Eccentric Isothermal Cylinder in Cylinder of Same Length Calculator

✖Length of Cylinder is the vertical height of the Cylinder.ⓘ Length of Cylinder [L_c]			+10% -10%
✖Diameter of Cylinder 1 is the diameter of the first cylinder.ⓘ Diameter of Cylinder 1 [D₁]			+10% -10%
✖Diameter of Cylinder 2 is the diameter of the second cylinder.ⓘ Diameter of Cylinder 2 [D₂]			+10% -10%
✖Eccentric Distance between Objects is the radial length from the center of one object which is at some distance from the center of another object.ⓘ Eccentric Distance Between Objects [z]			+10% -10%

✖Conduction shape factor is defined as the value used to determine the heat transfer rate for the configurations which are very complex and require high calculation time.ⓘ Eccentric Isothermal Cylinder in Cylinder of Same Length [S]

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Formula

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Eccentric Isothermal Cylinder in Cylinder of Same Length

Formula

S = \frac{2 \cdot π \cdot L c}{a} \cosh (\frac{{D 1}^{2} + {D 2}^{2} - 4 \cdot z^{2}}{2 \cdot D 1 \cdot D 2})

Example

28 m = \frac{2 \cdot π \cdot 4 m}{a} \cosh (\frac{{5.1 m}^{2} + {13.739222 m}^{2} - 4 \cdot {1.89 m}^{2}}{2 \cdot 5.1 m \cdot 13.739222 m})

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Eccentric Isothermal Cylinder in Cylinder of Same Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Conduction Shape Factor = (2*pi*Length of Cylinder)/acosh((Diameter of Cylinder 1^2+Diameter of Cylinder 2^2-4*Eccentric Distance Between Objects^2)/(2*Diameter of Cylinder 1*Diameter of Cylinder 2))
S = (2*pi*L_c)/acosh((D₁^2+D₂^2-4*z^2)/(2*D₁*D₂))
This formula uses 1 Constants, 2 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cosh - The hyperbolic cosine function is a mathematical function that is defined as the ratio of the sum of the exponential functions of x and negative x to 2., cosh(Number)
acosh - Hyperbolic cosine function, is a function that takes a real number as an input and returns the angle whose hyperbolic cosine is that number., acosh(Number)

Variables Used

Conduction Shape Factor - (Measured in Meter) - Conduction shape factor is defined as the value used to determine the heat transfer rate for the configurations which are very complex and require high calculation time.
Length of Cylinder - (Measured in Meter) - Length of Cylinder is the vertical height of the Cylinder.
Diameter of Cylinder 1 - (Measured in Meter) - Diameter of Cylinder 1 is the diameter of the first cylinder.
Diameter of Cylinder 2 - (Measured in Meter) - Diameter of Cylinder 2 is the diameter of the second cylinder.
Eccentric Distance Between Objects - (Measured in Meter) - Eccentric Distance between Objects is the radial length from the center of one object which is at some distance from the center of another object.

STEP 1: Convert Input(s) to Base Unit

Length of Cylinder: 4 Meter --> 4 Meter No Conversion Required
Diameter of Cylinder 1: 5.1 Meter --> 5.1 Meter No Conversion Required
Diameter of Cylinder 2: 13.739222 Meter --> 13.739222 Meter No Conversion Required
Eccentric Distance Between Objects: 1.89 Meter --> 1.89 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S = (2*pi*L_c)/acosh((D₁^2+D₂^2-4*z^2)/(2*D₁*D₂)) --> (2*pi*4)/acosh((5.1^2+13.739222^2-4*1.89^2)/(2*5.1*13.739222))

Evaluating ... ...

S = 28.0000042693262

STEP 3: Convert Result to Output's Unit

28.0000042693262 Meter --> No Conversion Required

FINAL ANSWER

28.0000042693262 ≈ 28 Meter <-- Conduction Shape Factor

(Calculation completed in 00.020 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Conduction Shape Factors for Different Configurations » Mechanical » Finite Medium » Eccentric Isothermal Cylinder in Cylinder of Same Length

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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National Institute Of Technology (NIT), Hamirpur

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Eccentric Isothermal Cylinder in Cylinder of Same Length

Go Conduction Shape Factor = (2*pi*Length of Cylinder)/acosh((Diameter of Cylinder 1^2+Diameter of Cylinder 2^2-4*Eccentric Distance Between Objects^2)/(2*Diameter of Cylinder 1*Diameter of Cylinder 2))

Long Hollow Cylindrical Layer

Go Conduction Shape Factor = (2*pi*Length of Cylinder)/(ln(Outer Radius of Cylinder/Inner Radius of Cylinder))

Isothermal Cylinder at Center of Square Solid Bar of Same Length

Go Conduction Shape Factor = (2*pi*Length of Cylinder)/ln((1.08*Width of Square Bar)/Diameter of Cylinder)

Large Plane Wall

Go Conduction Shape Factor = Cross-Sectional Area/Thickness

Eccentric Isothermal Cylinder in Cylinder of Same Length Formula

Why we use conduction shape factor?

