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Time taken to reach given temperature Solution

STEP 0: Pre-Calculation Summary
Formula Used
time_elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((-1)*(Density*Volume*Specific heat)/(Convection heat transfer coefficient*Surface Area))
t = ln((Tf-T∞)/(To-T∞))*((-1)*(ρ*V*s)/(h*SA))
This formula uses 1 Functions, 8 Variables
Functions Used
ln - Natural logarithm function (base e), ln(Number)
Variables Used
Final Temperature - The Final temperature is the temperature at which measurements are made in final state. (Measured in Kelvin)
Fluid temperature - Fluid temperature is the temperature of the fluid surrounding the object. (Measured in Kelvin)
Initial Temperature - The Initial temperature is defined as the measure of heat under initial state or conditions. (Measured in Kelvin)
Density - Density is the degree of compactness of a substance. (Measured in Kilogram per Meter³)
Volume - Volume is the amount of space that a substance or object occupies or that is enclosed within a container. (Measured in Cubic Meter)
Specific heat - The Specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. (Measured in Joule per Kilogram per K)
Convection heat transfer coefficient - Convection heat transfer coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit kellvin. (Measured in Watt per Meter² per K)
Surface Area - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides. (Measured in Square Meter)
STEP 1: Convert Input(s) to Base Unit
Final Temperature: 27 Kelvin --> 27 Kelvin No Conversion Required
Fluid temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
Initial Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
Density: 5.51 Kilogram per Meter³ --> 5.51 Kilogram per Meter³ No Conversion Required
Volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific heat: 100 Joule per Kilogram per K --> 100 Joule per Kilogram per K No Conversion Required
Convection heat transfer coefficient: 1 Watt per Meter² per K --> 1 Watt per Meter² per K No Conversion Required
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
t = ln((Tf-T∞)/(To-T∞))*((-1)*(ρ*V*s)/(h*SA)) --> ln((27-10)/(20-10))*((-1)*(5.51*63*100)/(1*50))
Evaluating ... ...
t = -368.393969582422
STEP 3: Convert Result to Output's Unit
-368.393969582422 Second --> No Conversion Required
FINAL ANSWER
-368.393969582422 Second <-- Time elapsed
(Calculation completed in 00.015 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

Time taken to reach given temperature Formula

time_elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((-1)*(Density*Volume*Specific heat)/(Convection heat transfer coefficient*Surface Area))
t = ln((Tf-T∞)/(To-T∞))*((-1)*(ρ*V*s)/(h*SA))

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 Time taken to reach given temperature?

Time taken to reach given temperature calculator uses time_elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((-1)*(Density*Volume*Specific heat)/(Convection heat transfer coefficient*Surface Area)) to calculate the Time elapsed, The Time taken to reach given temperature formula calculates the time required for a lumped body to reach a certain temperature by using the Temperature-Time relation for the lumped body. Time elapsed is denoted by t symbol.

How to calculate Time taken to reach given temperature using this online calculator? To use this online calculator for Time taken to reach given temperature, enter Final Temperature (Tf), Fluid temperature (T∞), Initial Temperature (To), Density (ρ), Volume (V), Specific heat (s), Convection heat transfer coefficient (h) & Surface Area (SA) and hit the calculate button. Here is how the Time taken to reach given temperature calculation can be explained with given input values -> -368.39397 = ln((27-10)/(20-10))*((-1)*(5.51*63*100)/(1*50)).

FAQ

What is Time taken to reach given temperature?
The Time taken to reach given temperature formula calculates the time required for a lumped body to reach a certain temperature by using the Temperature-Time relation for the lumped body and is represented as t = ln((Tf-T∞)/(To-T∞))*((-1)*(ρ*V*s)/(h*SA)) or time_elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((-1)*(Density*Volume*Specific heat)/(Convection heat transfer coefficient*Surface Area)). The Final temperature is the temperature at which measurements are made in final state, Fluid temperature is the temperature of the fluid surrounding the object, The Initial temperature is defined as the measure of heat under initial state or conditions, Density is the degree of compactness of a substance, Volume is the amount of space that a substance or object occupies or that is enclosed within a container, The Specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius, Convection heat transfer coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit kellvin & The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
How to calculate Time taken to reach given temperature?
The Time taken to reach given temperature formula calculates the time required for a lumped body to reach a certain temperature by using the Temperature-Time relation for the lumped body is calculated using time_elapsed = ln((Final Temperature-Fluid temperature)/(Initial Temperature-Fluid temperature))*((-1)*(Density*Volume*Specific heat)/(Convection heat transfer coefficient*Surface Area)). To calculate Time taken to reach given temperature, you need Final Temperature (Tf), Fluid temperature (T∞), Initial Temperature (To), Density (ρ), Volume (V), Specific heat (s), Convection heat transfer coefficient (h) & Surface Area (SA). With our tool, you need to enter the respective value for Final Temperature, Fluid temperature, Initial Temperature, Density, Volume, Specific heat, Convection heat transfer coefficient & Surface Area 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 Time elapsed?
In this formula, Time elapsed uses Final Temperature, Fluid temperature, Initial Temperature, Density, Volume, Specific heat, Convection heat transfer coefficient & Surface Area. 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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