Newton's Law of Cooling Calculator

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Basics of HMT

Conduction

Convection

Convective Mass Transfer

✖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.ⓘ Heat Transfer Coefficient [h_transfer]			+10% -10%
✖Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.ⓘ Surface Temperature [T_w]			+10% -10%
✖The Temperature of Characteristic Fluid is the temperature of fluid flowing over the surface due to which heat transfer takes place between the surface and the characteristic fluid.ⓘ Temperature of Characteristic Fluid [T_f]			+10% -10%

✖Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q".ⓘ Newton's Law of Cooling [q']

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Formula

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Newton's Law of Cooling

Formula

`"q'" = "h"_{"transfer"}*("T"_{"w"}-"T"_{"f"})`

Example

`"396W/m²"="13.2W/m²*K"*("305K"-"275K")`

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Newton's Law of Cooling Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)
q' = h_transfer*(T_w-T_f)
This formula uses 4 Variables

Variables Used

Heat Flux - (Measured in Watt per Square Meter) - Heat Flux is the heat transfer rate per unit area normal to the direction of heat flow. It is denoted by the letter "q".
Heat Transfer Coefficient - (Measured in Watt per Square Meter per Kelvin) - 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.
Surface Temperature - (Measured in Kelvin) - Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.
Temperature of Characteristic Fluid - (Measured in Kelvin) - The Temperature of Characteristic Fluid is the temperature of fluid flowing over the surface due to which heat transfer takes place between the surface and the characteristic fluid.

STEP 1: Convert Input(s) to Base Unit

Heat Transfer Coefficient: 13.2 Watt per Square Meter per Kelvin --> 13.2 Watt per Square Meter per Kelvin No Conversion Required
Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required
Temperature of Characteristic Fluid: 275 Kelvin --> 275 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q' = h_transfer*(T_w-T_f) --> 13.2*(305-275)

Evaluating ... ...

q' = 396

STEP 3: Convert Result to Output's Unit

396 Watt per Square Meter --> No Conversion Required

FINAL ANSWER

396 Watt per Square Meter <-- Heat Flux

(Calculation completed in 00.004 seconds)

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Created by Kethavath Srinath

Osmania University (OU), Hyderabad

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< 13 Heat and Mass Transfer Calculators

Heat Transfer by Conduction at Base

Go Rate of Conductive Heat Transfer = (Thermal Conductivity*Cross Sectional Area of Fin*Perimeter of the Fin*Convective Heat Transfer Coefficient)^0.5*(Base Temperature-Ambient Temperature)

Heat Exchange by Radiation due to Geometric Arrangement

Go Heat Transfer = Emissivity*Area*[Stefan-BoltZ]*Shape Factor*(Temperature of Surface 1^(4)-Temperature of Surface 2^(4))

Black Bodies Heat Exchange by Radiation

Go Heat Transfer = Emissivity*[Stefan-BoltZ]*Area*(Temperature of Surface 1^(4)-Temperature of Surface 2^(4))

Heat Transfer According to Fourier's Law

Go Heat Flow Through a Body = -(Thermal Conductivity of Material*Surface Area of Heat Flow*Temperature Difference/Thickness)

One Dimensional Heat Flux

Go Heat Flux = -Thermal Conductivity of Fin/Wall Thickness*(Temperature of Wall 2-Temperature of Wall 1)

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Non Ideal Body Surface Emittance

Go Real Surface Radiant Surface Emittance = Emissivity*[Stefan-BoltZ]*Surface Temperature^(4)

Convective Processes Heat Transfer Coefficient

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Recovery temperature)

Thermal Conductivity given Critical Thickness of Insulation for Cylinder

Go Thermal Conductivity of Fin = Critical Thickness of Insulation*Heat Transfer Coefficient at Outer Surface

Diameter of Rod Circular Fin given Area of Cross-Section

Go Diameter of Circular Rod = sqrt((Cross-sectional area*4)/pi)

Critical Thickness of Insulation for Cylinder

Go Critical Thickness of Insulation = Thermal Conductivity of Fin/Heat Transfer Coefficient

Thermal Resistance in Convection Heat Transfer

Go Thermal Resistance = 1/(Exposed Surface Area*Co-efficient of Convective Heat Transfer)

Heat Transfer

Go Heat Flow Rate = Thermal Potential Difference/Thermal Resistance

< 9 Heat Transfer from Extended Surfaces (Fins) Calculators

Heat Dissipation from Fin Losing Heat at End Tip

Go Fin Heat Transfer Rate = (sqrt(Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area))*(Surface Temperature-Surrounding Temperature)*((tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin)+(Heat Transfer Coefficient)/(Thermal Conductivity of Fin*(sqrt(Perimeter of Fin*Heat Transfer Coefficient/Thermal Conductivity of Fin*Cross Sectional Area)))))/(1+tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin*(Heat Transfer Coefficient)/(Thermal Conductivity of Fin*(sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area))))))

Heat Dissipation from Fin Insulated at End Tip

Go Fin Heat Transfer Rate = (sqrt((Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area)))*(Surface Temperature-Surrounding Temperature)*tanh((sqrt((Perimeter of Fin*Heat Transfer Coefficient)/(Thermal Conductivity of Fin*Cross Sectional Area)))*Length of Fin)

