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Time Constant of Thermal System Formula

GoTime Taken by Object for Heating or Cooling by Lumped Heat Capacity Method Formula

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

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

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

Time Constant of Thermal System Example

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Here is how the Time Constant of Thermal System equation looks like with Values.

Here is how the Time Constant of Thermal System equation looks like with Units.

Here is how the Time Constant of Thermal System equation looks like.

1874.8089 = \frac{15 \cdot 1.5 \cdot 6.541}{10 \cdot 0.0078}

1874.8089s = \frac{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³}{10W/m²*K \cdot 0.0078m²}

1874.8089 = \frac{15 \cdot 1.5 \cdot 6.541}{10 \cdot 0.0078}

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Time Constant of Thermal System Solution

Follow our step by step solution on how to calculate Time Constant of Thermal System?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

𝜏 = \frac{15 \cdot 1.5 \cdot 6.541}{10 \cdot 0.0078}

Next Step Evaluate

∴

𝜏 = 1874.80891719745s

LAST Step Rounding Answer

∴

𝜏 = 1874.8089s

Time Constant of Thermal System Formula Elements

Variables

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

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

Other Formulas to find Time Constant

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

𝜏 = (\frac{- ρ B \cdot c \cdot V}{h \cdot A c}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

Other formulas in Unsteady State Heat Conduction category

Go Biot Number using Heat Transfer Coefficient

Bi = \frac{h \cdot 𝓁}{k}

Go Fourier Number using Biot Number

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

Go Biot Number using Fourier Number

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

Go Initial Internal Energy Content of Body in Reference to Environment Temperature

Q o = ρ B \cdot c \cdot V \cdot (T i - T amb)

How to Evaluate Time Constant of Thermal System?

Time Constant of Thermal System evaluator uses Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection) to evaluate the Time Constant, The Time Constant of Thermal System formula is defined as the function of density of body, Specific heat capacity, volume of object, heat transfer coefficient, surface area of convection. At time 𝜏 it is noted that t the temperature difference T − T∞ has a value of 36.8 percent of the initial difference T0 − T∞. Time Constant is denoted by 𝜏 symbol.

How to evaluate Time Constant of Thermal System using this online evaluator? To use this online evaluator for Time Constant of Thermal System, enter Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V), Heat Transfer Coefficient (h) & Surface Area for Convection (A_c) and hit the calculate button.

FAQs on Time Constant of Thermal System

What is the formula to find Time Constant of Thermal System?

The formula of Time Constant of Thermal System is expressed as Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection). Here is an example- 1874.809 = (15*1.5*6.541)/(10*0.00785).

How to calculate Time Constant of Thermal System?

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

What are the other ways to Calculate Time Constant?

Here are the different ways to Calculate Time Constant-

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))

Can the Time Constant of Thermal System be negative?

Yes, the Time Constant of Thermal System, measured in Time can be negative.

Which unit is used to measure Time Constant of Thermal System?

Time Constant of Thermal System is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Constant of Thermal System can be measured.

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Time Constant of Thermal System Formula

​GoTime Taken by Object for Heating or Cooling by Lumped Heat Capacity Method Formula

Time Constant of Thermal System Example

Time Constant of Thermal System Solution

Time Constant of Thermal System Formula Elements

Other Formulas to find Time Constant

Other formulas in Unsteady State Heat Conduction category

How to Evaluate Time Constant of Thermal System?

FAQs on Time Constant of Thermal System

Variable Name

GoTime Taken by Object for Heating or Cooling by Lumped Heat Capacity Method Formula