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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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 00.004 seconds)

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Created by Ayush gupta

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

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< Unsteady State Heat Conduction Calculators

Fourier Number using Biot Number

LaTeX 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

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

Initial Internal Energy Content of Body in Reference to Environment Temperature

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

Biot Number using Heat Transfer Coefficient

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

< Co Relation of Dimensionless Numbers Calculators

Nusselt Number for Transitional and Rough Flow in Circular Tube

LaTeX 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))

Reynolds Number for Non-Circular Tubes

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

Reynolds Number for Circular Tubes

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

Prandtl Number

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

Fourier Number Formula

LaTeX Go

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 3 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)

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