Heat Dissipation from Infinitely Long Fin

Go Fin Heat Transfer Rate = ((Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area)^0.5)*(Surface Temperature-Surrounding Temperature)

Heat Transfer in Fins given Fin Efficiency

Go Fin Heat Transfer Rate = Overall Heat Transfer Coefficient*Area*Fin Efficiency*Overall Difference in Temperature

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Biot Number using Characteristic Length

Go Biot Number = (Heat Transfer Coefficient*Characteristic Length)/(Thermal Conductivity of Fin)

Correction Length for Cylindrical Fin with Non-Adiabatic Tip

Go Correction Length for Cylindrical Fin = Length of Fin+(Diameter of Cylindrical Fin/4)

Correction Length for Thin Rectangular Fin with Non-Adiabatic Tip

Go Correction Length for Thin Rectangular Fin = Length of Fin+(Thickness of Fin/2)

Correction Length for Square Fin with Non-Adiabatic Tip

Go Correction Length for Sqaure Fin = Length of Fin+(Width of Fin/4)

< 13 Factors of Thermodynamics Calculators

Van der Waals Equation

Go Van der Waals Equation = [R]*Temperature/(Molar Volume-Gas Constant b)-Gas Constant a/Molar Volume^2

Average Speed of Gases

Go Average Speed of Gas = sqrt((8*[R]*Temperature of Gas A)/(pi*Molar Mass))

Molar Mass of Gas given Average Speed of Gas

Go Molar Mass = (8*[R]*Temperature of Gas A)/(pi*Average Speed of Gas^2)

RMS Speed

Go Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass)

Most Probable Speed

Go Most Probable Speed = sqrt((2*[R]*Temperature of Gas A)/Molar Mass)

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Change in Momentum

Go Change in Momentum = Mass of Body*(Initial Velocity at Point 2-Initial Velocity at Point 1)

Input Power to Turbine or Power given to Turbine

Go Power = Density*Acceleration due to Gravity*Discharge*Head

Degree of Freedom given Equipartition Energy

Go Degree of Freedom = 2*Equipartition Energy/([BoltZ]*Temperature of Gas B)

Molar Mass of Gas given RMS Velocity of Gas

Go Molar Mass = (3*[R]*Temperature of Gas A)/Root Mean Square Velocity^2

Molar Mass of Gas given Most Probable Speed of Gas

Go Molar Mass = (2*[R]*Temperature of Gas A)/Most Probable Speed^2

Specific Gas Constant

Go Specific Gas Constant = [R]/Molar Mass

Absolute Humidity

Go Absolute Humidity = Weight/Volume of Gas

< 20 Heat Transfer from Extended Surfaces (Fins), Critical Thickness of Insulation and Thermal Resistance Calculators

Heat Dissipation from Fin Losing Heat at End Tip

Heat Dissipation from Fin Insulated at End Tip

Heat Dissipation from Infinitely Long Fin

Go Fin Heat Transfer Rate = ((Perimeter of Fin*Heat Transfer Coefficient*Thermal Conductivity of Fin*Cross Sectional Area)^0.5)*(Surface Temperature-Surrounding Temperature)

Thermal Resistance for Conduction at Tube Wall

Go Thermal Resistance = (ln(Outer Radius of Cylinder/Inner Radius of Cylinder))/(2*pi*Thermal Conductivity*Length of Cylinder)

Heat Transfer in Fins given Fin Efficiency

Go Fin Heat Transfer Rate = Overall Heat Transfer Coefficient*Area*Fin Efficiency*Overall Difference in Temperature

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Biot Number using Characteristic Length

Go Biot Number = (Heat Transfer Coefficient*Characteristic Length)/(Thermal Conductivity of Fin)

Critical Radius of Insulation of Hollow Sphere

Go Critical Radius of Insulation = 2*Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient

Critical Radius of Insulation of Cylinder

Go Critical Radius of Insulation = Thermal Conductivity of Insulation/External Convection Heat Transfer Coefficient

Correction Length for Cylindrical Fin with Non-Adiabatic Tip

Go Correction Length for Cylindrical Fin = Length of Fin+(Diameter of Cylindrical Fin/4)

Outside Heat Transfer Coefficient given Thermal Resistance

Go External Convection Heat Transfer Coefficient = 1/(Thermal Resistance*Outside Area)

Thermal Resistance for Convection at Outer Surface

Go Thermal Resistance = 1/(External Convection Heat Transfer Coefficient*Outside Area)

Outside Area given Outer Thermal Resistance

Go Outside Area = 1/(External Convection Heat Transfer Coefficient*Thermal Resistance)

Inner Heat Transfer Coefficient given Inner Thermal Resistance

Go Inside Convection Heat Transfer Coefficient = 1/(Inside Area*Thermal Resistance)

Inside Area given Thermal Resistance for Inner Surface

Go Inside Area = 1/(Inside Convection Heat Transfer Coefficient*Thermal Resistance)

