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Isothermal Ellipsoid Buried in Infinite Medium Formula

GoTwo parallel Isothermal Cylinders placed in Infinite medium Formula

GoIsothermal Sphere Buried in Infinite Medium Formula

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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. Check FAQs

S = \frac{4 \cdot π \cdot a \cdot \sqrt{1 - \frac{b}{a^{2}}}}{a \tanh (\sqrt{1 - \frac{b}{a^{2}}})}

S - Conduction Shape Factor?a - Semi Major Axis of Ellipse?b - Semi Minor Axis of Ellipse?π - Archimedes' constant?

Isothermal Ellipsoid Buried in Infinite Medium Example

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Here is how the Isothermal Ellipsoid Buried in Infinite Medium equation looks like with Values.

Here is how the Isothermal Ellipsoid Buried in Infinite Medium equation looks like with Units.

Here is how the Isothermal Ellipsoid Buried in Infinite Medium equation looks like.

28 = \frac{4 \cdot 3.1416 \cdot 5.7451 \cdot \sqrt{1 - \frac{0.8}{{5.7451}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8}{{5.7451}^{2}}})}

28m = \frac{4 \cdot 3.1416 \cdot 5.7451m \cdot \sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}})}

28 = \frac{4 \cdot 3.1416 \cdot 5.7451 \cdot \sqrt{1 - \frac{0.8}{{5.7451}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8}{{5.7451}^{2}}})}

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Isothermal Ellipsoid Buried in Infinite Medium Solution

Follow our step by step solution on how to calculate Isothermal Ellipsoid Buried in Infinite Medium?

FIRST Step Consider the formula

S = \frac{4 \cdot π \cdot a \cdot \sqrt{1 - \frac{b}{a^{2}}}}{a \tanh (\sqrt{1 - \frac{b}{a^{2}}})}

Next Step Substitute values of Variables

∴

S = \frac{4 \cdot π \cdot 5.7451m \cdot \sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}})}

Next Step Substitute values of Constants

∴

S = \frac{4 \cdot 3.1416 \cdot 5.7451m \cdot \sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8m}{{5.7451m}^{2}}})}

Next Step Prepare to Evaluate

∴

S = \frac{4 \cdot 3.1416 \cdot 5.7451 \cdot \sqrt{1 - \frac{0.8}{{5.7451}^{2}}}}{a \tanh (\sqrt{1 - \frac{0.8}{{5.7451}^{2}}})}

Next Step Evaluate

∴

S = 28.0000036371857m

LAST Step Rounding Answer

∴

S = 28m

Isothermal Ellipsoid Buried in Infinite Medium Formula Elements

Variables

Constants

Functions

Conduction Shape Factor

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.

Symbol: S

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Conduction Shape Factor

Semi Major Axis of Ellipse

The Semi Major Axis of Ellipse value is denoted by the symbol a.

Symbol: a

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Major Axis of Ellipse

Semi Minor Axis of Ellipse

The Semi Minor Axis of Ellipse is denoted by the value b.

Symbol: b

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Minor Axis of Ellipse

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

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.

Syntax: 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).

Syntax: tanh(Number)

atanh

The inverse hyperbolic tangent function returns the value whose hyperbolic tangent is a number.

Syntax: atanh(Number)

Other Formulas to find Conduction Shape Factor

Go Two parallel Isothermal Cylinders placed in Infinite medium

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

Go Isothermal Sphere Buried in Infinite Medium

S = 4 \cdot π \cdot R s

Go Isothermal Cylinder in Midplane of Infinite wall

S = \frac{8 \cdot d s}{π \cdot D}

How to Evaluate Isothermal Ellipsoid Buried in Infinite Medium?

Isothermal Ellipsoid Buried in Infinite Medium evaluator 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 evaluate 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 evaluate Isothermal Ellipsoid Buried in Infinite Medium using this online evaluator? To use this online evaluator 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.

FAQs on Isothermal Ellipsoid Buried in Infinite Medium

What is the formula to find Isothermal Ellipsoid Buried in Infinite Medium?

The formula of Isothermal Ellipsoid Buried in Infinite Medium is expressed as 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))). Here is an example- 13.67717 = (4*pi*5.745084*sqrt(1-0.8/5.745084^2))/(atanh(sqrt(1-0.8/5.745084^2))).

How to calculate Isothermal Ellipsoid Buried in Infinite Medium?

With Semi Major Axis of Ellipse (a) & Semi Minor Axis of Ellipse (b) we can find Isothermal Ellipsoid Buried in Infinite Medium using the 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))). This formula also uses Archimedes' constant and , Square Root (sqrt), Hyperbolic Tangent (tanh), Inverse Hyperbolic Tangent (atanh) function(s).

What are the other ways to Calculate Conduction Shape Factor?

Here are the different ways to Calculate Conduction Shape Factor-

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)

Can the Isothermal Ellipsoid Buried in Infinite Medium be negative?

No, the Isothermal Ellipsoid Buried in Infinite Medium, measured in Length cannot be negative.

Which unit is used to measure Isothermal Ellipsoid Buried in Infinite Medium?

Isothermal Ellipsoid Buried in Infinite Medium is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Isothermal Ellipsoid Buried in Infinite Medium can be measured.

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Isothermal Ellipsoid Buried in Infinite Medium Formula

​GoTwo parallel Isothermal Cylinders placed in Infinite medium Formula

​GoIsothermal Sphere Buried in Infinite Medium Formula

Isothermal Ellipsoid Buried in Infinite Medium Example

Isothermal Ellipsoid Buried in Infinite Medium Solution

Isothermal Ellipsoid Buried in Infinite Medium Formula Elements

Other Formulas to find Conduction Shape Factor

How to Evaluate Isothermal Ellipsoid Buried in Infinite Medium?

FAQs on Isothermal Ellipsoid Buried in Infinite Medium

Variable Name

GoTwo parallel Isothermal Cylinders placed in Infinite medium Formula

GoIsothermal Sphere Buried in Infinite Medium Formula