Change in internal energy of the lumped body Solution

STEP 0: Pre-Calculation Summary
Formula Used
Change in Internal Energy = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo))))
This formula uses 1 Constants, 1 Functions, 8 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Change in Internal Energy - (Measured in Joule) - The Change in Internal Energy of a thermodynamic system is the energy contained within it. It is the energy necessary to create or prepare the system in any given internal state.
Density - (Measured in Kilogram per Meter³) - Density is the degree of compactness of a substance.
Specific Heat - (Measured in Joule per Kilogram per K) - The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.
Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
Initial Temperature - (Measured in Kelvin) - The Initial temperature is defined as the measure of heat under initial state or conditions.
Fluid temperature - (Measured in Kelvin) - Fluid temperature is the temperature of the fluid surrounding the object.
Biot Number - Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.
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.
STEP 1: Convert Input(s) to Base Unit
Density: 5.51 Kilogram per Meter³ --> 5.51 Kilogram per Meter³ No Conversion Required
Specific Heat: 100 Joule per Kilogram per K --> 100 Joule per Kilogram per K No Conversion Required
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Initial Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
Fluid temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
Biot Number: 0.8 --> No Conversion Required
Fourier Number: 0.5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ΔU = ρ*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) --> 5.51*100*63*(20-10)*(1-(exp(-(0.8*0.5))))
Evaluating ... ...
ΔU = 114441.802419649
STEP 3: Convert Result to Output's Unit
114441.802419649 Joule --> No Conversion Required
FINAL ANSWER
114441.802419649 Joule <-- Change in Internal Energy
(Calculation completed in 00.031 seconds)

Credits

Created by Ravi Khiyani
Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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Temperature after given time elapsed
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Total heat transfer during a time interval
Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) Go
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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
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Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number
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Power on exponential of temperature-time relation in terms of Biot and Fourier Number
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Change in internal energy of the lumped body Formula

Change in Internal Energy = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo))))

What is a Lumped body?

In heat transfer analysis, some bodies whose interior temperature remains essentially uniform at any time during a heat transfer process is called lumped body. The temperature of such bodies can be taken to be a function of time only.

How to Calculate Change in internal energy of the lumped body?

Change in internal energy of the lumped body calculator uses Change in Internal Energy = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) to calculate the Change in Internal Energy, The Change in internal energy of the lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval. Change in Internal Energy is denoted by ΔU symbol.

How to calculate Change in internal energy of the lumped body using this online calculator? To use this online calculator for Change in internal energy of the lumped body, enter Density (ρ), Specific Heat (s), Volume (VT), Initial Temperature (To), Fluid temperature (T∞), Biot Number (Bi) & Fourier Number (Fo) and hit the calculate button. Here is how the Change in internal energy of the lumped body calculation can be explained with given input values -> 114441.8 = 5.51*100*63*(20-10)*(1-(exp(-(0.8*0.5)))).

FAQ

What is Change in internal energy of the lumped body?
The Change in internal energy of the lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval and is represented as ΔU = ρ*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) or Change in Internal Energy = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))). Density is the degree of compactness of a substance, The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius, Volume is the amount of space that a substance or object occupies or that is enclosed within a container, The Initial temperature is defined as the measure of heat under initial state or conditions, Fluid temperature is the temperature of the fluid surrounding the object, Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance & 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.
How to calculate Change in internal energy of the lumped body?
The Change in internal energy of the lumped body formula calculates the change in internal energy which is equal to the rate of heat transfer through the body for a time interval is calculated using Change in Internal Energy = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))). To calculate Change in internal energy of the lumped body, you need Density (ρ), Specific Heat (s), Volume (VT), Initial Temperature (To), Fluid temperature (T∞), Biot Number (Bi) & Fourier Number (Fo). With our tool, you need to enter the respective value for Density, Specific Heat, Volume, Initial Temperature, Fluid temperature, Biot Number & Fourier Number 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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