Temperature after given time elapsed Calculator

✖The Initial temperature is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature [T_o]			+10% -10%
✖Fluid temperature is the temperature of the fluid surrounding the object.ⓘ Fluid Temperature [t_f]			+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 Elapsed [t]			+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%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [C_o]			+10% -10%

✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature after given time elapsed [T]

⎘ Copy

👎

Formula

✖

Temperature after given time elapsed

Formula

`"T" = (("T"_{"o"}-"t"_{"f"})*(exp(-("h"*"A"*"t")/("ρ"*"V"_{"T"}*"C"_{"o"}))))+"t"_{"f"}`

Example

`"19.93797K"=(("20K"-"10K")*(exp(-("0.04W/m²*K"*"18m²"*"12s")/("5.51kg/m³"*"63m³"*"4J/(kg*K)"))))+"10K"`

Calculator

LaTeX

Reset

👍

Download Conduction Formula PDF PDF Image

Temperature after given time elapsed Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature
T = ((T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o))))+t_f
This formula uses 1 Functions, 9 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 - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Initial Temperature - (Measured in Kelvin) - The Initial temperature is defined as the measure of heat under initial state or conditions.
Fluid Temperature - (Measured in Kelvin) - Fluid temperature is the temperature of the fluid surrounding the object.
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.
Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
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 Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

STEP 1: Convert Input(s) to Base Unit

Initial Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
Fluid Temperature: 10 Kelvin --> 10 Kelvin 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
Time Elapsed: 12 Second --> 12 Second 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 Capacity: 4 Joule per Kilogram per K --> 4 Joule per Kilogram per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = ((T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o))))+t_f --> ((20-10)*(exp(-(0.04*18*12)/(5.51*63*4))))+10

Evaluating ... ...

T = 19.9379686668321

STEP 3: Convert Result to Output's Unit

19.9379686668321 Kelvin --> No Conversion Required

FINAL ANSWER

19.9379686668321 ≈ 19.93797 Kelvin <-- Temperature

(Calculation completed in 00.020 seconds)

You are here -

Home » Physics » Heat and Mass Transfer » Conduction » Transient Heat Conduction » Temperature after given time elapsed

Credits

Created by Ravi Khiyani

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

Ravi Khiyani has created this Calculator and 200+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Calculator and 2500+ more calculators!

< 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)

Temperature after given time elapsed 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 Temperature after given time elapsed?

Temperature after given time elapsed calculator uses Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature to calculate the Temperature, The Temperature after given time elapsed formula calculates the temperature of the lumped body for the given time by using Temperature-Time relation. Temperature is denoted by T symbol.

How to calculate Temperature after given time elapsed using this online calculator? To use this online calculator for Temperature after given time elapsed, enter Initial Temperature (T_o), Fluid Temperature (t_f), Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (V_T) & Specific Heat Capacity (C_o) and hit the calculate button. Here is how the Temperature after given time elapsed calculation can be explained with given input values -> 19.93797 = ((20-10)*(exp(-(0.04*18*12)/(5.51*63*4))))+10.

FAQ

What is Temperature after given time elapsed?

The Temperature after given time elapsed formula calculates the temperature of the lumped body for the given time by using Temperature-Time relation and is represented as T = ((T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o))))+t_f or Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature. The Initial temperature is defined as the measure of heat under initial state or conditions, Fluid temperature is the temperature of the fluid surrounding the object, 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, Time elapsed after a particular task is started, 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 & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

How to calculate Temperature after given time elapsed?

The Temperature after given time elapsed formula calculates the temperature of the lumped body for the given time by using Temperature-Time relation is calculated using Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature. To calculate Temperature after given time elapsed, you need Initial Temperature (T_o), Fluid Temperature (t_f), Convection Heat Transfer Coefficient (h), Surface Area (A), Time Elapsed (t), Density (ρ), Total volume (V_T) & Specific Heat Capacity (C_o). With our tool, you need to enter the respective value for Initial Temperature, Fluid Temperature, Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, Total volume & Specific Heat Capacity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

Home

FREE PDFs

🔍 Search