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Time Constant is defined as the total time taken for a body to attain final temperature from initial temperature. Check FAQs
𝜏=(-ρBcVhAc)ln(T-TT0-T)
𝜏 - Time Constant?ρB - Density of Body?c - Specific Heat Capacity?V - Volume of Object?h - Heat Transfer Coefficient?Ac - Surface Area for Convection?T - Temperature at Any Time T?T - Temperature of Bulk Fluid?T0 - Initial Temperature of Object?

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

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Here is how the Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method equation looks like with Values.

Here is how the Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method equation looks like with Units.

Here is how the Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method equation looks like.

1626.6686Edit=(-15Edit1.5Edit6.541Edit10Edit0.0078Edit)ln(589Edit-373Edit887.36Edit-373Edit)
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Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method Solution

Follow our step by step solution on how to calculate Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method?

FIRST Step Consider the formula
𝜏=(-ρBcVhAc)ln(T-TT0-T)
Next Step Substitute values of Variables
𝜏=(-15kg/m³1.5J/(kg*K)6.54110W/m²*K0.0078)ln(589K-373K887.36K-373K)
Next Step Prepare to Evaluate
𝜏=(-151.56.541100.0078)ln(589-373887.36-373)
Next Step Evaluate
𝜏=1626.66858618284s
LAST Step Rounding Answer
𝜏=1626.6686s

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

Variables
Functions
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: ρB
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:
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: Ac
Measurement: AreaUnit:
Note: Value can be positive or negative.
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.
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.
ln
The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.
Syntax: ln(Number)

Other Formulas to find Time Constant

​Go Time Constant of Thermal System
𝜏=ρBcVhAc

Other formulas in Unsteady State Heat Conduction category

​Go Biot Number using Heat Transfer Coefficient
Bi=h𝓁k
​Go Fourier Number using Biot Number
Fo=(-1Bi)ln(T-TT0-T)

How to Evaluate Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method?

Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method evaluator uses 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)) to evaluate the Time Constant, The Time Taken by Object for Heating or Cooling 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 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. Time Constant is denoted by 𝜏 symbol.

How to evaluate Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method using this online evaluator? To use this online evaluator for Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method, enter Density of Body B), Specific Heat Capacity (c), Volume of Object (V), Heat Transfer Coefficient (h), Surface Area for Convection (Ac), Temperature at Any Time T (T), Temperature of Bulk Fluid (T) & Initial Temperature of Object (T0) and hit the calculate button.

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

What is the formula to find Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method?
The formula of Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method is expressed as 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)). Here is an example- 1626.669 = ((-15*1.5*6.541)/(10*0.00785))*ln((589-373)/(887.36-373)).
How to calculate Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method?
With Density of Body B), Specific Heat Capacity (c), Volume of Object (V), Heat Transfer Coefficient (h), Surface Area for Convection (Ac), Temperature at Any Time T (T), Temperature of Bulk Fluid (T) & Initial Temperature of Object (T0) we can find Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method using the formula - 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)). This formula also uses Natural Logarithm (ln) function(s).
What are the other ways to Calculate Time Constant?
Here are the different ways to Calculate Time Constant-
  • Time Constant=(Density of Body*Specific Heat Capacity*Volume of Object)/(Heat Transfer Coefficient*Surface Area for Convection)OpenImg
Can the Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method be negative?
Yes, the Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method, measured in Time can be negative.
Which unit is used to measure Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method?
Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method is usually measured using the Second[s] for Time. Millisecond[s], Microsecond[s], Nanosecond[s] are the few other units in which Time Taken by Object for Heating or Cooling by Lumped Heat Capacity Method can be measured.
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