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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, 2 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, exp(Number)
Variables Used
Biot number- Biot number simple index of the ratio of the heat transfer resistances inside of a body and at the surface of a body.
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: 10 --> No Conversion Required
Fourier Number: 500 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tratio = exp(-(Bi*Fo)) --> exp(-(10*500))
Evaluating ... ...
Tratio = 0
STEP 3: Convert Result to Output's Unit
0 --> No Conversion Required
FINAL ANSWER
0 <-- Temperature Ratio
(Calculation completed in 00.000 seconds)

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_KJ = 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
constantt = -(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
constantt = (Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity) Go
Time Constant in unsteady state heat transfer
tau_mi = (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
constantt = -(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 = exp(-(10*500)).

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 simple index of the ratio of the heat transfer resistances inside of a body and at the surface of a body & 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 10 other way(s) to calculate the same, which is/are as follows -
  • 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)))
  • heat_transfer_KJ = Density*Specific heat*Volume*(Initial Temperature-Fluid temperature)*(1-(exp(-(Biot number*Fourier Number))))
  • tau_mi = (Density*Specific Heat Capacity*Volume)/(Convection heat transfer coefficient*Surface Area)
  • constantt = -(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)
  • constantt = -(Biot number*Fourier Number)
  • temperature_ratio = exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))
  • temperature_ratio = exp(-(Biot number*Fourier Number))
  • temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature
  • constantt = (Convection heat transfer coefficient*Surface Area*Time elapsed)/(Density*Volume*Specific Heat Capacity)
  • thermal_capacitance = Density*Specific Heat Capacity*Volume
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