Inner Surface Temperature of Cylindrical Wall in Conduction Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder)
Ti = To+(Q*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
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).
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.
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
Outer Surface Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Heat Flow Rate: 125 Watt --> 125 Watt 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
Ti = To+(Q*ln(r2/r1))/(2*pi*k*lcyl) --> 300+(125*ln(12/0.8))/(2*pi*10.18*0.4)
Evaluating ... ...
Ti = 313.230586187574
STEP 3: Convert Result to Output's Unit
313.230586187574 Kelvin --> No Conversion Required
FINAL ANSWER
313.230586187574 313.2306 Kelvin <-- Inner Surface Temperature
(Calculation completed in 00.020 seconds)

Credits

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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)

Inner Surface Temperature of Cylindrical Wall in Conduction Formula

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

What is temperature?

Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy when a body is in contact with another that is colder or hotter.

How to Calculate Inner Surface Temperature of Cylindrical Wall in Conduction?

Inner Surface Temperature of Cylindrical Wall in Conduction calculator uses Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder) to calculate the Inner Surface Temperature, The Inner Surface Temperature of Cylindrical Wall in Conduction formula is defined as the temperature at the inner surface of the cylindrical wall for a given heat flow rate, outer surface temperature, cylinder length, and thermal conductivity. Inner Surface Temperature is denoted by Ti symbol.

How to calculate Inner Surface Temperature of Cylindrical Wall in Conduction using this online calculator? To use this online calculator for Inner Surface Temperature of Cylindrical Wall in Conduction, enter Outer Surface Temperature (To), Heat Flow Rate (Q), Radius 2 (r2), Radius 1 (r1), Thermal Conductivity (k) & Length of Cylinder (lcyl) and hit the calculate button. Here is how the Inner Surface Temperature of Cylindrical Wall in Conduction calculation can be explained with given input values -> 313.2306 = 300+(125*ln(12/0.8))/(2*pi*10.18*0.4).

FAQ

What is Inner Surface Temperature of Cylindrical Wall in Conduction?
The Inner Surface Temperature of Cylindrical Wall in Conduction formula is defined as the temperature at the inner surface of the cylindrical wall for a given heat flow rate, outer surface temperature, cylinder length, and thermal conductivity and is represented as Ti = To+(Q*ln(r2/r1))/(2*pi*k*lcyl) or Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder). Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc), 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, 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 Inner Surface Temperature of Cylindrical Wall in Conduction?
The Inner Surface Temperature of Cylindrical Wall in Conduction formula is defined as the temperature at the inner surface of the cylindrical wall for a given heat flow rate, outer surface temperature, cylinder length, and thermal conductivity is calculated using Inner Surface Temperature = Outer Surface Temperature+(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder). To calculate Inner Surface Temperature of Cylindrical Wall in Conduction, you need Outer Surface Temperature (To), Heat Flow Rate (Q), Radius 2 (r2), Radius 1 (r1), Thermal Conductivity (k) & Length of Cylinder (lcyl). With our tool, you need to enter the respective value for Outer Surface Temperature, Heat Flow Rate, 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.
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