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Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula

GoTemperature of Body by Lumped Heat Capacity Method Formula

GoTemperature Response of Instantaneous Energy Pulse in Semi Infinite Solid at Surface Formula

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Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer. Check FAQs

T = T i + (\frac{Q}{A \cdot ρ B \cdot c \cdot {(π \cdot α \cdot 𝜏)}^{0.5}}) \cdot \exp (\frac{- x^{2}}{4 \cdot α \cdot 𝜏})

T - Temperature at Any Time T?T_i - Initial Temperature of Solid?Q - Heat Energy?A - Area?ρ_B - Density of Body?c - Specific Heat Capacity?α - Thermal Diffusivity?𝜏 - Time Constant?x - Depth of Semi Infinite Solid?π - Archimedes' constant?

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Example

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Here is how the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid equation looks like with Values.

Here is how the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid equation looks like with Units.

Here is how the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid equation looks like.

600.0201 = 600 + (\frac{4200}{50.3 \cdot 15 \cdot 1.5 \cdot {(3.1416 \cdot 5.58 \cdot 1937)}^{0.5}}) \cdot \exp (\frac{- {0.02}^{2}}{4 \cdot 5.58 \cdot 1937})

600.0201K = 600K + (\frac{4200J}{50.3m² \cdot 15kg/m³ \cdot 1.5J/(kg*K) \cdot {(3.1416 \cdot 5.58m²/s \cdot 1937s)}^{0.5}}) \cdot \exp (\frac{- {0.02m}^{2}}{4 \cdot 5.58m²/s \cdot 1937s})

600.0201 = 600 + (\frac{4200}{50.3 \cdot 15 \cdot 1.5 \cdot {(3.1416 \cdot 5.58 \cdot 1937)}^{0.5}}) \cdot \exp (\frac{- {0.02}^{2}}{4 \cdot 5.58 \cdot 1937})

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Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Solution

Follow our step by step solution on how to calculate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

FIRST Step Consider the formula

T = T i + (\frac{Q}{A \cdot ρ B \cdot c \cdot {(π \cdot α \cdot 𝜏)}^{0.5}}) \cdot \exp (\frac{- x^{2}}{4 \cdot α \cdot 𝜏})

Next Step Substitute values of Variables

∴

T = 600K + (\frac{4200J}{50.3m² \cdot 15kg/m³ \cdot 1.5J/(kg*K) \cdot {(π \cdot 5.58m²/s \cdot 1937s)}^{0.5}}) \cdot \exp (\frac{- {0.02m}^{2}}{4 \cdot 5.58m²/s \cdot 1937s})

Next Step Substitute values of Constants

∴

T = 600K + (\frac{4200J}{50.3m² \cdot 15kg/m³ \cdot 1.5J/(kg*K) \cdot {(3.1416 \cdot 5.58m²/s \cdot 1937s)}^{0.5}}) \cdot \exp (\frac{- {0.02m}^{2}}{4 \cdot 5.58m²/s \cdot 1937s})

Next Step Prepare to Evaluate

∴

T = 600 + (\frac{4200}{50.3 \cdot 15 \cdot 1.5 \cdot {(3.1416 \cdot 5.58 \cdot 1937)}^{0.5}}) \cdot \exp (\frac{- {0.02}^{2}}{4 \cdot 5.58 \cdot 1937})

Next Step Evaluate

∴

T = 600.02013918749K

LAST Step Rounding Answer

∴

T = 600.0201K

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula Elements

Variables

Constants

Functions

Temperature at Any Time T

Temperature at Any Time T is defined as the temperature of an object at any given time t measured using thermometer.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature at Any Time T

Initial Temperature of Solid

Initial Temperature of Solid is the temperature of the given solid initially.

Symbol: T_i

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Initial Temperature of Solid

Heat Energy

Heat Energy is the amount of total heat required.

Symbol: Q

Measurement: EnergyUnit: J

Note: Value should be greater than 0.

Formulas to find Heat Energy

Area

The area is the amount of two-dimensional space taken up by an object.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Area

Density of Body

Density of Body is the physical quantity that expresses the relationship between its mass and its volume.

Symbol: ρ_B

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Formulas to find Density of Body

Specific Heat Capacity

Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

Symbol: c

Measurement: Specific Heat CapacityUnit: J/(kg*K)

Note: Value should be greater than 0.

Formulas to find Specific Heat Capacity

Thermal Diffusivity

Thermal diffusivity is the thermal conductivity divided by density and specific heat capacity at constant pressure.

Symbol: α

Measurement: DiffusivityUnit: m²/s

Note: Value can be positive or negative.

Formulas to find Thermal Diffusivity

Time Constant

Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature.

Symbol: 𝜏

Measurement: TimeUnit: s

Note: Value can be positive or negative.

Formulas to find Time Constant

Depth of Semi Infinite Solid

Depth of Semi Infinite Solid is defined as the depth of solid.

Symbol: x

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Depth of Semi Infinite Solid

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

exp

n an exponential function, the value of the function changes by a constant factor for every unit change in the independent variable.

Syntax: exp(Number)

Other Formulas to find Temperature at Any Time T

Go Temperature of Body by Lumped Heat Capacity Method

T = (\exp (\frac{- h \cdot A c \cdot 𝜏}{ρ B \cdot c \cdot V})) \cdot (T 0 - T ∞) + T ∞

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

T = T i + (\frac{Q}{A \cdot ρ B \cdot c \cdot {(π \cdot α \cdot 𝜏)}^{0.5}})

Other formulas in Unsteady State Heat Conduction category

Go Biot Number using Heat Transfer Coefficient

Bi = \frac{h \cdot 𝓁}{k}

Go Fourier Number using Biot Number

F o = (- \frac{1}{Bi}) \cdot \ln (\frac{T - T ∞}{T 0 - T ∞})

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

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid evaluator 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 evaluate 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 evaluate Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid using this online evaluator? To use this online evaluator 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.

FAQs on Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid

What is the formula to find Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

The formula of Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid is expressed as 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)). Here is an example- 600.0119 = 600+(4200/(50.3*15*1.5*(pi*5.58*1937)^(0.5)))*exp((-0.02^2)/(4*5.58*1937)).

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

With 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) we can find Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid using the formula - 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)). This formula also uses Archimedes' constant and Exponential Growth (exp) function(s).

What are the other ways to Calculate Temperature at Any Time T?

Here are the different ways to Calculate Temperature at Any Time T-

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)))

Can the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid be negative?

No, the Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid, measured in Temperature cannot be negative.

Which unit is used to measure Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid?

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid can be measured.

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Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula

​GoTemperature of Body by Lumped Heat Capacity Method Formula

​GoTemperature Response of Instantaneous Energy Pulse in Semi Infinite Solid at Surface Formula

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Example

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Solution

Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula Elements

Other Formulas to find Temperature at Any Time T

Other formulas in Unsteady State Heat Conduction category

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

FAQs on Temperature Response of Instantaneous Energy Pulse in Semi Infinite Solid

Variable Name

GoTemperature of Body by Lumped Heat Capacity Method Formula

GoTemperature Response of Instantaneous Energy Pulse in Semi Infinite Solid at Surface Formula