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Thermal Conductivity of Cylindrical Wall given Temperature Difference Formula

GoThermal Conductivity given Critical Thickness of Insulation for Cylinder Formula

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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. Check FAQs

k = \frac{Q \cdot \ln (\frac{r 2}{r 1})}{2 \cdot π \cdot l cyl \cdot (T i - T o)}

k - Thermal Conductivity?Q - Heat Flow Rate?r₂ - Radius of 2nd Cylinder?r₁ - Radius of 1st Cylinder?l_cyl - Length of Cylinder?T_i - Inner Surface Temperature?T_o - Outer Surface Temperature?π - Archimedes' constant?

Thermal Conductivity of Cylindrical Wall given Temperature Difference Example

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Here is how the Thermal Conductivity of Cylindrical Wall given Temperature Difference equation looks like with Values.

Here is how the Thermal Conductivity of Cylindrical Wall given Temperature Difference equation looks like with Units.

Here is how the Thermal Conductivity of Cylindrical Wall given Temperature Difference equation looks like.

1.9977 = \frac{9.27 \cdot \ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 0.4 \cdot (305 - 300)}

1.9977W/(m*K) = \frac{9.27W \cdot \ln (\frac{12m}{0.8m})}{2 \cdot 3.1416 \cdot 0.4m \cdot (305K - 300K)}

1.9977 = \frac{9.27 \cdot \ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 0.4 \cdot (305 - 300)}

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Home » Physics » Mechanical » Heat and Mass Transfer » Thermal Conductivity of Cylindrical Wall given Temperature Difference

Thermal Conductivity of Cylindrical Wall given Temperature Difference Solution

Follow our step by step solution on how to calculate Thermal Conductivity of Cylindrical Wall given Temperature Difference?

FIRST Step Consider the formula

k = \frac{Q \cdot \ln (\frac{r 2}{r 1})}{2 \cdot π \cdot l cyl \cdot (T i - T o)}

Next Step Substitute values of Variables

∴

k = \frac{9.27W \cdot \ln (\frac{12m}{0.8m})}{2 \cdot π \cdot 0.4m \cdot (305K - 300K)}

Next Step Substitute values of Constants

∴

k = \frac{9.27W \cdot \ln (\frac{12m}{0.8m})}{2 \cdot 3.1416 \cdot 0.4m \cdot (305K - 300K)}

Next Step Prepare to Evaluate

∴

k = \frac{9.27 \cdot \ln (\frac{12}{0.8})}{2 \cdot 3.1416 \cdot 0.4 \cdot (305 - 300)}

Next Step Evaluate

∴

k = 1.99768303312115W/(m*K)

LAST Step Rounding Answer

∴

k = 1.9977W/(m*K)

Thermal Conductivity of Cylindrical Wall given Temperature Difference Formula Elements

Variables

Constants

Functions

Thermal Conductivity

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Heat Flow Rate

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.

Symbol: Q

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Radius of 2nd Cylinder

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.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Radius of 1st Cylinder

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.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Length of Cylinder

Length of Cylinder is the vertical height of the Cylinder.

Symbol: l_cyl

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Inner Surface Temperature

Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.

Symbol: T_i

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Outer Surface Temperature

Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

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 Formula and 100+ more formulas!

Verified by Vinay Mishra

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

Vinay Mishra has verified this Formula and 100+ more formulas!

Other Formulas to find Thermal Conductivity

Go Thermal Conductivity given Critical Thickness of Insulation for Cylinder

k = r c \cdot h o

Other formulas in Conduction in Cylinder category

Go Total Thermal Resistance of 2 Cylindrical Resistances Connected in Series

R th = \frac{\ln (\frac{r 2}{r 1})}{2 \cdot π \cdot k 1 \cdot l cyl} + \frac{\ln (\frac{r 3}{r 2})}{2 \cdot π \cdot k 2 \cdot l cyl}

Go Total Thermal Resistance of 3 Cylindrical Resistances Connected in Series

R th = \frac{\ln (\frac{r 2}{r 1})}{2 \cdot π \cdot k 1 \cdot l cyl} + \frac{\ln (\frac{r 3}{r 2})}{2 \cdot π \cdot k 2 \cdot l cyl} + \frac{\ln (\frac{r 4}{r 3})}{2 \cdot π \cdot k 3 \cdot l cyl}

How to Evaluate Thermal Conductivity of Cylindrical Wall given Temperature Difference?

