Time Constant of Thermal System Calculator

✖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%
✖Volume of Object is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of Object [V]			+10% -10%
✖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%
✖Surface Area for Convection is defined as the surface area of object which is in the process of heat transfer.ⓘ Surface Area for Convection [A_c]			+10% -10%

✖Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.ⓘ Time Constant of Thermal System [𝜏]

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Formula

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Time Constant of Thermal System

Formula

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

Example

1874.809 s = \frac{15 kg/m³ \cdot 1.5 J/(kg*K) \cdot 6.541 m³}{10 W/m²*K \cdot 0.00785 m²}

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Time Constant of Thermal System Solution

STEP 0: Pre-Calculation Summary

Formula Used

Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection)
𝜏 = (ρ_B*c*V)/(h*A_c)
This formula uses 6 Variables

Variables Used

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.
Volume of Object - (Measured in Cubic Meter) - Volume of Object is the amount of space that a substance or object occupies or that is enclosed within a container.
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.
Surface Area for Convection - (Measured in Square Meter) - Surface Area for Convection is defined as the surface area of object which is in the process of heat transfer.

STEP 1: Convert Input(s) to Base Unit

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
Volume of Object: 6.541 Cubic Meter --> 6.541 Cubic Meter No Conversion Required
Heat Transfer Coefficient: 10 Watt per Square Meter per Kelvin --> 10 Watt per Square Meter per Kelvin No Conversion Required
Surface Area for Convection: 0.00785 Square Meter --> 0.00785 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

𝜏 = (ρ_B*c*V)/(h*A_c) --> (15*1.5*6.541)/(10*0.00785)

Evaluating ... ...

𝜏 = 1874.80891719745

STEP 3: Convert Result to Output's Unit

1874.80891719745 Second --> No Conversion Required

FINAL ANSWER

1874.80891719745 ≈ 1874.809 Second <-- Time Constant

(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

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))

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)

Biot Number using Heat Transfer Coefficient

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

Time Constant of Thermal System Formula

Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection)
𝜏 = (ρ_B*c*V)/(h*A_c)

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 Time Constant of Thermal System?

Time Constant of Thermal System calculator uses Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection) to calculate 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 calculate Time Constant of Thermal System using this online calculator? To use this online calculator 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. Here is how the Time Constant of Thermal System calculation can be explained with given input values -> 1874.809 = (15*1.5*6.541)/(10*0.00785).

FAQ

What is Time Constant of Thermal System?

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∞ and is represented as 𝜏 = (ρ_B*c*V)/(h*A_c) or Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection). 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, Volume of Object is the amount of space that a substance or object occupies or that is enclosed within a container, 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 & Surface Area for Convection is defined as the surface area of object which is in the process of heat transfer.

How to calculate Time Constant of Thermal System?

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∞ is calculated using Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection). To calculate Time Constant of Thermal System, you need Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V), Heat Transfer Coefficient (h) & Surface Area for Convection (A_c). With our tool, you need to enter the respective value for Density of Body, Specific Heat Capacity, Volume of Object, Heat Transfer Coefficient & Surface Area for Convection 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 Time Constant?

In this formula, Time Constant uses Density of Body, Specific Heat Capacity, Volume of Object, Heat Transfer Coefficient & Surface Area for Convection. We can use 1 other way(s) to calculate the same, which is/are as follows -

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))

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