Heat Flow Rate through Cylindrical Composite Wall of 3 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 of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle.ⓘ Radius of 2nd Cylinder [r₂]			+10% -10%
✖Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series.ⓘ Radius of 1st Cylinder [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 of 3rd Cylinder 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 of 3rd Cylinder [r₃]			+10% -10%
✖Thermal Conductivity 2 is the thermal conductivity of the second body.ⓘ Thermal Conductivity 2 [k₂]			+10% -10%
✖Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle.ⓘ Radius of 4th Cylinder [r₄]			+10% -10%
✖Thermal Conductivity 3 is the thermal conductivity of the third body.ⓘ Thermal Conductivity 3 [k₃]			+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 3 Layers [Q]

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Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius of 4th Cylinder/Radius of 3rd Cylinder))/(2*pi*Thermal Conductivity 3*Length of Cylinder))
Q = (T_i-T_o)/((ln(r₂/r₁))/(2*pi*k₁*l_cyl)+(ln(r₃/r₂))/(2*pi*k₂*l_cyl)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl))
This formula uses 1 Constants, 1 Functions, 11 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 of 2nd Cylinder - (Measured in Meter) - Radius of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle.
Radius of 1st Cylinder - (Measured in Meter) - Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series.
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 of 3rd Cylinder - (Measured in Meter) - Radius of 3rd Cylinder 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.
Radius of 4th Cylinder - (Measured in Meter) - Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle.
Thermal Conductivity 3 - (Measured in Watt per Meter per K) - Thermal Conductivity 3 is the thermal conductivity of the third 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 of 2nd Cylinder: 12 Meter --> 12 Meter No Conversion Required
Radius of 1st Cylinder: 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 of 3rd Cylinder: 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
Radius of 4th Cylinder: 14 Meter --> 14 Meter No Conversion Required
Thermal Conductivity 3: 4 Watt per Meter per K --> 4 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)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl)) --> (305-300)/((ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4)+(ln(14/8))/(2*pi*4*0.4))

Evaluating ... ...

Q = 8.4081427045788

STEP 3: Convert Result to Output's Unit

8.4081427045788 Watt --> No Conversion Required

FINAL ANSWER

8.4081427045788 ≈ 8.408143 Watt <-- Heat Flow Rate

(Calculation completed in 00.020 seconds)

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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!

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

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< Conduction in Cylinder Calculators

Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

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

Total Thermal Resistance of Cylindrical Wall with Convection on Both Sides

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

Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

Thermal Resistance for Radial Heat Conduction in Cylinders

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

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers Formula

LaTeX Go

What is heat conduction?

Heat conduction is the transfer of internal thermal energy by the collisions of microscopic particles and the movement of electrons within a body. The microscopic particles in the heat conduction can be molecules, atoms, and electrons.

How to Calculate Heat Flow Rate through Cylindrical Composite Wall of 3 Layers?

Heat Flow Rate through Cylindrical Composite Wall of 3 Layers calculator uses Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius of 4th Cylinder/Radius of 3rd Cylinder))/(2*pi*Thermal Conductivity 3*Length of Cylinder)) to calculate the Heat Flow Rate, The Heat flow rate through cylindrical composite wall of 3 layers formula is the rate of heat flow through a cylindrical composite wall of 3 layers when the inner and outer surface temperatures, the radius of layers, length of the cylinders, and thermal conductivities are known. Heat Flow Rate is denoted by Q symbol.

How to calculate Heat Flow Rate through Cylindrical Composite Wall of 3 Layers using this online calculator? To use this online calculator for Heat Flow Rate through Cylindrical Composite Wall of 3 Layers, enter Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius of 3rd Cylinder (r₃), Thermal Conductivity 2 (k₂), Radius of 4th Cylinder (r₄) & Thermal Conductivity 3 (k₃) and hit the calculate button. Here is how the Heat Flow Rate through Cylindrical Composite Wall of 3 Layers calculation can be explained with given input values -> 1.471425 = (305-300)/((ln(12/0.8))/(2*pi*1.6*0.4)+(ln(8/12))/(2*pi*1.2*0.4)+(ln(14/8))/(2*pi*4*0.4)).

FAQ

What is Heat Flow Rate through Cylindrical Composite Wall of 3 Layers?

The Heat flow rate through cylindrical composite wall of 3 layers formula is the rate of heat flow through a cylindrical composite wall of 3 layers when the inner and outer surface temperatures, the radius of layers, length of the cylinders, and thermal conductivities 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)+(ln(r₄/r₃))/(2*pi*k₃*l_cyl)) or Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius of 4th Cylinder/Radius of 3rd Cylinder))/(2*pi*Thermal Conductivity 3*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 of 2nd Cylinder is the distance from the center of the concentric circles to any point on the Second concentric circle or radius of the third circle, Radius of 1st Cylinder is the distance from the center of the concentric circles to any point on the first/smallest concentric circle for the first cylinder in the series, Thermal Conductivity 1 is the thermal conductivity of the first body, Length of Cylinder is the vertical height of the Cylinder, Radius of 3rd Cylinder 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, Radius of 4th Cylinder is the distance from the center of the concentric circles to any point on the fourth concentric circle or radius of the third circle & Thermal Conductivity 3 is the thermal conductivity of the third body.

How to calculate Heat Flow Rate through Cylindrical Composite Wall of 3 Layers?

The Heat flow rate through cylindrical composite wall of 3 layers formula is the rate of heat flow through a cylindrical composite wall of 3 layers when the inner and outer surface temperatures, the radius of layers, length of the cylinders, and thermal conductivities are known is calculated using Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder)+(ln(Radius of 4th Cylinder/Radius of 3rd Cylinder))/(2*pi*Thermal Conductivity 3*Length of Cylinder)). To calculate Heat Flow Rate through Cylindrical Composite Wall of 3 Layers, you need Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Thermal Conductivity 1 (k₁), Length of Cylinder (l_cyl), Radius of 3rd Cylinder (r₃), Thermal Conductivity 2 (k₂), Radius of 4th Cylinder (r₄) & Thermal Conductivity 3 (k₃). With our tool, you need to enter the respective value for Inner Surface Temperature, Outer Surface Temperature, Radius of 2nd Cylinder, Radius of 1st Cylinder, Thermal Conductivity 1, Length of Cylinder, Radius of 3rd Cylinder, Thermal Conductivity 2, Radius of 4th Cylinder & Thermal Conductivity 3 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 of 2nd Cylinder, Radius of 1st Cylinder, Thermal Conductivity 1, Length of Cylinder, Radius of 3rd Cylinder, Thermal Conductivity 2, Radius of 4th Cylinder & Thermal Conductivity 3. 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 of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity*Length of Cylinder))
Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Thermal Conductivity 1*Length of Cylinder)+(ln(Radius of 3rd Cylinder/Radius of 2nd Cylinder))/(2*pi*Thermal Conductivity 2*Length of Cylinder))

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