Fourier Number given Characteristic Dimension and Biot Number Calculator

✖The Heat Transfer Coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place.ⓘ Heat Transfer Coefficient [h]			+10% -10%
✖Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.ⓘ Time Constant [𝜏]			+10% -10%
✖Density of Body is the physical quantity that expresses the relationship between its mass and its volume.ⓘ Density of Body [ρ_B]			+10% -10%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [c]			+10% -10%
✖Characteristic Dimension is the ratio of volume and the area.ⓘ Characteristic Dimension [s]			+10% -10%
✖Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.ⓘ Biot Number [Bi]			+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 given Characteristic Dimension and Biot Number [F_o]

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Fourier Number given Characteristic Dimension and Biot Number Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number)
F_o = (h*𝜏)/(ρ_B*c*s*Bi)
This formula uses 7 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.
Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - The Heat Transfer Coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place.
Time Constant - (Measured in Second) - Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.
Density of Body - (Measured in Kilogram per Cubic Meter) - Density of Body is the physical quantity that expresses the relationship between its mass and its volume.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Characteristic Dimension - (Measured in Meter) - Characteristic Dimension is the ratio of volume and the area.
Biot Number - Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.

STEP 1: Convert Input(s) to Base Unit

Heat Transfer Coefficient: 10 Watt per Square Meter per Kelvin --> 10 Watt per Square Meter per Kelvin No Conversion Required
Time Constant: 1937 Second --> 1937 Second No Conversion Required
Density of Body: 15 Kilogram per Cubic Meter --> 15 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity: 1.5 Joule per Kilogram per K --> 1.5 Joule per Kilogram per K No Conversion Required
Characteristic Dimension: 6.9 Meter --> 6.9 Meter No Conversion Required
Biot Number: 27.15 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

F_o = (h*𝜏)/(ρ_B*c*s*Bi) --> (10*1937)/(15*1.5*6.9*27.15)

Evaluating ... ...

F_o = 4.59545140464349

STEP 3: Convert Result to Output's Unit

4.59545140464349 --> No Conversion Required

FINAL ANSWER

4.59545140464349 ≈ 4.595451 <-- Fourier Number

(Calculation completed in 00.004 seconds)

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

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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

Fourier Number given Characteristic Dimension and Biot Number Formula

LaTeX Go

Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number)
F_o = (h*𝜏)/(ρ_B*c*s*Bi)

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 are Dimensionless Number?

Dimensionless numbers or non-dimensional numbers are those which are useful to determine the flow characteristics of a fluid. Inertia force always exists if there is any mass in motion. Dividing this inertia force with other forces like viscous force, gravity force, surface tension, elastic force, or pressure force, gives us the dimensionless numbers.

How to Calculate Fourier Number given Characteristic Dimension and Biot Number?

Fourier Number given Characteristic Dimension and Biot Number calculator uses Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number) to calculate the Fourier Number, The Fourier Number given Characteristic Dimension and Biot Number formula is defined as the function of heat transfer coefficient, time constant, density of body, specific heat capacity, characteristic dimension and fourier number. The exponential part of Lumped Heat capacity equation can also be expressed as the the product of Biot number and fourier number. Fourier Number is denoted by F_o symbol.

How to calculate Fourier Number given Characteristic Dimension and Biot Number using this online calculator? To use this online calculator for Fourier Number given Characteristic Dimension and Biot Number, enter Heat Transfer Coefficient (h), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Characteristic Dimension (s) & Biot Number (Bi) and hit the calculate button. Here is how the Fourier Number given Characteristic Dimension and Biot Number calculation can be explained with given input values -> 4.595451 = (10*1937)/(15*1.5*6.9*27.15).

FAQ

What is Fourier Number given Characteristic Dimension and Biot Number?

The Fourier Number given Characteristic Dimension and Biot Number formula is defined as the function of heat transfer coefficient, time constant, density of body, specific heat capacity, characteristic dimension and fourier number. The exponential part of Lumped Heat capacity equation can also be expressed as the the product of Biot number and fourier number and is represented as F_o = (h*𝜏)/(ρ_B*c*s*Bi) or Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number). The Heat Transfer Coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place, Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature, Density of Body is the physical quantity that expresses the relationship between its mass and its volume, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Characteristic Dimension is the ratio of volume and the area & Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.

How to calculate Fourier Number given Characteristic Dimension and Biot Number?

The Fourier Number given Characteristic Dimension and Biot Number formula is defined as the function of heat transfer coefficient, time constant, density of body, specific heat capacity, characteristic dimension and fourier number. The exponential part of Lumped Heat capacity equation can also be expressed as the the product of Biot number and fourier number is calculated using Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number). To calculate Fourier Number given Characteristic Dimension and Biot Number, you need Heat Transfer Coefficient (h), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Characteristic Dimension (s) & Biot Number (Bi). With our tool, you need to enter the respective value for Heat Transfer Coefficient, Time Constant, Density of Body, Specific Heat Capacity, Characteristic Dimension & Biot Number 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 Heat Transfer Coefficient, Time Constant, Density of Body, Specific Heat Capacity, Characteristic Dimension & Biot Number. 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 Diffusivity*Characteristic Time)/(Characteristic Dimension^2)
Fourier Number = ((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))

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