Heat Flow Rate through Cylindrical Wall 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*Length of Cylinder))
Q = (Ti-To)/((ln(r2/r1))/(2*pi*k*lcyl))
This formula uses 1 Constants, 1 Functions, 7 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 - (Measured in Watt per Meter per K) - Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
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: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Length of Cylinder: 0.4 Meter --> 0.4 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Q = (Ti-To)/((ln(r2/r1))/(2*pi*k*lcyl)) --> (305-300)/((ln(12/0.8))/(2*pi*10.18*0.4))
Evaluating ... ...
Q = 47.2390256288857
STEP 3: Convert Result to Output's Unit
47.2390256288857 Watt --> No Conversion Required
FINAL ANSWER
47.2390256288857 โ‰ˆ 47.23903 Watt <-- Heat Flow Rate
(Calculation completed in 00.004 seconds)

Credits

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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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
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))
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 Wall Formula

Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder))
Q = (Ti-To)/((ln(r2/r1))/(2*pi*k*lcyl))

What is heat flow rate?

The rate of heat flow 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.

How to Calculate Heat Flow Rate through Cylindrical Wall?

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

How to calculate Heat Flow Rate through Cylindrical Wall using this online calculator? To use this online calculator for Heat Flow Rate through Cylindrical Wall, enter Inner Surface Temperature (Ti), Outer Surface Temperature (To), Radius 2 (r2), Radius 1 (r1), Thermal Conductivity (k) & Length of Cylinder (lcyl) and hit the calculate button. Here is how the Heat Flow Rate through Cylindrical Wall calculation can be explained with given input values -> 47.23903 = (305-300)/((ln(12/0.8))/(2*pi*10.18*0.4)).

FAQ

What is Heat Flow Rate through Cylindrical Wall?
The Heat flow rate through cylindrical wall formula is defined as the rate of heat flow through a cylindrical wall in the radial direction when inner and outer surface temperatures, length of the cylinder, inner and outer radii and thermal conductivity are known and is represented as Q = (Ti-To)/((ln(r2/r1))/(2*pi*k*lcyl)) or Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*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 is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance & Length of Cylinder is the vertical height of the Cylinder.
How to calculate Heat Flow Rate through Cylindrical Wall?
The Heat flow rate through cylindrical wall formula is defined as the rate of heat flow through a cylindrical wall in the radial direction when inner and outer surface temperatures, length of the cylinder, inner and outer radii and thermal conductivity are known is calculated using Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)). To calculate Heat Flow Rate through Cylindrical Wall, you need Inner Surface Temperature (Ti), Outer Surface Temperature (To), Radius 2 (r2), Radius 1 (r1), Thermal Conductivity (k) & Length of Cylinder (lcyl). With our tool, you need to enter the respective value for Inner Surface Temperature, Outer Surface Temperature, Radius 2, Radius 1, Thermal Conductivity & Length of Cylinder 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 & Length of Cylinder. 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 1*Length of Cylinder)+(ln(Radius 3/Radius 2))/(2*pi*Thermal Conductivity 2*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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