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Temperature of Body by Lumped Heat Capacity Method Formula

GoTemperature Response of Instantaneous Energy Pulse in Semi Infinite Solid 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 = (\exp (\frac{- h \cdot A c \cdot 𝜏}{ρ B \cdot c \cdot V})) \cdot (T 0 - T ∞) + T ∞

T - Temperature at Any Time T?h - Heat Transfer Coefficient?A_c - Surface Area for Convection?𝜏 - Time Constant?ρ_B - Density of Body?c - Specific Heat Capacity?V - Volume of Object?T₀ - Initial Temperature of Object?T_∞ - Temperature of Bulk Fluid?

Temperature of Body by Lumped Heat Capacity Method Example

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Here is how the Temperature of Body by Lumped Heat Capacity Method equation looks like with Values.

Here is how the Temperature of Body by Lumped Heat Capacity Method equation looks like with Units.

Here is how the Temperature of Body by Lumped Heat Capacity Method equation looks like.

556.0486 = (\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})) \cdot (887.36 - 373) + 373

556.0486K = (\exp (\frac{- 10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³})) \cdot (887.36K - 373K) + 373K

556.0486 = (\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})) \cdot (887.36 - 373) + 373

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Temperature of Body by Lumped Heat Capacity Method Solution

Follow our step by step solution on how to calculate Temperature of Body by Lumped Heat Capacity Method?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T = (\exp (\frac{- 10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³})) \cdot (887.36K - 373K) + 373K

Next Step Prepare to Evaluate

∴

T = (\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})) \cdot (887.36 - 373) + 373

Next Step Evaluate

∴

T = 556.048556063287K

LAST Step Rounding Answer

∴

T = 556.0486K

Temperature of Body by Lumped Heat Capacity Method Formula Elements

Variables

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

Heat Transfer Coefficient

The Heat Transfer Coefficient is the heat transferred per unit area per kelvin. Thus area is included in the equation as it represents the area over which the transfer of heat takes place.

Symbol: h

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value can be positive or negative.

Formulas to find Heat Transfer Coefficient

Surface Area for Convection

Surface Area for Convection is defined as the surface area of object which is in the process of heat transfer.

Symbol: A_c

Measurement: AreaUnit: m²

Note: Value can be positive or negative.

Formulas to find Surface Area for Convection

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

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

Volume of Object

Volume of Object is the amount of space that a substance or object occupies or that is enclosed within a container.

Symbol: V

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Volume of Object

Initial Temperature of Object

The Initial temperature of Object is defined as the measure of heat under initial state or conditions.

Symbol: T₀

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Initial Temperature of Object

Temperature of Bulk Fluid

Temperature of Bulk Fluid is defined as the temperature of bulk fluid or fluid at given instant measured using thermometer.

Symbol: T_∞

Measurement: TemperatureUnit: K

Note: Value should be greater than 0.

Formulas to find Temperature of Bulk Fluid

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 Response of Instantaneous Energy Pulse in Semi Infinite Solid

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})

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 of Body by Lumped Heat Capacity Method?

Temperature of Body by Lumped Heat Capacity Method evaluator uses 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 to evaluate the Temperature at Any Time T, The Temperature of Body by Lumped Heat Capacity Method formula is defined as the function of heat transfer coefficient, surface area of convection, density of object, specific heat capacity of object, volume of body, initial temperature, temperature of convection environment, time taken for temperature change. This type of analysis is called the lumped-heat-capacity method. Such systems are obviously idealized because a temperature gradient must exist in a material if heat is to be conducted into or out of the material. In general, the smaller the physical size of the body, the more realistic the assumption of a uniform temperature throughout; in the limit a differential volume could be employed as in the derivation of the general heat-conduction equation. Temperature at Any Time T is denoted by T symbol.

How to evaluate Temperature of Body by Lumped Heat Capacity Method using this online evaluator? To use this online evaluator for Temperature of Body by Lumped Heat Capacity Method, enter Heat Transfer Coefficient (h), Surface Area for Convection (A_c), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V), Initial Temperature of Object (T₀) & Temperature of Bulk Fluid (T_∞) and hit the calculate button.

FAQs on Temperature of Body by Lumped Heat Capacity Method

What is the formula to find Temperature of Body by Lumped Heat Capacity Method?

The formula of Temperature of Body by Lumped Heat Capacity Method is expressed as 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. Here is an example- 556.0486 = (exp((-10*0.00785*1937)/(15*1.5*6.541)))*(887.36-373)+373.

How to calculate Temperature of Body by Lumped Heat Capacity Method?

With Heat Transfer Coefficient (h), Surface Area for Convection (A_c), Time Constant (𝜏), Density of Body (ρ_B), Specific Heat Capacity (c), Volume of Object (V), Initial Temperature of Object (T₀) & Temperature of Bulk Fluid (T_∞) we can find Temperature of Body by Lumped Heat Capacity Method using the formula - 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. This formula also uses 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=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))
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 of Body by Lumped Heat Capacity Method be negative?

No, the Temperature of Body by Lumped Heat Capacity Method, measured in Temperature cannot be negative.

Which unit is used to measure Temperature of Body by Lumped Heat Capacity Method?

Temperature of Body by Lumped Heat Capacity Method is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature of Body by Lumped Heat Capacity Method can be measured.

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Temperature of Body by Lumped Heat Capacity Method Formula

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

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

Temperature of Body by Lumped Heat Capacity Method Example

Temperature of Body by Lumped Heat Capacity Method Solution

Temperature of Body by Lumped Heat Capacity Method Formula Elements

Other Formulas to find Temperature at Any Time T

Other formulas in Unsteady State Heat Conduction category

How to Evaluate Temperature of Body by Lumped Heat Capacity Method?

FAQs on Temperature of Body by Lumped Heat Capacity Method

Variable Name

GoTemperature Response of Instantaneous Energy Pulse in Semi Infinite Solid Formula

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