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Initial Temperature of Body by Lumped Heat Capacity Method Formula

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

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

T₀ - Initial Temperature of Object?T - Temperature at Any Time T?T_∞ - Temperature of Bulk Fluid?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?

Initial Temperature of Body by Lumped Heat Capacity Method Example

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

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

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

979.9524 = \frac{589 - 373}{\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})} + 373

979.9524K = \frac{589K - 373K}{\exp (\frac{- 10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³})} + 373K

979.9524 = \frac{589 - 373}{\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})} + 373

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Home » Engineering » Chemical Engineering » Heat Transfer » Initial Temperature of Body by Lumped Heat Capacity Method

Initial Temperature of Body by Lumped Heat Capacity Method Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

T 0 = \frac{589K - 373K}{\exp (\frac{- 10W/m²*K \cdot 0.0078m² \cdot 1937s}{15kg/m³ \cdot 1.5J/(kg*K) \cdot 6.541m³})} + 373K

Next Step Prepare to Evaluate

∴

T 0 = \frac{589 - 373}{\exp (\frac{- 10 \cdot 0.0078 \cdot 1937}{15 \cdot 1.5 \cdot 6.541})} + 373

Next Step Evaluate

∴

T 0 = 979.952397710188K

LAST Step Rounding Answer

∴

T 0 = 979.9524K

Initial Temperature of Body by Lumped Heat Capacity Method Formula Elements

Variables

Functions

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.

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.

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.

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.

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.

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.

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.

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.

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.

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)

Credits

Created by Ayush gupta

University School of Chemical Technology-USCT (GGSIPU), New Delhi

Ayush gupta has created this Formula and 300+ more formulas!

Verified by Prerana Bakli

University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA

Prerana Bakli has verified this Formula and 1600+ more formulas!

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 Initial Temperature of Body by Lumped Heat Capacity Method?

Initial Temperature of Body by Lumped Heat Capacity Method evaluator uses 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 to evaluate the Initial Temperature of Object, The Initial 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, temperature of convection environment and equilibrium temperature. 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. Initial Temperature of Object is denoted by T₀ symbol.

How to evaluate Initial Temperature of Body by Lumped Heat Capacity Method using this online evaluator? To use this online evaluator for Initial Temperature of Body by Lumped Heat Capacity Method, enter Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞), 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) and hit the calculate button.

FAQs on Initial Temperature of Body by Lumped Heat Capacity Method

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

The formula of Initial Temperature of Body by Lumped Heat Capacity Method is expressed as 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. Here is an example- 979.9524 = (589-373)/(exp((-10*0.00785*1937)/(15*1.5*6.541)))+373.

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

With Temperature at Any Time T (T), Temperature of Bulk Fluid (T_∞), 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) we can find Initial Temperature of Body by Lumped Heat Capacity Method using the formula - 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. This formula also uses Exponential Growth (exp) function(s).

Can the Initial Temperature of Body by Lumped Heat Capacity Method be negative?

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

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

Initial 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 Initial Temperature of Body by Lumped Heat Capacity Method can be measured.

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Initial Temperature of Body by Lumped Heat Capacity Method Formula

Initial Temperature of Body by Lumped Heat Capacity Method Example

Initial Temperature of Body by Lumped Heat Capacity Method Solution

Initial Temperature of Body by Lumped Heat Capacity Method Formula Elements

Credits

Other formulas in Unsteady State Heat Conduction category

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

FAQs on Initial Temperature of Body by Lumped Heat Capacity Method

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