Heat Flow Rate through Cylindrical Composite Wall of 2 Layers Calculator

✖Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.ⓘ Inner Surface Temperature [T_i]			+10% -10%
✖Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).ⓘ Outer Surface Temperature [T_o]			+10% -10%
✖Radius 2 is the radius of the second concentric circle or circle.ⓘ Radius 2 [r₂]			+10% -10%
✖Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle.ⓘ Radius 1 [r₁]			+10% -10%
✖Thermal Conductivity 1 is the thermal conductivity of the first body.ⓘ Thermal Conductivity 1 [k₁]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l_cyl]			+10% -10%
✖Radius 3 is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle.ⓘ Radius 3 [r₃]			+10% -10%
✖Thermal Conductivity 2 is the thermal conductivity of the second body.ⓘ Thermal Conductivity 2 [k₂]			+10% -10%

✖Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.ⓘ Heat Flow Rate through Cylindrical Composite Wall of 2 Layers [Q]

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Heat Flow Rate through Cylindrical Composite Wall of 2 Layers

Formula

`"Q" = ("T"_{"i"}-"T"_{"o"})/((ln("r"_{"2"}/"r"_{"1"}))/(2*pi*"k"_{"1"}*"l"_{"cyl"})+(ln("r"_{"3"}/"r"_{"2"}))/(2*pi*"k"_{"2"}*"l"_{"cyl"}))`

Example

`"9.276513W"=("305K"-"300K")/((ln("12m"/"0.8m"))/(2*pi*"1.6W/(m*K)"*"0.4m")+(ln("8m"/"12m"))/(2*pi*"1.2W/(m*K)"*"0.4m"))`

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Heat Flow Rate through Cylindrical Composite Wall of 2 Layers Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder))
Q = (T_i-T_o)/((ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl))
This formula uses 1 Constants, 1 Functions, 9 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Heat Flow Rate - (Measured in Watt) - Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.
Inner Surface Temperature - (Measured in Kelvin) - Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.
Outer Surface Temperature - (Measured in Kelvin) - Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).
Radius 2 - (Measured in Meter) - Radius 2 is the radius of the second concentric circle or circle.
Radius 1 - (Measured in Meter) - Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle.
Thermal Conductivity 1 - (Measured in Watt per Meter per K) - Thermal Conductivity 1 is the thermal conductivity of the first body.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Radius 3 - (Measured in Meter) - Radius 3 is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle.
Thermal Conductivity 2 - (Measured in Watt per Meter per K) - Thermal Conductivity 2 is the thermal conductivity of the second body.

STEP 1: Convert Input(s) to Base Unit

Inner Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required
Outer Surface Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Radius 2: 12 Meter --> 12 Meter No Conversion Required
Radius 1: 0.8 Meter --> 0.8 Meter No Conversion Required
Thermal Conductivity 1: 1.6 Watt per Meter per K --> 1.6 Watt per Meter per K No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
Radius 3: 8 Meter --> 8 Meter No Conversion Required
Thermal Conductivity 2: 1.2 Watt per Meter per K --> 1.2 Watt per Meter per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = (T_i-T_o)/((ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)) --> (305-300)/((ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4))

Evaluating ... ...

Q = 9.27651294602508

STEP 3: Convert Result to Output's Unit

9.27651294602508 Watt --> No Conversion Required

FINAL ANSWER

9.27651294602508 ≈ 9.276513 Watt <-- Heat Flow Rate

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Conduction in Cylinder » Heat Flow Rate through Cylindrical Composite Wall of 2 Layers

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Created by Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

Sai Venkata Phanindra Chary Arendra has created this Calculator and 100+ more calculators!

Verified by Vinay Mishra

Indian Institute for Aeronautical Engineering and Information Technology (IIAEIT), Pune

Vinay Mishra has verified this Calculator and 100+ more calculators!

< 14 Conduction in Cylinder Calculators

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers

Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius 4/Radius 3))/(2*pi*Thermal Conductivity 3*Length of Cylinder))

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

Go Thermal Resistance = (ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius 4/Radius 3))/(2*pi*Thermal Conductivity 3*Length of Cylinder)

Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides

Go Thermal Resistance = 1/(2*pi*Radius 1*Length of Cylinder*Inside Convection Heat Transfer Coefficient)+(ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)+1/(2*pi*Radius 2*Length of Cylinder*External Convection Heat Transfer Coefficient)

Heat Flow Rate through Cylindrical Composite Wall of 2 Layers

Outer Surface Temperature of Cylindrical Composite Wall of 2 Layers

Go Outer Surface Temperature = Inner Surface Temperature-Heat Flow Rate*((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder))

