Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Calculator

✖Initial Temperature of Solid is the temperature of the given solid initially.ⓘ Initial Temperature of Solid [T_i]			+10% -10%
✖Heat Energy is the amount of total heat required.ⓘ Heat Energy [Q]			+10% -10%
✖The area is the amount of two-dimensional space taken up by an object.ⓘ Area [A]			+10% -10%
✖Density of Body is the physical quantity that expresses the relationship between its mass and its volume.ⓘ Density of Body [ρ_B]			+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]			+10% -10%
✖Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.ⓘ Thermal Diffusivity [α]			+10% -10%
✖Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.ⓘ Time Constant [𝜏]			+10% -10%
✖Depth of Semi Infinite Solid is defined as the depth of solid.ⓘ Depth of Semi Infinite Solid [x]			+10% -10%

✖Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.ⓘ Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid [T]

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Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid

Formula

`"T" = "T"_{"i"}+("Q"/("A"*"ρ"_{"B"}*"c"*(pi*"α"*"𝜏")^(0.5)))*exp((-"x"^2)/(4*"α"*"𝜏"))`

Example

`"600.0201K"="600K"+("4200J"/("50.3m²"*"15kg/m³"*"1.5J/(kg*K)"*(pi*"5.58m²/s"*"1937s")^(0.5)))*exp((-("0.02m")^2)/(4*"5.58m²/s"*"1937s"))`

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Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant))
T = T_i+(Q/(A*ρ_B*c*(pi*α*𝜏)^(0.5)))*exp((-x^2)/(4*α*𝜏))
This formula uses 1 Constants, 1 Functions, 9 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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 at Any Time T - (Measured in Kelvin) - Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.
Initial Temperature of Solid - (Measured in Kelvin) - Initial Temperature of Solid is the temperature of the given solid initially.
Heat Energy - (Measured in Joule) - Heat Energy is the amount of total heat required.
Area - (Measured in Square Meter) - The area is the amount of two-dimensional space taken up by an object.
Density of Body - (Measured in Kilogram per Cubic Meter) - Density of Body is the physical quantity that expresses the relationship between its mass and its volume.
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.
Thermal Diffusivity - (Measured in Square Meter Per Second) - Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.
Time Constant - (Measured in Second) - Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.
Depth of Semi Infinite Solid - (Measured in Meter) - Depth of Semi Infinite Solid is defined as the depth of solid.

STEP 1: Convert Input(s) to Base Unit

Initial Temperature of Solid: 600 Kelvin --> 600 Kelvin No Conversion Required
Heat Energy: 4200 Joule --> 4200 Joule No Conversion Required
Area: 50.3 Square Meter --> 50.3 Square Meter No Conversion Required
Density of Body: 15 Kilogram per Cubic Meter --> 15 Kilogram per Cubic Meter No Conversion Required
Specific Heat Capacity: 1.5 Joule per Kilogram per K --> 1.5 Joule per Kilogram per K No Conversion Required
Thermal Diffusivity: 5.58 Square Meter Per Second --> 5.58 Square Meter Per Second No Conversion Required
Time Constant: 1937 Second --> 1937 Second No Conversion Required
Depth of Semi Infinite Solid: 0.02 Meter --> 0.02 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = T_i+(Q/(A*ρ_B*c*(pi*α*𝜏)^(0.5)))*exp((-x^2)/(4*α*𝜏)) --> 600+(4200/(50.3*15*1.5*(pi*5.58*1937)^(0.5)))*exp((-0.02^2)/(4*5.58*1937))

Evaluating ... ...

T = 600.02013918749

STEP 3: Convert Result to Output's Unit

600.02013918749 Kelvin --> No Conversion Required

FINAL ANSWER

600.02013918749 ≈ 600.0201 Kelvin <-- Temperature at Any Time T

(Calculation completed in 00.004 seconds)

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< 18 Unsteady State Heat Conduction Calculators

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid

Go Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant))

Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method

Go Time Constant = ((-Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Initial Temperature of Body by Lumped Heat Capacity Method

Go Initial Temperature of Object = (Temperature at Any Time T-Temperature of Bulk Fluid)/(exp((-Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object)))+Temperature of Bulk Fluid

Temperature of Body by Lumped Heat Capacity Method

Go Temperature at Any Time T = (exp((-Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object)))*(Initial Temperature of Object-Temperature of Bulk Fluid)+Temperature of Bulk Fluid

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid at Surface

Go Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))

Fourier Number given Heat Transfer Coefficient and Time Constant

Go Fourier Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Biot Number)

Biot Number given Heat Transfer Coefficient and Time Constant

Go Biot Number = (Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object*Fourier Number)

Fourier Number using Biot Number

Go Fourier Number = (-1/(Biot Number))*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Biot Number using Fourier Number

Go Biot Number = (-1/Fourier Number)*ln((Temperature at Any Time T-Temperature of Bulk Fluid)/(Initial Temperature of Object-Temperature of Bulk Fluid))

Biot Number given Characteristic Dimension and Fourier Number

Go Biot Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Fourier Number)

Fourier Number given Characteristic Dimension and Biot Number

Go Fourier Number = (Heat Transfer Coefficient*Time Constant)/(Density of Body*Specific Heat Capacity*Characteristic Dimension*Biot Number)

Initial Internal Energy Content of Body in Reference to Environment Temperature

Go Initial Energy Content = Density of Body*Specific Heat Capacity*Volume of Object*(Initial Temperature of Solid-Ambient Temperature)

