Conversion Required

FINAL ANSWER

0.293005671077505 ≈ 0.293006 <-- Fourier Number

(Calculation completed in 00.006 seconds)

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Created by Ayush gupta

University School of Chemical Technology-USCT (GGSIPU), New Delhi

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University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

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< 18 Unsteady State Heat Conduction Calculators

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid

Go Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant))

Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method

Go Time Constant = ((-Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Initial Temperature of Body by Lumped Heat Capacity Method

Go Initial Temperature of Object = (Temperature at Any Time T-Temperature of Bulk Fluid)/(exp((-Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object)))+Temperature of Bulk Fluid

Temperature of Body by Lumped Heat Capacity Method

Go Temperature at Any Time T = (exp((-Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object)))*(Initial Temperature of Object-Temperature of Bulk Fluid)+Temperature of Bulk Fluid

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid at Surface

Go Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))

Fourier Number given Heat Transfer Coefficient and Time Constant

Go Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number)

Biot Number given Heat Transfer Coefficient and Time Constant

Go Biot Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Fourier Number)

Fourier Number using Biot Number

Go Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Biot Number using Fourier Number

Go Biot Number = (-1/Fourier Number)*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Biot Number given Characteristic Dimension and Fourier Number

Go Biot Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Fourier Number)

Fourier Number given Characteristic Dimension and Biot Number

Go Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number)

Initial Internal Energy Content of Body in Reference to Environment Temperature

Go Initial Energy Content = Density of Body*Specific Heat Capacity*Volume of Object*(Initial Temperature of Solid-Ambient Temperature)

Fourier Number using Thermal Conductivity

Go Fourier Number = ((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))

Time Constant of Thermal System

Go Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection)

Capacitance of Thermal System by Lumped Heat Capacity Method

Go Capacitance of Thermal System = Density of Body*Specific Heat Capacity*Volume of Object

Fourier Number

Go Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)

Biot Number using Heat Transfer Coefficient

Go Biot Number = (Heat Transfer Coefficient*Thickness of Wall)/Thermal Conductivity

Thermal Conductivity given Biot Number

Go Thermal Conductivity = (Heat Transfer Coefficient*Thickness of Wall)/Biot Number

< 11 Co-Relation of Dimensionless Numbers Calculators

Nusselt Number for Transitional and Rough Flow in Circular Tube

Go Nusselt Number = (Darcy Friction Factor/8)*(Reynolds Number-1000)*Prandtl Number/(1+12.7*((Darcy Friction Factor/8)^(0.5))*((Prandtl Number)^(2/3)-1))

Stanton Number using Basic Fluid Properties

Go Stanton Number = External Convection Heat Transfer Coefficient/(Specific Heat Capacity*Fluid Velocity*Density)

Reynolds Number for Non-Circular Tubes

Go Reynolds Number = Density*Fluid Velocity*Characteristic Length/Dynamic Viscosity

Reynolds Number for Circular Tubes

Go Reynolds Number = Density*Fluid Velocity*Diameter of Tube/Dynamic Viscosity

Fourier Number

Go Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)

Prandtl Number

Go Prandtl Number = Specific Heat Capacity*Dynamic Viscosity/Thermal Conductivity

Stanton Number using Dimensionless Numbers

Go Stanton Number = Nusselt Number/(Reynolds Number*Prandtl Number)

Stanton Number given Fanning Friction Factor

Go Stanton Number = (Fanning Friction Factor/2)/(Prandtl Number)^(2/3)

Nusselt Number using Dittus Boelter Equation for Cooling

Go Nusselt Number = 0.023*(Reynolds Number)^0.8*(Prandtl Number)^0.3

Nusselt Number using Dittus Boelter Equation for Heating

Go Nusselt Number = 0.023*(Reynolds Number)^0.8*(Prandtl Number)^0.4

Prandtl Number using Diffusivities

Go Prandtl Number = Momentum Diffusivity/Thermal Diffusivity

Fourier Number Formula

Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)
F_o = (α*𝜏_c)/(s^2)

What is Unsteady State Heat Transfer?

Unsteady State Heat Transfer refers to the heat transfer process in which a system's temperature changes with time. This type of heat transfer can happen in different forms, such as conduction, convection, and radiation. It occurs in various systems, including solid materials, fluids, and gases. The heat transfer rate in an unsteady state is directly proportional to the rate of temperature change. This means that the heat transfer rate is not constant and can vary over time. It's an important aspect in the design and optimization of thermal systems, and understanding this process is crucial in many research areas, such as combustion, electronics, and aerospace.

What is Lumped Parameter Model?

Interior temperatures of some bodies remain essentially uniform at all times during a heat transfer process. The temperature of such bodies are only a function of time, T = T(t). The heat transfer analysis based on this idealization is called lumped system analysis.

How to Calculate Fourier Number?

Fourier Number calculator uses Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2) to calculate the Fourier Number, The Fourier Number is a dimensionless number that characterizes transient heat conduction. Conceptually, it is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat (thermal energy) or matter (particles). Fourier Number is denoted by F_o symbol.

How to calculate Fourier Number using this online calculator? To use this online calculator for Fourier Number, enter Thermal Diffusivity (α), Characteristic Time (𝜏_c) & Characteristic Dimension (s) and hit the calculate button. Here is how the Fourier Number calculation can be explained with given input values -> 0.293006 = (5.58*2.5)/(6.9^2).

FAQ

What is Fourier Number?

The Fourier Number is a dimensionless number that characterizes transient heat conduction. Conceptually, it is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat (thermal energy) or matter (particles) and is represented as F_o = (α*𝜏_c)/(s^2) or Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2). Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure, Characteristic Time is an estimate of the order of magnitude of the reaction time scale of a system & Characteristic Dimension is the ratio of volume and the area.

How to calculate Fourier Number?

The Fourier Number is a dimensionless number that characterizes transient heat conduction. Conceptually, it is the ratio of diffusive or conductive transport rate to the quantity storage rate, where the quantity may be either heat (thermal energy) or matter (particles) is calculated using Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2). To calculate Fourier Number, you need Thermal Diffusivity (α), Characteristic Time (𝜏_c) & Characteristic Dimension (s). With our tool, you need to enter the respective value for Thermal Diffusivity, Characteristic Time & Characteristic Dimension 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 Fourier Number?

In this formula, Fourier Number uses Thermal Diffusivity, Characteristic Time & Characteristic Dimension. We can use 4 other way(s) to calculate the same, which is/are as follows -

Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))
Fourier Number = ((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))
Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number)
Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number)

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