Total Heat Transfer during Time Interval Calculator

✖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.ⓘ Density [ρ]			+10% -10%
✖The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.ⓘ Specific Heat [c]			+10% -10%
✖Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Total volume [V_T]			+10% -10%
✖The Initial temperature is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature [T_o]			+10% -10%
✖Fluid temperature is the temperature of the fluid surrounding the object.ⓘ Fluid Temperature [t_f]			+10% -10%
✖Biot Number is a dimensionless quantity having the ratio of internal conduction resistance to the surface convection resistance.ⓘ Biot Number [Bi]			+10% -10%
✖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.ⓘ Fourier Number [Fo]			+10% -10%

✖Heat transfer is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings.ⓘ Total Heat Transfer during Time Interval [Q]

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Formula

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Total Heat Transfer during Time Interval

Formula

`"Q" = "ρ"*"c"*"V"_{"T"}*("T"_{"o"}-"t"_{"f"})*(1-(exp(-("Bi"*"Fo"))))`

Example

`"2583.765J"="5.51kg/m³"*"120J/(kg*K)"*"63m³"*("20K"-"10K")*(1-(exp(-("0.012444"*"0.5"))))`

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Total Heat Transfer during Time Interval Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Q = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo))))
This formula uses 1 Functions, 8 Variables

Functions Used

exp - n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable., exp(Number)

Variables Used

Heat Transfer - (Measured in Joule) - Heat transfer is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings.
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: 0.012444 --> No Conversion Required
Fourier Number: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo)))) --> 5.51*120*63*(20-10)*(1-(exp(-(0.012444*0.5))))

Evaluating ... ...

Q = 2583.76500357691

STEP 3: Convert Result to Output's Unit

2583.76500357691 Joule --> No Conversion Required

FINAL ANSWER

2583.76500357691 ≈ 2583.765 Joule <-- Heat Transfer

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Transient Heat Conduction » Total Heat Transfer during Time Interval

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Created by Ravi Khiyani

Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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National Institute Of Technology (NIT), Hamirpur

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< 13 Transient Heat Conduction Calculators

Instantaneous heat transfer rate

Go 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

Go 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

Go 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

Go 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

Go 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

Go Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))

Product of Biot and Fourier Number given System Properties

Go Product of Biot And Fourier Numbers = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Power on exponential of temperature-time relation

Go Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Time Constant in unsteady state heat transfer

Go Time Constant = (Density*Specific Heat Capacity*Total volume)/(Convection Heat Transfer Coefficient*Surface Area)

Thermal Diffusivity

Go Thermal Diffusivity = Thermal Conductivity/(Density*Specific Heat Capacity)

Thermal Capacitance

Go Thermal Capacitance = Density*Specific Heat Capacity*Volume

Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number

Go Temperature Ratio = exp(-(Biot Number*Fourier Number))

Power on Exponential of Temperature-time Relation given Biot and Fourier Number

Go Constant B = -(Biot Number*Fourier Number)

Total Heat Transfer during Time Interval Formula

Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Q = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo))))

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Total Heat Transfer during Time Interval?

Total Heat Transfer during Time Interval calculator uses Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number)))) to calculate the Heat Transfer, The Total Heat Transfer during Time Interval formula calculates the rate of heat transfer through a lumped body in a given period of time using that it will be equal to the change in internal energy of the lumped body. Heat Transfer is denoted by Q symbol.

How to calculate Total Heat Transfer during Time Interval using this online calculator? To use this online calculator for Total Heat Transfer during Time Interval, enter Density (ρ), Specific Heat (c), Total volume (V_T), Initial Temperature (T_o), Fluid Temperature (t_f), Biot Number (Bi) & Fourier Number (Fo) and hit the calculate button. Here is how the Total Heat Transfer during Time Interval calculation can be explained with given input values -> 2583.765 = 5.51*120*63*(20-10)*(1-(exp(-(0.012444*0.5)))).

FAQ

What is Total Heat Transfer during Time Interval?

The Total Heat Transfer during Time Interval formula calculates the rate of heat transfer through a lumped body in a given period of time using that it will be equal to the change in internal energy of the lumped body and is represented as Q = ρ*c*V_T*(T_o-t_f)*(1-(exp(-(Bi*Fo)))) or Heat Transfer = 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 Total Heat Transfer during Time Interval?

The Total Heat Transfer during Time Interval formula calculates the rate of heat transfer through a lumped body in a given period of time using that it will be equal to the change in internal energy of the lumped body is calculated using Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number)))). To calculate Total Heat Transfer during Time Interval, you need Density (ρ), Specific Heat (c), Total volume (V_T), Initial Temperature (T_o), Fluid Temperature (t_f), 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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