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*Volume*Specific Heat Capacity))))+Fluid temperature
T = ((To-T∞)*(exp(-(h*SA*t)/(ρ*VT*c))))+T∞
This formula uses 1 Constants, 1 Functions, 9 Variables
Constants Used
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
exp - Exponential function, 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 Meter² per K) - 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 Meter³) - Density is the degree of compactness of a substance.
Volume - (Measured in Cubic Meter) - Volume is the 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: 2.2 Watt per Meter² per K --> 2.2 Watt per Meter² per K No Conversion Required
Surface Area: 50 Square Meter --> 50 Square Meter No Conversion Required
Time Elapsed: 12 Second --> 12 Second 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 Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = ((To-T∞)*(exp(-(h*SA*t)/(ρ*VT*c))))+T∞ --> ((20-10)*(exp(-(2.2*50*12)/(5.51*63*4184))))+10
Evaluating ... ...
T = 19.9909156727918
STEP 3: Convert Result to Output's Unit
19.9909156727918 Kelvin --> No Conversion Required
FINAL ANSWER
19.9909156727918 Kelvin <-- Temperature
(Calculation completed in 00.032 seconds)

Credits

Created by Ravi Khiyani
Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore
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National Institute Of Technology (NIT), Hamirpur
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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 = 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
Constant = -(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
Constant = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity) Go
Time Constant in unsteady state heat transfer
Time Constant = (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
Constant = -(Biot Number*Fourier Number) Go

Temperature after given time elapsed Formula

Temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Volume*Specific Heat Capacity))))+Fluid temperature
T = ((To-T∞)*(exp(-(h*SA*t)/(ρ*VT*c))))+T∞

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*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 (To), Fluid temperature (T∞), Convection Heat Transfer Coefficient (h), Surface Area (SA), Time Elapsed (t), Density (ρ), Volume (VT) & Specific Heat Capacity (c) and hit the calculate button. Here is how the Temperature after given time elapsed calculation can be explained with given input values -> 19.99092 = ((20-10)*(exp(-(2.2*50*12)/(5.51*63*4184))))+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 = ((To-T∞)*(exp(-(h*SA*t)/(ρ*VT*c))))+T∞ or Temperature = ((Initial Temperature-Fluid temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*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, 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 & 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*Volume*Specific Heat Capacity))))+Fluid temperature. To calculate Temperature after given time elapsed, you need Initial Temperature (To), Fluid temperature (T∞), Convection Heat Transfer Coefficient (h), Surface Area (SA), Time Elapsed (t), Density (ρ), Volume (VT) & Specific Heat Capacity (c). With our tool, you need to enter the respective value for Initial Temperature, Fluid temperature, Convection Heat Transfer Coefficient, Surface Area, Time Elapsed, Density, 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.
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