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Fourier Number given Heat Transfer Coefficient and Time Constant Formula

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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. Check FAQs

F o = \frac{h \cdot A c \cdot 𝜏}{ρ B \cdot c \cdot V \cdot Bi}

F_o - Fourier Number?h - Heat Transfer Coefficient?A_c - Surface Area for Convection?𝜏 - Time Constant?ρ_B - Density of Body?c - Specific Heat Capacity?V - Volume of Object?Bi - Biot Number?

Fourier Number given Heat Transfer Coefficient and Time Constant Example

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Here is how the Fourier Number given Heat Transfer Coefficient and Time Constant equation looks like with Values.

Here is how the Fourier Number given Heat Transfer Coefficient and Time Constant equation looks like with Units.

Here is how the Fourier Number given Heat Transfer Coefficient and Time Constant equation looks like.

0.0381 = \frac{10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541 \cdot 27.15}

0.0381 = \frac{10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³ \cdot 27.15}

0.0381 = \frac{10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541 \cdot 27.15}

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Fourier Number given Heat Transfer Coefficient and Time Constant Solution

Follow our step by step solution on how to calculate Fourier Number given Heat Transfer Coefficient and Time Constant?

FIRST Step Consider the formula

F o = \frac{h \cdot A c \cdot 𝜏}{ρ B \cdot c \cdot V \cdot Bi}

Next Step Substitute values of Variables

∴

F o = \frac{10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³ \cdot 27.15}

Next Step Prepare to Evaluate

∴

F o = \frac{10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541 \cdot 27.15}

Next Step Evaluate

∴

F o = 0.0380542157670868

LAST Step Rounding Answer

∴

F o = 0.0381

Fourier Number given Heat Transfer Coefficient and Time Constant Formula Elements

Variables

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.

Symbol: F_o

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Fourier Number

Heat Transfer Coefficient

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.

Symbol: h

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value can be positive or negative.

Formulas to find Heat Transfer Coefficient

Surface Area for Convection

Surface Area for Convection is defined as the surface area of object which is in the process of heat transfer.

Symbol: A_c

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area for Convection

Time Constant

Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.

Symbol: 𝜏

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Constant

Density of Body

Density of Body is the physical quantity that expresses the relationship between its mass and its volume.

Symbol: ρ_B

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Body

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value should be greater than 0.

Formulas to find Specific Heat Capacity

Volume of Object

Volume of Object is the amount of space that a substance or object occupies or that is enclosed within a container.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Object

Biot Number

Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.

Symbol: Bi

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Biot Number

Other Formulas to find Fourier Number

Go Fourier Number using Biot Number

F o = (- \frac{1}{Bi}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

Go Fourier Number

F o = \frac{α \cdot 𝜏 c}{s^{2}}

Other formulas in Unsteady State Heat Conduction category

Go Biot Number using Heat Transfer Coefficient

Bi = \frac{h \cdot 𝓁}{k}

Go Biot Number using Fourier Number

Bi = (- \frac{1}{F o}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

How to Evaluate Fourier Number given Heat Transfer Coefficient and Time Constant?

Fourier Number given Heat Transfer Coefficient and Time Constant evaluator uses Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number) to evaluate the Fourier Number, The Fourier Number given Heat Transfer Coefficient and Time Constant formula is defined as the function of heat transfer coefficient, surface area for convection, time constant, density of body, specific heat capacity, volume of object and Biot 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 evaluate Fourier Number given Heat Transfer Coefficient and Time Constant using this online evaluator? To use this online evaluator for Fourier Number given Heat Transfer Coefficient and Time Constant, enter Heat Transfer Coefficient (h), Surface Area for Convection (A_c), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V) & Biot Number (Bi) and hit the calculate button.

FAQs on Fourier Number given Heat Transfer Coefficient and Time Constant

What is the formula to find Fourier Number given Heat Transfer Coefficient and Time Constant?

The formula of Fourier Number given Heat Transfer Coefficient and Time Constant is expressed as Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number). Here is an example- 0.038054 = (10*0.00785*1937)/(15*1.5*6.541*27.15).

How to calculate Fourier Number given Heat Transfer Coefficient and Time Constant?

With Heat Transfer Coefficient (h), Surface Area for Convection (A_c), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V) & Biot Number (Bi) we can find Fourier Number given Heat Transfer Coefficient and Time Constant using the formula - Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number).

What are the other ways to Calculate Fourier Number?

Here are the different ways to Calculate Fourier Number-

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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: Value
: Unit

Fourier Number given Heat Transfer Coefficient and Time Constant Formula

​GoFourier Number using Biot Number Formula

​GoFourier Number Formula

Fourier Number given Heat Transfer Coefficient and Time Constant Example

Fourier Number given Heat Transfer Coefficient and Time Constant Solution

Fourier Number given Heat Transfer Coefficient and Time Constant Formula Elements

Other Formulas to find Fourier Number

Other formulas in Unsteady State Heat Conduction category

How to Evaluate Fourier Number given Heat Transfer Coefficient and Time Constant?

FAQs on Fourier Number given Heat Transfer Coefficient and Time Constant

Variable Name

GoFourier Number using Biot Number Formula

GoFourier Number Formula