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Isothermal ellipsoid buried in an infinite medium Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
S = (4*pi*a*sqrt(1-(b/a)^2))/(atanh(sqrt(1-(b/a)^2)))
This formula uses 1 Constants, 5 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
tan - Trigonometric tangent function, tan(Angle)
atan - Inverse trigonometric tangent function, atan(Number)
sqrt - Squre root function, sqrt(Number)
tanh - Hyperbolic tangent function, tanh(Number)
atanh - Inverse hyperbolic tangent function, atanh(Number)
Variables Used
Semi Major Axis of Ellipse - The Semi Major Axis of Ellipse value is denoted by the symbol a. (Measured in Meter)
Semi Minor Axis of Ellipse - The Semi Minor Axis of Ellipse is denoted by the value b. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Semi Major Axis of Ellipse: 2 Meter --> 2 Meter No Conversion Required
Semi Minor Axis of Ellipse: 1 Meter --> 1 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
S = (4*pi*a*sqrt(1-(b/a)^2))/(atanh(sqrt(1-(b/a)^2))) --> (4*pi*2*sqrt(1-(1/2)^2))/(atanh(sqrt(1-(1/2)^2)))
Evaluating ... ...
S = 16.5271740437828
STEP 3: Convert Result to Output's Unit
16.5271740437828 Meter --> No Conversion Required
FINAL ANSWER
16.5271740437828 Meter <-- Conduction shape factor
(Calculation completed in 00.015 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 surafce 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 surafce 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 surafce to centre of object)/(pi*Diameter of cylinder) Go
Large plane wall
conduction_shape_factor = Cross-sectional area/Thickness Go

Isothermal ellipsoid buried in an infinite medium Formula

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)))
S = (4*pi*a*sqrt(1-(b/a)^2))/(atanh(sqrt(1-(b/a)^2)))

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 ellipsoid buried in an infinite medium?

Isothermal ellipsoid buried in an infinite medium calculator uses 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))) to calculate the Conduction shape factor, Isothermal ellipsoid buried in an infinite medium formula calculates the shape factor for ellipsoid surrounded by an infinite medium for heat conduction. Conduction shape factor is denoted by S symbol.

How to calculate Isothermal ellipsoid buried in an infinite medium using this online calculator? To use this online calculator for Isothermal ellipsoid buried in an infinite medium, enter Semi Major Axis of Ellipse (a) & Semi Minor Axis of Ellipse (b) and hit the calculate button. Here is how the Isothermal ellipsoid buried in an infinite medium calculation can be explained with given input values -> 16.52717 = (4*pi*2*sqrt(1-(1/2)^2))/(atanh(sqrt(1-(1/2)^2))).

FAQ

What is Isothermal ellipsoid buried in an infinite medium?
Isothermal ellipsoid buried in an infinite medium formula calculates the shape factor for ellipsoid surrounded by an infinite medium for heat conduction and is represented as S = (4*pi*a*sqrt(1-(b/a)^2))/(atanh(sqrt(1-(b/a)^2))) or 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))). The Semi Major Axis of Ellipse value is denoted by the symbol a & The Semi Minor Axis of Ellipse is denoted by the value b.
How to calculate Isothermal ellipsoid buried in an infinite medium?
Isothermal ellipsoid buried in an infinite medium formula calculates the shape factor for ellipsoid surrounded by an infinite medium for heat conduction is calculated using 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))). To calculate Isothermal ellipsoid buried in an infinite medium, you need Semi Major Axis of Ellipse (a) & Semi Minor Axis of Ellipse (b). With our tool, you need to enter the respective value for Semi Major Axis of Ellipse & Semi Minor Axis of Ellipse 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 Semi Major Axis of Ellipse & Semi Minor Axis of Ellipse. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • conduction_shape_factor = (2*pi*Length of Cylinder)/(ln((4*Distance from surafce 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 surafce to centre of object)/Distance between centers)))
  • conduction_shape_factor = (8*Distance from surafce to centre of object)/(pi*Diameter of cylinder)
  • conduction_shape_factor = (2*pi*Length of Cylinder)/ln((1.08*Width of square bar)/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)
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