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Isothermal cylinder at center of square solid bar of same length Solution

STEP 0: Pre-Calculation Summary
Formula Used
Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder)
S = (2*pi*l)/ln((1.08*w)/D)
This formula uses 1 Constants, 1 Functions, 3 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
ln - Natural logarithm function (base e), ln(Number)
Variables Used
Length of Cylinder - Length of Cylinder is the vertical height of the Cylinder. (Measured in Meter)
Width of square bar - Width of square bar is length of the side of cross-section of the square bar. (Measured in Meter)
Diameter of cylinder - Diameter of cylinder is the maximum width of cylinder in transverse direction. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Length of Cylinder: 1 Meter --> 1 Meter No Conversion Required
Width of square bar: 50 Meter --> 50 Meter No Conversion Required
Diameter of cylinder: 5 Centimeter --> 0.05 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S = (2*pi*l)/ln((1.08*w)/D) --> (2*pi*1)/ln((1.08*50)/0.05)
Evaluating ... ...
S = 0.899561989236694
STEP 3: Convert Result to Output's Unit
0.899561989236694 Meter --> No Conversion Required
FINAL ANSWER
0.899561989236694 Meter <-- Conduction shape factor
(Calculation completed in 00.031 seconds)

10+ Conduction shape factors for different configurations Calculators

Row of equally spaced parallel isothermal cylinders buried in a semi-infinite medium
Conduction shape factor = (2*pi*Length of Cylinder)/(ln(((2*Distance between centers)/(pi*Diameter of cylinder))*sinh((2*pi*Distance from surface to centre of object)/Distance between centers))) Go
Eccentric isothermal cylinder in a cylinder of same length
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)) Go
Two parallel isothermal cylinders placed in an infinite medium
Conduction shape factor = (2*pi*Length of Cylinder)/acosh(((4*(Distance between centers)^2)-(Diameter of cylinder 1)^2-(Diameter of cylinder 2)^2)/(2*Diameter of cylinder 1*Diameter of cylinder 2)) Go
Isothermal cylinder buried in semi-infinite medium
Conduction shape factor = (2*pi*Length of Cylinder)/(ln((4*Distance from surface to centre of object)/Diameter of cylinder)) Go
Long hollow cylindrical layer
Conduction shape factor = (2*pi*Length of Cylinder)/(ln(Outer Radius of Cylinder/Inner Radius of Cylinder)) Go
Isothermal cylinder at center of square solid bar of same length
Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder) Go
Vertical isothermal cylinder buried in semi-infinite medium
Conduction shape factor = (2*pi*Length of Cylinder)/(ln((4*Length of Cylinder)/Diameter of cylinder)) Go
Hollow spherical layer
Conduction shape factor = (4*pi*Inner radius*Outer radius)/(Outer radius-Inner radius) Go
Isothermal cylinder in midplane of an infinite wall
Conduction shape factor = (8*Distance from surface to centre of object)/(pi*Diameter of cylinder) Go
Large plane wall
Conduction shape factor = Cross-sectional area/Thickness Go

Isothermal cylinder at center of square solid bar of same length Formula

Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder)
S = (2*pi*l)/ln((1.08*w)/D)

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 Isothermal cylinder at center of square solid bar of same length?

Isothermal cylinder at center of square solid bar of same length calculator uses Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder) to calculate the Conduction shape factor, The Isothermal cylinder at center of square solid bar of same length formula gives the shape factor when a cylinder is placed at the center of a solid square bar for heat conduction. Both cylinder and square bar is of the same length. Conduction shape factor is denoted by S symbol.

How to calculate Isothermal cylinder at center of square solid bar of same length using this online calculator? To use this online calculator for Isothermal cylinder at center of square solid bar of same length, enter Length of Cylinder (l), Width of square bar (w) & Diameter of cylinder (D) and hit the calculate button. Here is how the Isothermal cylinder at center of square solid bar of same length calculation can be explained with given input values -> 0.899562 = (2*pi*1)/ln((1.08*50)/0.05).