Fourier Number using Thermal Conductivity

Go Fourier Number = ((Thermal Conductivity*Characteristic Time)/(Density of Body*Specific Heat Capacity*(Characteristic Dimension^2)))

Time Constant of Thermal System

Go Time Constant = (Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection)

Capacitance of Thermal System by Lumped Heat Capacity Method

Go Capacitance of Thermal System = Density of Body*Specific Heat Capacity*Volume of Object

Fourier Number

Go Fourier Number = (Thermal Diffusivity*Characteristic Time)/(Characteristic Dimension^2)

Biot Number using Heat Transfer Coefficient

Go Biot Number = (Heat Transfer Coefficient*Thickness of Wall)/Thermal Conductivity

Thermal Conductivity given Biot Number

Go Thermal Conductivity = (Heat Transfer Coefficient*Thickness of Wall)/Biot Number

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula

What is Unsteady State Heat Transfer?

Unsteady State Heat Transfer refers to the heat transfer process in which a system's temperature changes with time. This type of heat transfer can happen in different forms, such as conduction, convection, and radiation. It occurs in various systems, including solid materials, fluids, and gases. The heat transfer rate in an unsteady state is directly proportional to the rate of temperature change. This means that the heat transfer rate is not constant and can vary over time. It's an important aspect in the design and optimization of thermal systems, and understanding this process is crucial in many research areas, such as combustion, electronics, and aerospace.

What is Lumped Parameter Model?

Interior temperatures of some bodies remain essentially uniform at all times during a heat transfer process. The temperature of such bodies are only a function of time, T = T(t). The heat transfer analysis based on this idealization is called lumped system analysis.

How to Calculate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid calculator uses Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant)) to calculate the Temperature at Any Time T, The Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid formula is defined as the function of initial temperature of solid, heat energy required, heat transfer area, density of fluid dynamics, specific heat capacity, thermal diffusivity, time constant. The above Calculator presents the temperature response that results from a surface heat flux that remains constant with time. A related boundary condition is that of a short, instantaneous pulse of energy at the surface having a magnitude of Q/A. Temperature at Any Time T is denoted by T symbol.

How to calculate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid using this online calculator? To use this online calculator for Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid, enter Initial Temperature of Solid (T_i), Heat Energy (Q), Area (A), Density of Body (ρ_B), Specific Heat Capacity (c), Thermal Diffusivity (α), Time Constant (𝜏) & Depth of Semi Infinite Solid (x) and hit the calculate button. Here is how the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid calculation can be explained with given input values -> 600.0119 = 600+(4200/(50.3*15*1.5*(pi*5.58*1937)^(0.5)))*exp((-0.02^2)/(4*5.58*1937)).

FAQ

What is Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

The Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid formula is defined as the function of initial temperature of solid, heat energy required, heat transfer area, density of fluid dynamics, specific heat capacity, thermal diffusivity, time constant. The above Calculator presents the temperature response that results from a surface heat flux that remains constant with time. A related boundary condition is that of a short, instantaneous pulse of energy at the surface having a magnitude of Q/A and is represented as T = T_i+(Q/(A*ρ_B*c*(pi*α*𝜏)^(0.5)))*exp((-x^2)/(4*α*𝜏)) or Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant)). Initial Temperature of Solid is the temperature of the given solid initially, Heat Energy is the amount of total heat required, The area is the amount of two-dimensional space taken up by an object, Density of Body is the physical quantity that expresses the relationship between its mass and its volume, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount, Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure, Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature & Depth of Semi Infinite Solid is defined as the depth of solid.

How to calculate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

The Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid formula is defined as the function of initial temperature of solid, heat energy required, heat transfer area, density of fluid dynamics, specific heat capacity, thermal diffusivity, time constant. The above Calculator presents the temperature response that results from a surface heat flux that remains constant with time. A related boundary condition is that of a short, instantaneous pulse of energy at the surface having a magnitude of Q/A is calculated using Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))*exp((-Depth of Semi Infinite Solid^2)/(4*Thermal Diffusivity*Time Constant)). To calculate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid, you need Initial Temperature of Solid (T_i), Heat Energy (Q), Area (A), Density of Body (ρ_B), Specific Heat Capacity (c), Thermal Diffusivity (α), Time Constant (𝜏) & Depth of Semi Infinite Solid (x). With our tool, you need to enter the respective value for Initial Temperature of Solid, Heat Energy, Area, Density of Body, Specific Heat Capacity, Thermal Diffusivity, Time Constant & Depth of Semi Infinite Solid 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 at Any Time T?

In this formula, Temperature at Any Time T uses Initial Temperature of Solid, Heat Energy, Area, Density of Body, Specific Heat Capacity, Thermal Diffusivity, Time Constant & Depth of Semi Infinite Solid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Temperature at Any Time T = (exp((-Heat Transfer Coefficient*Surface Area for Convection*Time Constant)/(Density of Body*Specific Heat Capacity*Volume of Object)))*(Initial Temperature of Object-Temperature of Bulk Fluid)+Temperature of Bulk Fluid
Temperature at Any Time T = Initial Temperature of Solid+(Heat Energy/(Area*Density of Body*Specific Heat Capacity*(pi*Thermal Diffusivity*Time Constant)^(0.5)))

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