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

✖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%

✖Temperature ratio is the ratio of temperatures at different instances of any process or environment.ⓘ Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number [T_ratio]

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

Formula

`"T"_{"ratio"} = exp(-("Bi"*"Fo"))`

Example

`"0.993797"=exp(-("0.012444"*"0.5"))`

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

STEP 0: Pre-Calculation Summary

Formula Used

Temperature Ratio = exp(-(Biot Number*Fourier Number))
T_ratio = exp(-(Bi*Fo))
This formula uses 1 Functions, 3 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

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: 0.012444 --> No Conversion Required
Fourier Number: 0.5 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_ratio = exp(-(Bi*Fo)) --> exp(-(0.012444*0.5))

Evaluating ... ...

T_ratio = 0.993797316558693

STEP 3: Convert Result to Output's Unit

0.993797316558693 --> No Conversion Required

FINAL ANSWER

0.993797316558693 ≈ 0.993797 <-- Temperature Ratio

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Transient Heat Conduction » Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number

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Created by Ravi Khiyani

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

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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)

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

Temperature Ratio = exp(-(Biot Number*Fourier Number))
T_ratio = 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 Time Elapsed given Biot and Fourier Number?

Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number calculator uses Temperature Ratio = exp(-(Biot Number*Fourier Number)) to calculate the Temperature Ratio, The Ratio of Temperature difference for Time Elapsed given 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 T_ratio symbol.

How to calculate Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number using this online calculator? To use this online calculator for Ratio of Temperature difference for Time Elapsed given 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 Time Elapsed given Biot and Fourier Number calculation can be explained with given input values -> 0.993797 = exp(-(0.012444*0.5)).

FAQ

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

The Ratio of Temperature difference for Time Elapsed given 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 T_ratio = 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 Time Elapsed given Biot and Fourier Number?

The Ratio of Temperature difference for Time Elapsed given 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 Time Elapsed given 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*Total volume*Specific Heat Capacity))

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