Instantaneous heat transfer rate Calculator

✖Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.ⓘ Convection Heat Transfer Coefficient [h]			+10% -10%
✖The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.ⓘ Surface Area [A]			+10% -10%
✖The Initial temperature is defined as the measure of heat under initial state or conditions.ⓘ Initial Temperature [T_o]			+10% -10%
✖Fluid temperature is the temperature of the fluid surrounding the object.ⓘ Fluid Temperature [t_f]			+10% -10%
✖Time elapsed after a particular task is started.ⓘ Time Elapsed [t]			+10% -10%
✖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.ⓘ Density [ρ]			+10% -10%
✖Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Total volume [V_T]			+10% -10%
✖Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.ⓘ Specific Heat Capacity [C_o]			+10% -10%

✖Heat rate is the amount of energy required by an electrical generator or a power plant to produce a one-kilowatt hour of electricity.ⓘ Instantaneous heat transfer rate [Q_rate]

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Formula

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Instantaneous heat transfer rate

Formula

`"Q"_{"rate"} = "h"*"A"*("T"_{"o"}-"t"_{"f"})*(exp(-("h"*"A"*"t")/("ρ"*"V"_{"T"}*"C"_{"o"})))`

Example

`"7.155337W"="0.04W/m²*K"*"18m²"*("20K"-"10K")*(exp(-("0.04W/m²*K"*"18m²"*"12s")/("5.51kg/m³"*"63m³"*"4J/(kg*K)")))`

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Instantaneous heat transfer rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
Q_rate = h*A*(T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o)))
This formula uses 1 Functions, 9 Variables

Functions Used

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

Variables Used

Heat Rate - (Measured in Watt) - Heat rate is the amount of energy required by an electrical generator or a power plant to produce a one-kilowatt hour of electricity.
Convection Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature.
Surface Area - (Measured in Square Meter) - The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides.
Initial Temperature - (Measured in Kelvin) - The Initial temperature is defined as the measure of heat under initial state or conditions.
Fluid Temperature - (Measured in Kelvin) - Fluid temperature is the temperature of the fluid surrounding the object.
Time Elapsed - (Measured in Second) - Time elapsed after a particular task is started.
Density - (Measured in Kilogram per Cubic Meter) - 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.
Total volume - (Measured in Cubic Meter) - Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

STEP 1: Convert Input(s) to Base Unit

Convection Heat Transfer Coefficient: 0.04 Watt per Square Meter per Kelvin --> 0.04 Watt per Square Meter per Kelvin No Conversion Required
Surface Area: 18 Square Meter --> 18 Square Meter No Conversion Required
Initial Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
Fluid Temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
Time Elapsed: 12 Second --> 12 Second No Conversion Required
Density: 5.51 Kilogram per Cubic Meter --> 5.51 Kilogram per Cubic Meter No Conversion Required
Total volume: 63 Cubic Meter --> 63 Cubic Meter No Conversion Required
Specific Heat Capacity: 4 Joule per Kilogram per K --> 4 Joule per Kilogram per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q_rate = h*A*(T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o))) --> 0.04*18*(20-10)*(exp(-(0.04*18*12)/(5.51*63*4)))

Evaluating ... ...

Q_rate = 7.15533744011914

STEP 3: Convert Result to Output's Unit

7.15533744011914 Watt --> No Conversion Required

FINAL ANSWER

7.15533744011914 ≈ 7.155337 Watt <-- Heat Rate

(Calculation completed in 00.020 seconds)

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< 13 Transient Heat Conduction Calculators

Instantaneous heat transfer rate

Go 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)))

Temperature after given time elapsed

Go Temperature = ((Initial Temperature-Fluid Temperature)*(exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))))+Fluid Temperature

Time taken to reach given temperature

Go Time Elapsed = ln((Final Temperature-Fluid Temperature)/(Initial Temperature-Fluid Temperature))*((Density*Total volume*Specific Heat)/(Convection Heat Transfer Coefficient*Surface Area))

Change in Internal energy of Lumped body

Go Change in Internal Energy = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))

Total Heat Transfer during Time Interval

Go Heat Transfer = Density*Specific Heat*Total volume*(Initial Temperature-Fluid Temperature)*(1-(exp(-(Biot Number*Fourier Number))))

Ratio of temperature difference for given time elapsed

Go Temperature Ratio = exp(-(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity))

Product of Biot and Fourier Number given System Properties

Go Product of Biot And Fourier Numbers = (Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Power on exponential of temperature-time relation

Go Constant B = -(Convection Heat Transfer Coefficient*Surface Area*Time Elapsed)/(Density*Total volume*Specific Heat Capacity)

Time Constant in unsteady state heat transfer

Go Time Constant = (Density*Specific Heat Capacity*Total volume)/(Convection Heat Transfer Coefficient*Surface Area)

Thermal Diffusivity

Go Thermal Diffusivity = Thermal Conductivity/(Density*Specific Heat Capacity)

Thermal Capacitance

Go Thermal Capacitance = Density*Specific Heat Capacity*Volume

Ratio of Temperature difference for Time Elapsed given Biot and Fourier Number

Go Temperature Ratio = exp(-(Biot Number*Fourier Number))

Power on Exponential of Temperature-time Relation given Biot and Fourier Number

Go Constant B = -(Biot Number*Fourier Number)

Instantaneous heat transfer rate Formula

What is Temperature-Time relation?

The temperature-time relationship of unsteady-state heat transfer helps to determine the rate of heat transfer that has been conducted in the lumped system in a given time period.

How to Calculate Instantaneous heat transfer rate?

Instantaneous heat transfer rate calculator 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 calculate 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 calculate Instantaneous heat transfer rate using this online calculator? To use this online calculator 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. Here is how the Instantaneous heat transfer rate calculation can be explained with given input values -> 7.155337 = 0.04*18*(20-10)*(exp(-(0.04*18*12)/(5.51*63*4))).

FAQ

What is Instantaneous heat transfer 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 and is represented as Q_rate = h*A*(T_o-t_f)*(exp(-(h*A*t)/(ρ*V_T*C_o))) or 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))). Convection Heat Transfer Coefficient is the rate of heat transfer between a solid surface and a fluid per unit surface area per unit temperature, The Surface Area of a three-dimensional shape is the sum of all of the surface areas of each of the sides, The Initial temperature is defined as the measure of heat under initial state or conditions, Fluid temperature is the temperature of the fluid surrounding the object, Time elapsed after a particular task is started, 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, Total volume is the overall amount of space that a substance or object occupies or that is enclosed within a container & Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.

How to calculate Instantaneous heat transfer 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 is calculated using 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 calculate Instantaneous heat transfer rate, you need 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). With our tool, you need to enter the respective value for Convection Heat Transfer Coefficient, Surface Area, Initial Temperature, Fluid Temperature, Time Elapsed, Density, Total volume & Specific Heat Capacity and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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