Isothermal Ellipsoid Buried in Infinite Medium Calculator

✖The Semi Major Axis of Ellipse value is denoted by the symbol a.ⓘ Semi Major Axis of Ellipse [a]			+10% -10%
✖The Semi Minor Axis of Ellipse is denoted by the value b.ⓘ Semi Minor Axis of Ellipse [b]			+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.ⓘ Isothermal Ellipsoid Buried in Infinite Medium [S]

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Isothermal Ellipsoid Buried in 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, 3 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
tanh - The hyperbolic tangent function (tanh) is a function that is defined as the ratio of the hyperbolic sine function (sinh) to the hyperbolic cosine function (cosh)., tanh(Number)
atanh - The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number., atanh(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.
Semi Major Axis of Ellipse - (Measured in Meter) - The Semi Major Axis of Ellipse value is denoted by the symbol a.
Semi Minor Axis of Ellipse - (Measured in Meter) - The Semi Minor Axis of Ellipse is denoted by the value b.

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis of Ellipse: 5.745084 Meter --> 5.745084 Meter No Conversion Required
Semi Minor Axis of Ellipse: 0.8 Meter --> 0.8 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*5.745084*sqrt(1-0.8/5.745084^2))/(atanh(sqrt(1-0.8/5.745084^2)))

Evaluating ... ...

S = 28.0000036371857

STEP 3: Convert Result to Output's Unit

28.0000036371857 Meter --> No Conversion Required

FINAL ANSWER

28.0000036371857 ≈ 28 Meter <-- Conduction Shape Factor

(Calculation completed in 00.004 seconds)

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< Infinite Medium Calculators

Isothermal Ellipsoid Buried in Infinite Medium

LaTeX Go 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)))

Two parallel Isothermal Cylinders placed in Infinite medium

LaTeX Go 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))

Isothermal Cylinder in Midplane of Infinite wall

LaTeX Go Conduction Shape Factor = (8*Distance from Surface to Centre of Object)/(pi*Diameter of Cylinder)

Isothermal Sphere Buried in Infinite Medium

LaTeX Go Conduction Shape Factor = 4*pi*Radius of Sphere

Isothermal Ellipsoid Buried in Infinite Medium Formula

LaTeX Go

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 Infinite Medium?

Isothermal Ellipsoid Buried in 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 Infinite Medium formula is defined as a mathematical representation of the electric potential at a point in space due to a charge distribution within an ellipsoidal shape buried in an infinite homogeneous medium. It provides a way to calculate the electric potential at any point in space, taking into account the shape and size of the ellipsoid and the properties of the surrounding medium. Conduction Shape Factor is denoted by S symbol.

How to calculate Isothermal Ellipsoid Buried in Infinite Medium using this online calculator? To use this online calculator for Isothermal Ellipsoid Buried in 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 Infinite Medium calculation can be explained with given input values -> 13.67717 = (4*pi*5.745084*sqrt(1-0.8/5.745084^2))/(atanh(sqrt(1-0.8/5.745084^2))).

FAQ

What is Isothermal Ellipsoid Buried in Infinite Medium?

Isothermal Ellipsoid Buried in Infinite Medium formula is defined as a mathematical representation of the electric potential at a point in space due to a charge distribution within an ellipsoidal shape buried in an infinite homogeneous medium. It provides a way to calculate the electric potential at any point in space, taking into account the shape and size of the ellipsoid and the properties of the surrounding medium 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 Infinite Medium?

Isothermal Ellipsoid Buried in Infinite Medium formula is defined as a mathematical representation of the electric potential at a point in space due to a charge distribution within an ellipsoidal shape buried in an infinite homogeneous medium. It provides a way to calculate the electric potential at any point in space, taking into account the shape and size of the ellipsoid and the properties of the surrounding medium 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 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 3 other way(s) to calculate the same, which is/are as follows -

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 = 4*pi*Radius of Sphere
Conduction Shape Factor = (8*Distance from Surface to Centre of Object)/(pi*Diameter of Cylinder)

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