Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number Solution

STEP 0: Pre-Calculation Summary
Formula Used
Temperature Ratio = exp(-(Biot Number*Fourier Number))
Tratio = exp(-(Bi*Fo))
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Temperature Ratio - Temperature ratio is the ratio of temperatures at different instances of any process or environment.
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
Biot Number: 0.8 --> No Conversion Required
Fourier Number: 0.5 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tratio = exp(-(Bi*Fo)) --> exp(-(0.8*0.5))
Evaluating ... ...
Tratio = 0.670320046035639
STEP 3: Convert Result to Output's Unit
0.670320046035639 --> No Conversion Required
FINAL ANSWER
0.670320046035639 <-- Temperature Ratio
(Calculation completed in 00.000 seconds)

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

Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number Formula

Temperature Ratio = exp(-(Biot Number*Fourier Number))
Tratio = 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 Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number?

Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number calculator uses Temperature Ratio = exp(-(Biot Number*Fourier Number)) to calculate the Temperature Ratio, The Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number formula calculates the temperature ratio present in the temperature-time relationship for the lumped body when the Biot Number and Fourier Number are present. Temperature Ratio is denoted by Tratio symbol.

How to calculate Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number using this online calculator? To use this online calculator for Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number, enter Biot Number (Bi) & Fourier Number (Fo) and hit the calculate button. Here is how the Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number calculation can be explained with given input values -> 0.67032 = exp(-(0.8*0.5)).

FAQ

What is Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number?
The Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number formula calculates the temperature ratio present in the temperature-time relationship for the lumped body when the Biot Number and Fourier Number are present and is represented as Tratio = exp(-(Bi*Fo)) or Temperature Ratio = exp(-(Biot Number*Fourier Number)). 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 Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number?
The Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number formula calculates the temperature ratio present in the temperature-time relationship for the lumped body when the Biot Number and Fourier Number are present is calculated using Temperature Ratio = exp(-(Biot Number*Fourier Number)). To calculate Ratio of temperature difference for given time elapsed in terms of Biot and Fourier Number, you need Biot Number (Bi) & Fourier Number (Fo). With our tool, you need to enter the respective value for 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.
How many ways are there to calculate Temperature Ratio?
In this formula, Temperature Ratio uses Biot Number & Fourier Number. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))
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