Total heat transfer during a time interval Solution

STEP 0: Pre-Calculation Summary
Formula Used
Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Q = 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
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 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
Q = ρ*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) --> 5.51*100*63*(20-10)*(1-(exp(-(0.8*0.5))))
Evaluating ... ...
Q = 114441.802419649
STEP 3: Convert Result to Output's Unit
114441.802419649 Joule -->114.441802419649 Kilojoule (Check conversion here)
FINAL ANSWER
114.441802419649 Kilojoule <-- Heat transfer
(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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10+ 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*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

Total heat transfer during a time interval Formula

Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number))))
Q = ρ*s*VT*(To-T∞)*(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 a time interval?

Total heat transfer during a time interval calculator uses Heat transfer = Density*Specific Heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))) to calculate the Heat transfer, The Total heat transfer during a 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 a time interval using this online calculator? To use this online calculator for Total heat transfer during a time interval, 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 Total heat transfer during a time interval calculation can be explained with given input values -> 114.4418 = 5.51*100*63*(20-10)*(1-(exp(-(0.8*0.5)))).

FAQ

What is Total heat transfer during a time interval?
The Total heat transfer during a 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*s*VT*(To-T∞)*(1-(exp(-(Bi*Fo)))) or Heat transfer = 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 Total heat transfer during a time interval?
The Total heat transfer during a 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*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot Number*Fourier Number)))). To calculate Total heat transfer during a time interval, 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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