FAQ

What is Isothermal cylinder at center of square solid bar of same length?
The Isothermal cylinder at center of square solid bar of same length formula gives the shape factor when a cylinder is placed at the center of a solid square bar for heat conduction. Both cylinder and square bar is of the same length and is represented as S = (2*pi*l)/ln((1.08*w)/D) or Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder). Length of Cylinder is the vertical height of the Cylinder, Width of square bar is length of the side of cross-section of the square bar & Diameter of cylinder is the maximum width of cylinder in transverse direction.
How to calculate Isothermal cylinder at center of square solid bar of same length?
The Isothermal cylinder at center of square solid bar of same length formula gives the shape factor when a cylinder is placed at the center of a solid square bar for heat conduction. Both cylinder and square bar is of the same length is calculated using Conduction shape factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/Diameter of cylinder). To calculate Isothermal cylinder at center of square solid bar of same length, you need Length of Cylinder (l), Width of square bar (w) & Diameter of cylinder (D). With our tool, you need to enter the respective value for Length of Cylinder, Width of square bar & Diameter 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 Conduction shape factor?
In this formula, Conduction shape factor uses Length of Cylinder, Width of square bar & Diameter of cylinder. We can use 20 other way(s) to calculate the same, which is/are as follows -
  • Conduction shape factor = (2*pi*Length of Cylinder)/(ln((4*Distance from surface to centre of object)/Diameter of cylinder))
  • Conduction shape factor = (2*pi*Length of Cylinder)/(ln((4*Length of Cylinder)/Diameter of cylinder))
  • Conduction shape factor = (2*pi*Length of Cylinder)/acosh(((4*(Distance between centers)^2)-(Diameter of cylinder 1)^2-(Diameter of cylinder 2)^2)/(2*Diameter of cylinder 1*Diameter of cylinder 2))
  • Conduction shape factor = (2*pi*Length of Cylinder)/(ln(((2*Distance between centers)/(pi*Diameter of cylinder))*sinh((2*pi*Distance from surface to centre of object)/Distance between centers)))
  • Conduction shape factor = (8*Distance from surface to centre of object)/(pi*Diameter of cylinder)
  • 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))
  • Conduction shape factor = Cross-sectional area/Thickness
  • Conduction shape factor = (2*pi*Length of Cylinder)/(ln(Outer Radius of Cylinder/Inner Radius of Cylinder))
  • Conduction shape factor = (4*pi*Inner radius*Outer radius)/(Outer radius-Inner radius)
  • Conduction shape factor = (2*pi*Length of Pipe)/(0.93*ln(0.948*(Outer width/Inner width)))
  • Conduction shape factor = (2*pi*Length of Pipe)/(0.785*ln(Outer width/Inner width))
  • Conduction shape factor = 4*Diameter of disk
  • Conduction shape factor = 0.15*Thickness of Wall
  • Conduction shape factor = 0.54*Length of wall
  • Conduction shape factor = (2*pi*Diameter of Sphere)/(1-((0.25*Diameter of Sphere)/Distance from surface to centre of object))
  • Conduction shape factor = (2*pi*Diameter of Sphere)/(1+((0.25*Diameter of Sphere)/Distance from surface to centre of object))
  • Conduction shape factor = 1.685*Length of parallelepiped*((log10(1+(Distance from surafce to surface of object/Width of parallelepiped)))^(-0.59))*(Distance from surafce to surface of object/Height of parallelepiped)^(-0.078)
  • Conduction shape factor = (2*pi*Width of plate)/ln((4*Width of plate)/Length of Plate)
  • Conduction shape factor = 4*pi*Radius of Sphere
  • Conduction shape factor = (4*pi*Semi Major Axis of Ellipse*sqrt(1-(Semi Minor Axis of Ellipse/Semi Major Axis of Ellipse)^2))/(atanh(sqrt(1-(Semi Minor Axis of Ellipse/Semi Major Axis of Ellipse)^2)))
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