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Instantaneous heat transfer rate Formula

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Heat Rate is the amount of energy required by an electrical generator or a power plant to produce a one-kilowatt hour of electricity. Check FAQs

Q rate = h \cdot A \cdot (T o - t f) \cdot (\exp (- \frac{h \cdot A \cdot t}{ρ \cdot V T \cdot C o}))

Q_rate - Heat Rate?h - Convection Heat Transfer Coefficient?A - Surface Area?T_o - Initial Temperature?t_f - Fluid Temperature?t - Time Elapsed?ρ - Density?V_T - Total Volume?C_o - Specific Heat Capacity?

Instantaneous heat transfer rate Example

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Here is how the Instantaneous heat transfer rate equation looks like with Values.

Here is how the Instantaneous heat transfer rate equation looks like with Units.

Here is how the Instantaneous heat transfer rate equation looks like.

7.1553 = 0.04 \cdot 18 \cdot (20 - 10) \cdot (\exp (- \frac{0.04 \cdot 18 \cdot 12}{5.51 \cdot 63 \cdot 4}))

7.1553W = 0.04W/m²*K \cdot 18m² \cdot (20K - 10K) \cdot (\exp (- \frac{0.04W/m²*K \cdot 18m² \cdot 12s}{5.51kg/m³ \cdot 63m³ \cdot 4J/(kg*K)}))

7.1553 = 0.04 \cdot 18 \cdot (20 - 10) \cdot (\exp (- \frac{0.04 \cdot 18 \cdot 12}{5.51 \cdot 63 \cdot 4}))

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Instantaneous heat transfer rate Solution

Follow our step by step solution on how to calculate Instantaneous heat transfer rate?

FIRST Step Consider the formula

Q rate = h \cdot A \cdot (T o - t f) \cdot (\exp (- \frac{h \cdot A \cdot t}{ρ \cdot V T \cdot C o}))

Next Step Substitute values of Variables

∴

Q rate = 0.04W/m²*K \cdot 18m² \cdot (20K - 10K) \cdot (\exp (- \frac{0.04W/m²*K \cdot 18m² \cdot 12s}{5.51kg/m³ \cdot 63m³ \cdot 4J/(kg*K)}))

Next Step Prepare to Evaluate

∴

Q rate = 0.04 \cdot 18 \cdot (20 - 10) \cdot (\exp (- \frac{0.04 \cdot 18 \cdot 12}{5.51 \cdot 63 \cdot 4}))

Next Step Evaluate

∴

Q rate = 7.15533744011914W

LAST Step Rounding Answer

∴

Q rate = 7.1553W

Instantaneous heat transfer rate Formula Elements

Variables

Functions

Heat Rate

Heat Rate is the amount of energy required by an electrical generator or a power plant to produce a one-kilowatt hour of electricity.

Symbol: Q_rate

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Convection Heat Transfer Coefficient

Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.

Symbol: h

Measurement: Heat Transfer CoefficientUnit: W/m²*K

Note: Value should be greater than 0.

Surface Area

The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.

Symbol: A

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Initial Temperature

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

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Fluid Temperature

Fluid Temperature is the temperature of the fluid surrounding the object.

Symbol: t_f

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Time Elapsed

Time Elapsed after a particular task is started.

Symbol: t

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Density

The Density of a material shows the denseness of that material in a specific given area. This is taken as mass per unit volume of a given object.

Symbol: ρ

Measurement: DensityUnit: kg/m³

Note: Value should be greater than 0.

Total Volume

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

Symbol: V_T

Measurement: VolumeUnit: 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_o

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

Note: Value can be positive or negative.

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 Ravi Khiyani

Indian Institute of Technology, Madras (IIT Madras), Chennai

Ravi Khiyani has created this Formula and 200+ more formulas!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

Anshika Arya has verified this Formula and 2500+ more formulas!

Other formulas in Transient Heat Conduction category

Go Total Heat Transfer during Time Interval

Q = ρ \cdot c \cdot V T \cdot (T o - t f) \cdot (1 - (\exp (- (Bi \cdot Fo))))

Go Time Constant in unsteady state heat transfer

T c = \frac{ρ \cdot C o \cdot V T}{h \cdot A}

How to Evaluate Instantaneous heat transfer rate?

Instantaneous heat transfer rate evaluator uses Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total Volume*Specific Heat Capacity))) to evaluate the Heat Rate, The instantaneous heat transfer rate formula calculates the rate of heat transfer at the given instant when a lumped body is going for unsteady-state heat conduction. Heat Rate is denoted by Q_rate symbol.

How to evaluate Instantaneous heat transfer rate using this online evaluator? To use this online evaluator for Instantaneous heat transfer rate, enter Convection Heat Transfer Coefficient (h), Surface Area (A), Initial Temperature (T_o), Fluid Temperature (t_f), Time Elapsed (t), Density (ρ), Total Volume (V_T) & Specific Heat Capacity (C_o) and hit the calculate button.

FAQs on Instantaneous heat transfer rate

What is the formula to find Instantaneous heat transfer rate?

The formula of Instantaneous heat transfer rate is expressed as Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total Volume*Specific Heat Capacity))). Here is an example- 7.155337 = 0.04*18*(20-10)*(exp(-(0.04*18*12)/(5.51*63*4))).

How to calculate Instantaneous heat transfer rate?

With Convection Heat Transfer Coefficient (h), Surface Area (A), Initial Temperature (T_o), Fluid Temperature (t_f), Time Elapsed (t), Density (ρ), Total Volume (V_T) & Specific Heat Capacity (C_o) we can find Instantaneous heat transfer rate using the formula - Heat Rate = Convection Heat Transfer Coefficient*Surface Area*(Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total Volume*Specific Heat Capacity))). This formula also uses Exponential Growth (exp) function(s).

Can the Instantaneous heat transfer rate be negative?

Yes, the Instantaneous heat transfer rate, measured in Power can be negative.

Which unit is used to measure Instantaneous heat transfer rate?

Instantaneous heat transfer rate is usually measured using the Watt[W] for Power. Kilowatt[W], Milliwatt[W], Microwatt[W] are the few other units in which Instantaneous heat transfer rate can be measured.

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Instantaneous heat transfer rate Formula

Instantaneous heat transfer rate Example

Instantaneous heat transfer rate Solution

Instantaneous heat transfer rate Formula Elements

Credits

Other formulas in Transient Heat Conduction category

How to Evaluate Instantaneous heat transfer rate?

FAQs on Instantaneous heat transfer rate

Variable Name