Thermal Conductivity of Cylindrical Wall given Temperature Difference evaluator uses Thermal Conductivity = (Heat Flow Rate*ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Length of Cylinder*(Inner Surface Temperature-Outer Surface Temperature)) to evaluate the Thermal Conductivity, The Thermal Conductivity of Cylindrical Wall given Temperature Difference formula is defined as the thermal conductivity of the material of the cylindrical wall required to maintain inner and outer surfaces at given temperatures when the heat flows through it in the radial direction. Thermal Conductivity is denoted by k symbol.

How to evaluate Thermal Conductivity of Cylindrical Wall given Temperature Difference using this online evaluator? To use this online evaluator for Thermal Conductivity of Cylindrical Wall given Temperature Difference, enter Heat Flow Rate (Q), Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Length of Cylinder (l_cyl), Inner Surface Temperature (T_i) & Outer Surface Temperature (T_o) and hit the calculate button.

FAQs on Thermal Conductivity of Cylindrical Wall given Temperature Difference

What is the formula to find Thermal Conductivity of Cylindrical Wall given Temperature Difference?

The formula of Thermal Conductivity of Cylindrical Wall given Temperature Difference is expressed as Thermal Conductivity = (Heat Flow Rate*ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Length of Cylinder*(Inner Surface Temperature-Outer Surface Temperature)). Here is an example- 11.41533 = (9.27*ln(12/0.8))/(2*pi*0.4*(305-300)).

How to calculate Thermal Conductivity of Cylindrical Wall given Temperature Difference?

With Heat Flow Rate (Q), Radius of 2nd Cylinder (r₂), Radius of 1st Cylinder (r₁), Length of Cylinder (l_cyl), Inner Surface Temperature (T_i) & Outer Surface Temperature (T_o) we can find Thermal Conductivity of Cylindrical Wall given Temperature Difference using the formula - Thermal Conductivity = (Heat Flow Rate*ln(Radius of 2nd Cylinder/Radius of 1st Cylinder))/(2*pi*Length of Cylinder*(Inner Surface Temperature-Outer Surface Temperature)). This formula also uses Archimedes' constant and Natural Logarithm (ln) function(s).

What are the other ways to Calculate Thermal Conductivity?

Here are the different ways to Calculate Thermal Conductivity-

Thermal Conductivity=Critical Thickness of Insulation*Heat Transfer Coefficient at Outer Surface

Can the Thermal Conductivity of Cylindrical Wall given Temperature Difference be negative?

No, the Thermal Conductivity of Cylindrical Wall given Temperature Difference, measured in Thermal Conductivity cannot be negative.

Which unit is used to measure Thermal Conductivity of Cylindrical Wall given Temperature Difference?

Thermal Conductivity of Cylindrical Wall given Temperature Difference is usually measured using the Watt per Meter per K[W/(m*K)] for Thermal Conductivity. Kilowatt per Meter per K[W/(m*K)], Calorie (IT) per Second per Centimeter per °C[W/(m*K)], Kilocalorie (th) per Hour per Meter per °C[W/(m*K)] are the few other units in which Thermal Conductivity of Cylindrical Wall given Temperature Difference can be measured.

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Thermal Conductivity of Cylindrical Wall given Temperature Difference Formula

​GoThermal Conductivity given Critical Thickness of Insulation for Cylinder Formula

Thermal Conductivity of Cylindrical Wall given Temperature Difference Example

Thermal Conductivity of Cylindrical Wall given Temperature Difference Solution

Thermal Conductivity of Cylindrical Wall given Temperature Difference Formula Elements

Credits

Other Formulas to find Thermal Conductivity

Other formulas in Conduction in Cylinder category

How to Evaluate Thermal Conductivity of Cylindrical Wall given Temperature Difference?

FAQs on Thermal Conductivity of Cylindrical Wall given Temperature Difference

Variable Name

GoThermal Conductivity given Critical Thickness of Insulation for Cylinder Formula