Thermal Resistance for Convection at Inner Surface

Go Thermal Resistance = 1/(Inside Area*Inside Convection Heat Transfer Coefficient)

Correction Length for Thin Rectangular Fin with Non-Adiabatic Tip

Go Correction Length for Thin Rectangular Fin = Length of Fin+(Thickness of Fin/2)

Volumetric Heat Generation in Current Carrying Electrical Conductor

Go Volumetric Heat Generation = (Electric Current Density^2)*Resistivity

Total Thermal Resistance

Go Total Thermal Resistance = 1/(Overall Heat Transfer Coefficient*Area)

Correction Length for Square Fin with Non-Adiabatic Tip

Go Correction Length for Sqaure Fin = Length of Fin+(Width of Fin/4)

< 13 Conduction, Convection and Radiation Calculators

Heat Transfer by Conduction at Base

Go Rate of Conductive Heat Transfer = (Thermal Conductivity*Cross Sectional Area of Fin*Perimeter of the Fin*Convective Heat Transfer Coefficient)^0.5*(Base Temperature-Ambient Temperature)

Heat Exchange by Radiation due to Geometric Arrangement

Go Heat Transfer = Emissivity*Area*[Stefan-BoltZ]*Shape Factor*(Temperature of Surface 1^(4)-Temperature of Surface 2^(4))

Black Bodies Heat Exchange by Radiation

Go Heat Transfer = Emissivity*[Stefan-BoltZ]*Area*(Temperature of Surface 1^(4)-Temperature of Surface 2^(4))

Heat Transfer According to Fourier's Law

Go Heat Flow Through a Body = -(Thermal Conductivity of Material*Surface Area of Heat Flow*Temperature Difference/Thickness)

One Dimensional Heat Flux

Go Heat Flux = -Thermal Conductivity of Fin/Wall Thickness*(Temperature of Wall 2-Temperature of Wall 1)

Newton's Law of Cooling

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)

Non Ideal Body Surface Emittance

Go Real Surface Radiant Surface Emittance = Emissivity*[Stefan-BoltZ]*Surface Temperature^(4)

Thermal Resistance in Conduction

Go Thermal Resistance = (Thickness)/(Thermal Conductivity of Fin*Cross Sectional Area)

Convective Processes Heat Transfer Coefficient

Go Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Recovery temperature)

Thermal Conductivity given Critical Thickness of Insulation for Cylinder

Go Thermal Conductivity of Fin = Critical Thickness of Insulation*Heat Transfer Coefficient at Outer Surface

Critical Thickness of Insulation for Cylinder

Go Critical Thickness of Insulation = Thermal Conductivity of Fin/Heat Transfer Coefficient

Thermal Resistance in Convection Heat Transfer

Go Thermal Resistance = 1/(Exposed Surface Area*Co-efficient of Convective Heat Transfer)

Heat Transfer

Go Heat Flow Rate = Thermal Potential Difference/Thermal Resistance

Newton's Law of Cooling Formula

Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid)
q' = h_transfer*(T_w-T_f)

Define newton's law of cooling?

Newton’s law of cooling describes the rate at which an exposed body changes temperature through radiation which is approximately proportional to the difference between the object’s temperature and its surroundings, provided the difference is small

How to Calculate Newton's Law of Cooling?

Newton's Law of Cooling calculator uses Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid) to calculate the Heat Flux, Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings. Heat Flux is denoted by q' symbol.

How to calculate Newton's Law of Cooling using this online calculator? To use this online calculator for Newton's Law of Cooling, enter Heat Transfer Coefficient (h_transfer), Surface Temperature (T_w) & Temperature of Characteristic Fluid (T_f) and hit the calculate button. Here is how the Newton's Law of Cooling calculation can be explained with given input values -> 396 = 13.2*(305-275).

FAQ

What is Newton's Law of Cooling?

Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings and is represented as q' = h_transfer*(T_w-T_f) or Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid). 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, Surface Temperature is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth & The Temperature of Characteristic Fluid is the temperature of fluid flowing over the surface due to which heat transfer takes place between the surface and the characteristic fluid.

How to calculate Newton's Law of Cooling?

Newton's law of cooling states that the rate of heat loss of a body is directly proportional to the difference in the temperatures between the body and its surroundings is calculated using Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Temperature of Characteristic Fluid). To calculate Newton's Law of Cooling, you need Heat Transfer Coefficient (h_transfer), Surface Temperature (T_w) & Temperature of Characteristic Fluid (T_f). With our tool, you need to enter the respective value for Heat Transfer Coefficient, Surface Temperature & Temperature of Characteristic Fluid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Heat Flux?

In this formula, Heat Flux uses Heat Transfer Coefficient, Surface Temperature & Temperature of Characteristic Fluid. We can use 4 other way(s) to calculate the same, which is/are as follows -

Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Recovery temperature)
Heat Flux = -Thermal Conductivity of Fin/Wall Thickness*(Temperature of Wall 2-Temperature of Wall 1)
Heat Flux = Heat Transfer Coefficient*(Surface Temperature-Recovery temperature)
Heat Flux = -Thermal Conductivity of Fin/Wall Thickness*(Temperature of Wall 2-Temperature of Wall 1)

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