Time Constant in unsteady state heat transfer Solution

STEP 0: Pre-Calculation Summary
Formula Used
Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area)
τ = (ρ*c*VT)/(h*SA)
This formula uses 6 Variables
Variables Used
Time Constant - Time Constant gives the time constant for a moving iron instrument based ammeter.
Density - (Measured in Kilogram per Meter³) - Density is the degree of compactness of a substance.
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 - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
Convection Heat Transfer Coefficient - (Measured in Watt per Meter² per K) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
STEP 1: Convert Input(s) to Base Unit
Density: 5.51 Kilogram per Meter³ --> 5.51 Kilogram per Meter³ No Conversion Required
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Convection Heat Transfer Coefficient: 2.2 Watt per Meter² per K --> 2.2 Watt per Meter² per K No Conversion Required
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
τ = (ρ*c*VT)/(h*SA) --> (5.51*4184*63)/(2.2*50)
Evaluating ... ...
τ = 13203.5629090909
STEP 3: Convert Result to Output's Unit
13203.5629090909 --> No Conversion Required
FINAL ANSWER
13203.5629090909 <-- Time Constant
(Calculation completed in 00.031 seconds)

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Instantaneous heat transfer rate
Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))) Go
Temperature after given time elapsed
Temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature Go
Total heat transfer during a time interval
Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) Go
Ratio of temperature difference for given time elapsed
Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity)) Go
Power on exponential of temperature-time relation
Constant = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity) Go
Product of Biot and Fourier Number in terms of system properties
Constant = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity) Go
Time Constant in unsteady state heat transfer
Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area) Go
Thermal Capacitance
Thermal capacitance = Density*Specific Heat Capacity*Volume Go
Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number
Temperature Ratio = exp(-(Biot Number*Fourier Number)) Go
Power on exponential of temperature-time relation in terms of Biot and Fourier Number
Constant = -(Biot Number*Fourier Number) Go

Time Constant in unsteady state heat transfer Formula

Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area)
τ = (ρ*c*VT)/(h*SA)

What is Time Constant?

The time constant is the time to reach the temperature gradient equals 63.21 % of the initial temperature gradient. It indicates the response of the system or object to the change in the surrounding temperature. The system with a higher value of time constant takes much time to achieve temperature change.

How to Calculate Time Constant in unsteady state heat transfer?

Time Constant in unsteady state heat transfer calculator uses Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area) to calculate the Time Constant, Time Constant in unsteady state heat transfer formula gives the value of time constant which is the time to reach the temperature gradient equals 63.21 % of the initial temperature gradient. Time Constant is denoted by τ symbol.

How to calculate Time Constant in unsteady state heat transfer using this online calculator? To use this online calculator for Time Constant in unsteady state heat transfer, enter Density (ρ), Specific Heat Capacity (c), Volume (VT), Convection Heat Transfer Coefficient (h) & Surface Area (SA) and hit the calculate button. Here is how the Time Constant in unsteady state heat transfer calculation can be explained with given input values -> 13203.56 = (5.51*4184*63)/(2.2*50).

FAQ

What is Time Constant in unsteady state heat transfer?
Time Constant in unsteady state heat transfer formula gives the value of time constant which is the time to reach the temperature gradient equals 63.21 % of the initial temperature gradient and is represented as τ = (ρ*c*VT)/(h*SA) or Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area). Density is the degree of compactness of a substance, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Volume is the amount of space that a substance or object occupies or that is enclosed within a container, Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature & The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
How to calculate Time Constant in unsteady state heat transfer?
Time Constant in unsteady state heat transfer formula gives the value of time constant which is the time to reach the temperature gradient equals 63.21 % of the initial temperature gradient is calculated using Time Constant = (Density*Specific Heat Capacity*Volume)/(Convection Heat Transfer Coefficient*Surface Area). To calculate Time Constant in unsteady state heat transfer, you need Density (ρ), Specific Heat Capacity (c), Volume (VT), Convection Heat Transfer Coefficient (h) & Surface Area (SA). With our tool, you need to enter the respective value for Density, Specific Heat Capacity, Volume, Convection Heat Transfer Coefficient & Surface Area and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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