Fourier Number using Biot Number Calculator

✖Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.ⓘ Biot Number [Bi]			+10% -10%
✖Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.ⓘ Temperature at Any Time T [T]			+10% -10%
✖Temperature of Bulk Fluid is defined as the temperature of bulk fluid or fluid at given instant measured using thermometer.ⓘ Temperature of Bulk Fluid [T_∞]			+10% -10%
✖The Initial temperature of Object is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature of Object [T₀]			+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 using Biot Number [F_o]

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Formula

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Fourier Number using Biot Number

Formula

`"F"_{"o"} = (-1/("Bi"))*ln(("T"-"T"_{"∞"})/("T"_{"0"}-"T"_{"∞"}))`

Example

`"0.031957"=(-1/("27.15"))*ln(("589K"-"373K")/("887.36K"-"373K"))`

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Download Unsteady State Heat Conduction Formulas PDF

Fourier Number using Biot Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))
F_o = (-1/(Bi))*ln((T-T_∞)/(T₀-T_∞))
This formula uses 1 Functions, 5 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

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.
Biot Number - Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.
Temperature at Any Time T - (Measured in Kelvin) - Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.
Temperature of Bulk Fluid - (Measured in Kelvin) - Temperature of Bulk Fluid is defined as the temperature of bulk fluid or fluid at given instant measured using thermometer.
Initial Temperature of Object - (Measured in Kelvin) - The Initial temperature of Object is defined as the measure of heat under initial state or conditions.

STEP 1: Convert Input(s) to Base Unit

Biot Number: 27.15 --> No Conversion Required
Temperature at Any Time T: 589 Kelvin --> 589 Kelvin No Conversion Required
Temperature of Bulk Fluid: 373 Kelvin --> 373 Kelvin No Conversion Required
Initial Temperature of Object: 887.36 Kelvin --> 887.36 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_o = (-1/(Bi))*ln((T-T_∞)/(T₀-T_∞)) --> (-1/(27.15))*ln((589-373)/(887.36-373))

Evaluating ... ...

F_o = 0.0319574586268167

STEP 3: Convert Result to Output's Unit

0.0319574586268167 --> No Conversion Required

FINAL ANSWER

0.0319574586268167 ≈ 0.031957 <-- Fourier Number

(Calculation completed in 00.004 seconds)

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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

Fourier Number using Biot Number Formula

Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))
F_o = (-1/(Bi))*ln((T-T_∞)/(T₀-T_∞))

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 using Biot Number?

Fourier Number using Biot Number calculator uses Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid)) to calculate the Fourier Number, The Fourier Number using Biot Number formula is defined as the function of temp at any time t , temp of bulk fluid, initial temp and biot number. Fourier Number is denoted by F_o symbol.

How to calculate Fourier Number using Biot Number using this online calculator? To use this online calculator for Fourier Number using Biot Number, enter Biot Number (Bi), Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞) & Initial Temperature of Object (T₀) and hit the calculate button. Here is how the Fourier Number using Biot Number calculation can be explained with given input values -> 0.031957 = (-1/(27.15))*ln((589-373)/(887.36-373)).

FAQ

What is Fourier Number using Biot Number?

The Fourier Number using Biot Number formula is defined as the function of temp at any time t , temp of bulk fluid, initial temp and biot number and is represented as F_o = (-1/(Bi))*ln((T-T_∞)/(T₀-T_∞)) or 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 is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance, Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer, Temperature of Bulk Fluid is defined as the temperature of bulk fluid or fluid at given instant measured using thermometer & The Initial temperature of Object is defined as the measure of heat under initial state or conditions.

How to calculate Fourier Number using Biot Number?

The Fourier Number using Biot Number formula is defined as the function of temp at any time t , temp of bulk fluid, initial temp and biot number is calculated using Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid)). To calculate Fourier Number using Biot Number, you need Biot Number (Bi), Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞) & Initial Temperature of Object (T₀). With our tool, you need to enter the respective value for Biot Number, Temperature at Any Time T, Temperature of Bulk Fluid & Initial Temperature of Object 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 Biot Number, Temperature at Any Time T, Temperature of Bulk Fluid & Initial Temperature of Object. We can use 4 other way(s) to calculate the same, which is/are as follows -

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