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

Go Thermal Resistance = (ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)

Heat Flow Rate through Cylindrical Wall

Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder))

Thermal Conductivity of Cylindrical Wall given Temperature Difference

Go Thermal Conductivity = (Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Length of Cylinder*(Inner Surface Temperature-Outer Surface Temperature))

Length of Cylindrical Wall for given Heat Flow Rate

Go Length of Cylinder = (Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*(Inner Surface Temperature-Outer Surface Temperature))

Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate

Go Outer Surface Temperature = Inner Surface Temperature-(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)

Inner Surface Temperature of Cylindrical Wall in Conduction

Go Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)

Thickness of Cylindrical Wall to Maintain given Temperature Difference

Go Thickness = Radius 1*(e^(((Inner Surface Temperature-Outer Surface Temperature)*2*pi*Thermal Conductivity*Length of Cylinder)/Heat Flow Rate)-1)

Thermal Resistance for Radial Heat Conduction in Cylinders

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

Convection Resistance for Cylindrical Layer

Go Thermal Resistance = 1/(Convection heat transfer*2*pi*Cylinder Radius*Length of Cylinder)

Heat Flow Rate through Cylindrical Composite Wall of 2 Layers Formula

What is Fourier's law of heat transfer?

The law of heat conduction, also known as Fourier's law, states that the rate of heat transfer through a material is proportional to the negative gradient in the temperature and to the area, at right angles to that gradient, through which the heat flows.

How to Calculate Heat Flow Rate through Cylindrical Composite Wall of 2 Layers?

Heat Flow Rate through Cylindrical Composite Wall of 2 Layers calculator uses Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)) to calculate the Heat Flow Rate, The Heat flow rate through cylindrical composite wall of 2 layers formula is defined as the rate of heat flow through a cylindrical composite wall of 2 layers in when the inner and outer surface temperatures, thermal conductivities, length of the cylinder, and radius of each layer are known. Heat Flow Rate is denoted by Q symbol.

How to calculate Heat Flow Rate through Cylindrical Composite Wall of 2 Layers using this online calculator? To use this online calculator for Heat Flow Rate through Cylindrical Composite Wall of 2 Layers, enter Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius 2 (r₂), Radius 1 (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius 3 (r₃) & Thermal Conductivity 2 (k₂) and hit the calculate button. Here is how the Heat Flow Rate through Cylindrical Composite Wall of 2 Layers calculation can be explained with given input values -> 9.276513 = (305-300)/((ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4)).

FAQ

What is Heat Flow Rate through Cylindrical Composite Wall of 2 Layers?

The Heat flow rate through cylindrical composite wall of 2 layers formula is defined as the rate of heat flow through a cylindrical composite wall of 2 layers in when the inner and outer surface temperatures, thermal conductivities, length of the cylinder, and radius of each layer are known and is represented as Q = (T_i-T_o)/((ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)) or Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)). Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc, Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc), Radius 2 is the radius of the second concentric circle or circle, Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle, Thermal Conductivity 1 is the thermal conductivity of the first body, Length of Cylinder is the vertical height of the Cylinder, Radius 3 is the distance from the center of the concentric circles to any point on the third concentric circle or radius of the third circle & Thermal Conductivity 2 is the thermal conductivity of the second body.

How to calculate Heat Flow Rate through Cylindrical Composite Wall of 2 Layers?

The Heat flow rate through cylindrical composite wall of 2 layers formula is defined as the rate of heat flow through a cylindrical composite wall of 2 layers in when the inner and outer surface temperatures, thermal conductivities, length of the cylinder, and radius of each layer are known is calculated using Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)). To calculate Heat Flow Rate through Cylindrical Composite Wall of 2 Layers, you need Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius 2 (r₂), Radius 1 (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius 3 (r₃) & Thermal Conductivity 2 (k₂). With our tool, you need to enter the respective value for Inner Surface Temperature, Outer Surface Temperature, Radius 2, Radius 1, Thermal Conductivity 1, Length of Cylinder, Radius 3 & Thermal Conductivity 2 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 Flow Rate?

In this formula, Heat Flow Rate uses Inner Surface Temperature, Outer Surface Temperature, Radius 2, Radius 1, Thermal Conductivity 1, Length of Cylinder, Radius 3 & Thermal Conductivity 2. We can use 2 other way(s) to calculate the same, which is/are as follows -

Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder))
Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius 4/Radius 3))/(2*pi*Thermal Conductivity 3*Length of Cylinder))

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