Conduction shape factors are generally used when the geometries and configurations of the system are complex which makes the calculation of heat transfer very difficult.

How to Calculate Eccentric Isothermal Cylinder in Cylinder of Same Length?

Eccentric Isothermal Cylinder in Cylinder of Same Length calculator uses Conduction Shape Factor = (2*pi*Length of Cylinder)/acosh((Diameter of Cylinder 1^2+Diameter of Cylinder 2^2-4*Eccentric Distance Between Objects^2)/(2*Diameter of Cylinder 1*Diameter of Cylinder 2)) to calculate the Conduction Shape Factor, Eccentric Isothermal Cylinder in Cylinder of Same Length formula is defined as a mathematical representation that determines the surface area of a cylinder within another cylinder of the same length, considering the eccentricity and isothermal properties of the cylinders. Conduction Shape Factor is denoted by S symbol.

How to calculate Eccentric Isothermal Cylinder in Cylinder of Same Length using this online calculator? To use this online calculator for Eccentric Isothermal Cylinder in Cylinder of Same Length, enter Length of Cylinder (L_c), Diameter of Cylinder 1 (D₁), Diameter of Cylinder 2 (D₂) & Eccentric Distance Between Objects (z) and hit the calculate button. Here is how the Eccentric Isothermal Cylinder in Cylinder of Same Length calculation can be explained with given input values -> 58.01586 = (2*pi*4)/acosh((5.1^2+13.739222^2-4*1.89^2)/(2*5.1*13.739222)).

FAQ

What is Eccentric Isothermal Cylinder in Cylinder of Same Length?

Eccentric Isothermal Cylinder in Cylinder of Same Length formula is defined as a mathematical representation that determines the surface area of a cylinder within another cylinder of the same length, considering the eccentricity and isothermal properties of the cylinders and is represented as S = (2*pi*L_c)/acosh((D₁^2+D₂^2-4*z^2)/(2*D₁*D₂)) or Conduction Shape Factor = (2*pi*Length of Cylinder)/acosh((Diameter of Cylinder 1^2+Diameter of Cylinder 2^2-4*Eccentric Distance Between Objects^2)/(2*Diameter of Cylinder 1*Diameter of Cylinder 2)). Length of Cylinder is the vertical height of the Cylinder, Diameter of Cylinder 1 is the diameter of the first cylinder, Diameter of Cylinder 2 is the diameter of the second cylinder & Eccentric Distance between Objects is the radial length from the center of one object which is at some distance from the center of another object.

How to calculate Eccentric Isothermal Cylinder in Cylinder of Same Length?

Eccentric Isothermal Cylinder in Cylinder of Same Length formula is defined as a mathematical representation that determines the surface area of a cylinder within another cylinder of the same length, considering the eccentricity and isothermal properties of the cylinders is calculated using Conduction Shape Factor = (2*pi*Length of Cylinder)/acosh((Diameter of Cylinder 1^2+Diameter of Cylinder 2^2-4*Eccentric Distance Between Objects^2)/(2*Diameter of Cylinder 1*Diameter of Cylinder 2)). To calculate Eccentric Isothermal Cylinder in Cylinder of Same Length, you need Length of Cylinder (L_c), Diameter of Cylinder 1 (D₁), Diameter of Cylinder 2 (D₂) & Eccentric Distance Between Objects (z). With our tool, you need to enter the respective value for Length of Cylinder, Diameter of Cylinder 1, Diameter of Cylinder 2 & Eccentric Distance Between Objects 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 Conduction Shape Factor?

In this formula, Conduction Shape Factor uses Length of Cylinder, Diameter of Cylinder 1, Diameter of Cylinder 2 & Eccentric Distance Between Objects. We can use 3 other way(s) to calculate the same, which is/are as follows -

Conduction Shape Factor = (2*pi*Length of Cylinder)/ln((1.08*Width of Square Bar)/Diameter of Cylinder)
Conduction Shape Factor = Cross-Sectional Area/Thickness
Conduction Shape Factor = (2*pi*Length of Cylinder)/(ln(Outer Radius of Cylinder/Inner Radius of Cylinder))

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