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Inner Surface Temperature of Spherical Wall Formula

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Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc. Check FAQs

T i = T o + \frac{Q}{4 \cdot π \cdot k} \cdot (\frac{1}{r 1} - \frac{1}{r 2})

T_i - Inner Surface Temperature?T_o - Outer Surface Temperature?Q - Heat Flow Rate?k - Thermal Conductivity?r₁ - Radius of 1st Concentric Sphere?r₂ - Radius of 2nd Concentric Sphere?π - Archimedes' constant?

Inner Surface Temperature of Spherical Wall Example

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Here is how the Inner Surface Temperature of Spherical Wall equation looks like with Values.

Here is how the Inner Surface Temperature of Spherical Wall equation looks like with Units.

Here is how the Inner Surface Temperature of Spherical Wall equation looks like.

305 = 300 + \frac{3769.9112}{4 \cdot 3.1416 \cdot 2} \cdot (\frac{1}{5} - \frac{1}{6})

305K = 300K + \frac{3769.9112W}{4 \cdot 3.1416 \cdot 2W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m})

305 = 300 + \frac{3769.9112}{4 \cdot 3.1416 \cdot 2} \cdot (\frac{1}{5} - \frac{1}{6})

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Inner Surface Temperature of Spherical Wall Solution

Follow our step by step solution on how to calculate Inner Surface Temperature of Spherical Wall?

FIRST Step Consider the formula

T i = T o + \frac{Q}{4 \cdot π \cdot k} \cdot (\frac{1}{r 1} - \frac{1}{r 2})

Next Step Substitute values of Variables

∴

T i = 300K + \frac{3769.9112W}{4 \cdot π \cdot 2W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m})

Next Step Substitute values of Constants

∴

T i = 300K + \frac{3769.9112W}{4 \cdot 3.1416 \cdot 2W/(m*K)} \cdot (\frac{1}{5m} - \frac{1}{6m})

Next Step Prepare to Evaluate

∴

T i = 300 + \frac{3769.9112}{4 \cdot 3.1416 \cdot 2} \cdot (\frac{1}{5} - \frac{1}{6})

Next Step Evaluate

∴

T i = 304.99999999999K

LAST Step Rounding Answer

∴

T i = 305K

Inner Surface Temperature of Spherical Wall Formula Elements

Variables

Constants

Inner Surface Temperature

Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.

Symbol: T_i

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Inner Surface Temperature

Outer Surface Temperature

Outer Surface Temperature is the temperature at the outer surface of the wall either plane wall or cylindrical wall or spherical wall, etc.

Symbol: T_o

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Outer Surface Temperature

Heat Flow Rate

Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.

Symbol: Q

Measurement: PowerUnit: W

Note: Value can be positive or negative.

Formulas to find Heat Flow Rate

Thermal Conductivity

Thermal Conductivity is rate of heat passes through specified material, expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.

Symbol: k

Measurement: Thermal ConductivityUnit: W/(m*K)

Note: Value should be greater than 0.

Formulas to find Thermal Conductivity

Radius of 1st Concentric Sphere

Radius of 1st Concentric Sphere is the distance from the center of the concentric spheres to any point on the first concentric sphere or radius of the first sphere.

Symbol: r₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of 1st Concentric Sphere

Radius of 2nd Concentric Sphere

Radius of 2nd Concentric Sphere is the distance from the center of the concentric spheres to any point on the second concentric sphere or radius of the second sphere.

Symbol: r₂

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of 2nd Concentric Sphere

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

Other formulas in Conduction in Sphere category

Go Convection Resistance for Spherical Layer

r th = \frac{1}{4 \cdot π \cdot r^{2} \cdot h}

Go Total Thermal Resistance of Spherical Wall with Convection on Both Side

R tr = \frac{1}{4 \cdot π \cdot {r 1}^{2} \cdot h i} + \frac{r 2 - r 1}{4 \cdot π \cdot k \cdot r 1 \cdot r 2} + \frac{1}{4 \cdot π \cdot {r 2}^{2} \cdot h o}

Go Total Thermal Resistance of Spherical wall of 3 Layers without Convection

R tr = \frac{r 2 - r 1}{4 \cdot π \cdot k 1 \cdot r 1 \cdot r 2} + \frac{r 3 - r 2}{4 \cdot π \cdot k 2 \cdot r 2 \cdot r 3} + \frac{r 4 - r 3}{4 \cdot π \cdot k 3 \cdot r 3 \cdot r 4}

Go Total Thermal Resistance of Spherical Wall of 2 Layers without Convection

r tr = \frac{r 2 - r 1}{4 \cdot π \cdot k 1 \cdot r 1 \cdot r 2} + \frac{r 3 - r 2}{4 \cdot π \cdot k 2 \cdot r 2 \cdot r 3}

How to Evaluate Inner Surface Temperature of Spherical Wall?

Inner Surface Temperature of Spherical Wall evaluator uses Inner Surface Temperature = Outer Surface Temperature+Heat Flow Rate/(4*pi*Thermal Conductivity)*(1/Radius of 1st Concentric Sphere-1/Radius of 2nd Concentric Sphere) to evaluate the Inner Surface Temperature, The Inner surface temperature of spherical wall formula is defined as the temperature at the inner surface of the hollow spherical wall without convection when the heat flow rate, radii, outer surface temperature and thermal conductivity are known. Inner Surface Temperature is denoted by T_i symbol.

How to evaluate Inner Surface Temperature of Spherical Wall using this online evaluator? To use this online evaluator for Inner Surface Temperature of Spherical Wall, enter Outer Surface Temperature (T_o), Heat Flow Rate (Q), Thermal Conductivity (k), Radius of 1st Concentric Sphere (r₁) & Radius of 2nd Concentric Sphere (r₂) and hit the calculate button.

FAQs on Inner Surface Temperature of Spherical Wall

What is the formula to find Inner Surface Temperature of Spherical Wall?

The formula of Inner Surface Temperature of Spherical Wall is expressed as Inner Surface Temperature = Outer Surface Temperature+Heat Flow Rate/(4*pi*Thermal Conductivity)*(1/Radius of 1st Concentric Sphere-1/Radius of 2nd Concentric Sphere). Here is an example- 305 = 300+3769.9111843/(4*pi*2)*(1/5-1/6).

How to calculate Inner Surface Temperature of Spherical Wall?

With Outer Surface Temperature (T_o), Heat Flow Rate (Q), Thermal Conductivity (k), Radius of 1st Concentric Sphere (r₁) & Radius of 2nd Concentric Sphere (r₂) we can find Inner Surface Temperature of Spherical Wall using the formula - Inner Surface Temperature = Outer Surface Temperature+Heat Flow Rate/(4*pi*Thermal Conductivity)*(1/Radius of 1st Concentric Sphere-1/Radius of 2nd Concentric Sphere). This formula also uses Archimedes' constant .

Can the Inner Surface Temperature of Spherical Wall be negative?

Yes, the Inner Surface Temperature of Spherical Wall, measured in Temperature can be negative.

Which unit is used to measure Inner Surface Temperature of Spherical Wall?

Inner Surface Temperature of Spherical Wall is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Inner Surface Temperature of Spherical Wall can be measured.

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Inner Surface Temperature of Spherical Wall Formula

Inner Surface Temperature of Spherical Wall Example

Inner Surface Temperature of Spherical Wall Solution

Inner Surface Temperature of Spherical Wall Formula Elements

Other formulas in Conduction in Sphere category

How to Evaluate Inner Surface Temperature of Spherical Wall?

FAQs on Inner Surface Temperature of Spherical Wall

Variable Name