Time taken to reach given temperature Calculator

✖The Final temperature is the temperature at which measurements are made in final state.ⓘ Final Temperature [T_f]			+10% -10%
✖Fluid temperature is the temperature of the fluid surrounding the object.ⓘ Fluid Temperature [t_f]			+10% -10%
✖The Initial temperature is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature [T_o]			+10% -10%
✖The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.ⓘ Density [ρ]			+10% -10%
✖Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Total volume [V_T]			+10% -10%
✖The Specific Heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius.ⓘ Specific Heat [c]			+10% -10%
✖Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.ⓘ Convection Heat Transfer Coefficient [h]			+10% -10%
✖The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.ⓘ Surface Area [A]			+10% -10%

✖Time elapsed after a particular task is started.ⓘ Time taken to reach given temperature [t]

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Formula

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Time taken to reach given temperature

Formula

`"t" = ln(("T"_{"f"}-"t"_{"f"})/("T"_{"o"}-"t"_{"f"}))*(("ρ"*"V"_{"T"}*"c")/("h"*"A"))`

Example

`"12s"=ln(("20.002074366K"-"10K")/("20K"-"10K"))*(("5.51kg/m³"*"63m³"*"120J/(kg*K)")/("0.04W/m²*K"*"18m²"))`

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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))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area))
t = ln((T_f-t_f)/(T_o-t_f))*((ρ*V_T*c)/(h*A))
This formula uses 1 Functions, 9 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
Final Temperature - (Measured in Kelvin) - The Final temperature is the temperature at which measurements are made in final state.
Fluid Temperature - (Measured in Kelvin) - Fluid temperature is the temperature of the fluid surrounding the object.
Initial Temperature - (Measured in Kelvin) - The Initial temperature is defined as the measure of heat under initial state or conditions.
Density - (Measured in Kilogram per Cubic Meter) - The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.
Total volume - (Measured in Cubic Meter) - Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.
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.
Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.

STEP 1: Convert Input(s) to Base Unit

Final Temperature: 20.002074366 Kelvin --> 20.002074366 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 Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Total volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat: 120 Joule per Kilogram per K --> 120 Joule per Kilogram per K No Conversion Required
Convection Heat Transfer Coefficient: 0.04 Watt per Square Meter per Kelvin --> 0.04 Watt per Square Meter per Kelvin No Conversion Required
Surface Area: 18 Square Meter --> 18 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t = ln((T_f-t_f)/(T_o-t_f))*((ρ*V_T*c)/(h*A)) --> ln((20.002074366-10)/(20-10))*((5.51*63*120)/(0.04*18))

Evaluating ... ...

t = 11.9999999164213

STEP 3: Convert Result to Output's Unit

11.9999999164213 Second --> No Conversion Required

FINAL ANSWER

11.9999999164213 ≈ 12 Second <-- Time Elapsed

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Transient Heat Conduction » Time taken to reach given temperature

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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)

Time taken to reach given temperature Formula

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))*((Density*Total 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 (T_f), Fluid Temperature (t_f), Initial Temperature (T_o), Density (ρ), Total volume (V_T), Specific Heat (c), Convection Heat Transfer Coefficient (h) & Surface Area (A) and hit the calculate button. Here is how the Time taken to reach given temperature calculation can be explained with given input values -> 30699.5 = ln((20.002074366-10)/(20-10))*((5.51*63*120)/(0.04*18)).

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((T_f-t_f)/(T_o-t_f))*((ρ*V_T*c)/(h*A)) or Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total 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, The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object, Total volume is the overall 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 temperature & 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))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area)). To calculate Time taken to reach given temperature, you need Final Temperature (T_f), Fluid Temperature (t_f), Initial Temperature (T_o), Density (ρ), Total volume (V_T), Specific Heat (c), Convection Heat Transfer Coefficient (h) & Surface Area (A). With our tool, you need to enter the respective value for Final Temperature, Fluid Temperature, Initial Temperature, Density, Total 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.

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