## Change in Internal energy of Lumped body Solution

STEP 0: Pre-Calculation Summary
Formula Used
Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*c*VT*(To-T∞)*(1-(exp(-(Bi*Fo))))
This formula uses 1 Functions, 8 Variables
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 Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
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.
Total volume - (Measured in Cubic Meter) - Total volume is the overall 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 Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Specific Heat: 120 Joule per Kilogram per K --> 120 Joule per Kilogram per K No Conversion Required
Total 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*c*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) --> 5.51*120*63*(20-10)*(1-(exp(-(0.8*0.5))))
Evaluating ... ...
ΔU = 137330.162903578
STEP 3: Convert Result to Output's Unit
137330.162903578 Joule --> No Conversion Required
137330.162903578 137330.2 Joule <-- Change in Internal Energy
(Calculation completed in 00.019 seconds)
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## < 13 Transient Heat Conduction Calculators

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*Total volume*Specific Heat Capacity)))
Temperature after given time elapsed
Temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid temperature
Time taken to reach given temperature
Time Elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area))
Change in Internal energy of Lumped body
Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Total Heat Transfer during Time Interval
Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Ratio of temperature difference for given time elapsed
Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))
Power on exponential of temperature-time relation
Constant = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
Product of Biot and Fourier Number given System Properties
Constant = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)
Time Constant in unsteady state heat transfer
Time Constant = (Density*Specific Heat Capacity*Total volume)/(Convection Heat Transfer Coefficient*Surface Area)
Thermal Diffusivity
Thermal Diffusivity = Thermal Conductivity/(Density*Specific Heat Capacity)
Thermal Capacitance
Thermal Capacitance = Density*Specific Heat Capacity*Volume
Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number
Temperature Ratio = exp(-(Biot Number*Fourier Number))
Power on Exponential of Temperature-time Relation given Biot and Fourier Number
Constant = -(Biot Number*Fourier Number)

## Change in Internal energy of Lumped body Formula

Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
ΔU = ρ*c*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 Lumped body?

Change in Internal energy of Lumped body calculator uses Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) to calculate the Change in Internal Energy, The Change in Internal energy of 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 Lumped body using this online calculator? To use this online calculator for Change in Internal energy of Lumped body, enter Density (ρ), Specific Heat (c), Total 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 Lumped body calculation can be explained with given input values -> 137330.2 = 5.51*120*63*(20-10)*(1-(exp(-(0.8*0.5)))).

### FAQ

What is Change in Internal energy of Lumped body?
The Change in Internal energy of 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*c*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) or Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))). The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius, Total volume is the overall 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 Lumped body?
The Change in Internal energy of 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*Total volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))). To calculate Change in Internal energy of Lumped body, you need Density (ρ), Specific Heat (c), Total 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, Total 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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