Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate 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%
✖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 [Q]			+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 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.ⓘ Thermal Conductivity [k]			+10% -10%
✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [l_cyl]			+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 of Cylindrical Wall given Heat Flow Rate [T_o]

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Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate

Formula

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

Example

`"291.7694K"="305K"-("125W"*ln("12m"/"0.8m"))/(2*pi*"10.18W/(m*K)"*"0.4m")`

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Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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).
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.
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

Inner Surface Temperature: 305 Kelvin --> 305 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

T_o = T_i-(Q*ln(r₂/r₁))/(2*pi*k*l_cyl) --> 305-(125*ln(12/0.8))/(2*pi*10.18*0.4)

Evaluating ... ...

T_o = 291.769413812426

STEP 3: Convert Result to Output's Unit

291.769413812426 Kelvin --> No Conversion Required

FINAL ANSWER

291.769413812426 ≈ 291.7694 Kelvin <-- Outer Surface Temperature

(Calculation completed in 00.004 seconds)

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Credits

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)

Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate Formula

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

What happens when the inner and outer surface temperatures are same?

Same inner and outer surface temperatures at steady-state indicate that there is no thermal potential difference and hence there will no heat transfer.

How to Calculate Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate?

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

How to calculate Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate using this online calculator? To use this online calculator for Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate, enter Inner Surface Temperature (T_i), Heat Flow Rate (Q), Radius 2 (r₂), Radius 1 (r₁), Thermal Conductivity (k) & Length of Cylinder (l_cyl) and hit the calculate button. Here is how the Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate calculation can be explained with given input values -> 291.7694 = 305-(125*ln(12/0.8))/(2*pi*10.18*0.4).

FAQ

What is Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate?

The Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate formula is defined as the temperature at the outer surface of the cylindrical wall for a given heat flow rate through it in the radial direction, inner wall temperature, inner and outer radii, and length of the cylinder and is represented as T_o = T_i-(Q*ln(r₂/r₁))/(2*pi*k*l_cyl) or Outer Surface Temperature = Inner Surface Temperature-(Heat Flow Rate*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, 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 Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate?

The Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate formula is defined as the temperature at the outer surface of the cylindrical wall for a given heat flow rate through it in the radial direction, inner wall temperature, inner and outer radii, and length of the cylinder is calculated using Outer Surface Temperature = Inner Surface Temperature-(Heat Flow Rate*ln(Radius 2/Radius 1))/(2*pi*Thermal Conductivity*Length of Cylinder). To calculate Outer Surface Temperature of Cylindrical Wall given Heat Flow Rate, you need Inner Surface Temperature (T_i), Heat Flow Rate (Q), Radius 2 (r₂), Radius 1 (r₁), Thermal Conductivity (k) & Length of Cylinder (l_cyl). With our tool, you need to enter the respective value for Inner 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.

How many ways are there to calculate Outer Surface Temperature?

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

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))

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