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Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Formula

GoTemperature at given Thickness x Inside Plane Wall Surrounded by Fluid Formula

GoTemperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Formula

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Temperature is the degree or intensity of heat present in a substance or object. Check FAQs

T = \frac{q G}{4 \cdot k} \cdot ({r o}^{2} - r^{2}) + T o + \frac{\ln (\frac{r}{r o})}{\ln (\frac{r o}{r i})} \cdot (\frac{q G}{4 \cdot k} \cdot ({r o}^{2} - {r i}^{2}) + (T o - T i))

T - Temperature?q_G - Internal Heat Generation?k - Thermal Conductivity?r_o - Outer Radius of Cylinder?r - Radius?T_o - Outer Surface Temperature?r_i - Inner Radius of Cylinder?T_i - Inner Surface Temperature?

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Example

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Here is how the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius equation looks like with Values.

Here is how the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius equation looks like with Units.

Here is how the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius equation looks like.

460 = \frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - 4^{2}) + 300 + \frac{\ln (\frac{4}{30.1826})}{\ln (\frac{30.1826}{2.5})} \cdot (\frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - {2.5}^{2}) + (300 - 10))

460K = \frac{100W/m³}{4 \cdot 10.18W/(m*K)} \cdot ({30.1826m}^{2} - {4m}^{2}) + 300K + \frac{\ln (\frac{4m}{30.1826m})}{\ln (\frac{30.1826m}{2.5m})} \cdot (\frac{100W/m³}{4 \cdot 10.18W/(m*K)} \cdot ({30.1826m}^{2} - {2.5m}^{2}) + (300K - 10K))

460 = \frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - 4^{2}) + 300 + \frac{\ln (\frac{4}{30.1826})}{\ln (\frac{30.1826}{2.5})} \cdot (\frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - {2.5}^{2}) + (300 - 10))

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Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Solution

Follow our step by step solution on how to calculate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

FIRST Step Consider the formula

T = \frac{q G}{4 \cdot k} \cdot ({r o}^{2} - r^{2}) + T o + \frac{\ln (\frac{r}{r o})}{\ln (\frac{r o}{r i})} \cdot (\frac{q G}{4 \cdot k} \cdot ({r o}^{2} - {r i}^{2}) + (T o - T i))

Next Step Substitute values of Variables

∴

T = \frac{100W/m³}{4 \cdot 10.18W/(m*K)} \cdot ({30.1826m}^{2} - {4m}^{2}) + 300K + \frac{\ln (\frac{4m}{30.1826m})}{\ln (\frac{30.1826m}{2.5m})} \cdot (\frac{100W/m³}{4 \cdot 10.18W/(m*K)} \cdot ({30.1826m}^{2} - {2.5m}^{2}) + (300K - 10K))

Next Step Prepare to Evaluate

∴

T = \frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - 4^{2}) + 300 + \frac{\ln (\frac{4}{30.1826})}{\ln (\frac{30.1826}{2.5})} \cdot (\frac{100}{4 \cdot 10.18} \cdot ({30.1826}^{2} - {2.5}^{2}) + (300 - 10))

Next Step Evaluate

∴

T = 459.999983082048K

LAST Step Rounding Answer

∴

T = 460K

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Formula Elements

Variables

Functions

Temperature

Temperature is the degree or intensity of heat present in a substance or object.

Symbol: T

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature

Internal Heat Generation

Internal Heat Generation is defined as the conversion of electrical, chemical, or nuclear energy into heat (or thermal) energy which leads to a rise in temperature throughout the medium.

Symbol: q_G

Measurement: Power DensityUnit: W/m³

Note: Value should be greater than 0.

Formulas to find Internal Heat Generation

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

Outer Radius of Cylinder

The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.

Symbol: r_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Outer Radius of Cylinder

Radius

Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius

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

Inner Radius of Cylinder

The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inner Radius of Cylinder

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

The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function.

Syntax: ln(Number)

Other Formulas to find Temperature

Go Temperature at given Thickness x Inside Plane Wall Surrounded by Fluid

T = \frac{q G}{8 \cdot k} \cdot (b^{2} - 4 \cdot x^{2}) + \frac{q G \cdot b}{2 \cdot h c} + T ∞

Go Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius

T = T w + \frac{q G}{6 \cdot k} \cdot ({r 2}^{2} - r^{2}) + \frac{q G \cdot {r 1}^{3}}{3 \cdot k} \cdot (\frac{1}{r 2} - \frac{1}{r})

Other formulas in Steady State Heat Conduction with Heat Generation category

Go Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

T max = T 1 + \frac{q G \cdot b^{2}}{8 \cdot k}

Go Location of Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

X = \frac{b}{2}

How to Evaluate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius evaluator uses Temperature = Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Radius^2)+Outer Surface Temperature+ln(Radius/Outer Radius of Cylinder)/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)*(Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Inner Radius of Cylinder^2)+(Outer Surface Temperature-Inner Surface Temperature)) to evaluate the Temperature, The Temperature inside hollow cylinder at given radius between inner and outer radius formula gives the value of temperature along with the thickness of the hollow cylinder provided with an internal heat generation source. Temperature is denoted by T symbol.

How to evaluate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius using this online evaluator? To use this online evaluator for Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius, enter Internal Heat Generation (q_G), Thermal Conductivity (k), Outer Radius of Cylinder (r_o), Radius (r), Outer Surface Temperature (T_o), Inner Radius of Cylinder (r_i) & Inner Surface Temperature (T_i) and hit the calculate button.

FAQs on Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius

What is the formula to find Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

The formula of Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius is expressed as Temperature = Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Radius^2)+Outer Surface Temperature+ln(Radius/Outer Radius of Cylinder)/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)*(Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Inner Radius of Cylinder^2)+(Outer Surface Temperature-Inner Surface Temperature)). Here is an example- 162.654 = 100/(4*10.18)*(30.18263^2-4^2)+300+ln(4/30.18263)/ln(30.18263/2.5)*(100/(4*10.18)*(30.18263^2-2.5^2)+(300-10)).

How to calculate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

With Internal Heat Generation (q_G), Thermal Conductivity (k), Outer Radius of Cylinder (r_o), Radius (r), Outer Surface Temperature (T_o), Inner Radius of Cylinder (r_i) & Inner Surface Temperature (T_i) we can find Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius using the formula - Temperature = Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Radius^2)+Outer Surface Temperature+ln(Radius/Outer Radius of Cylinder)/ln(Outer Radius of Cylinder/Inner Radius of Cylinder)*(Internal Heat Generation/(4*Thermal Conductivity)*(Outer Radius of Cylinder^2-Inner Radius of Cylinder^2)+(Outer Surface Temperature-Inner Surface Temperature)). This formula also uses Natural Logarithm (ln) function(s).

What are the other ways to Calculate Temperature?

Here are the different ways to Calculate Temperature-

Temperature=Internal Heat Generation/(8*Thermal Conductivity)*(Wall Thickness^2-4*Thickness^2)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature
Temperature=Surface Temperature of Wall+Internal Heat Generation/(6*Thermal Conductivity)*(Outer Radius of Sphere^2-Radius^2)+(Internal Heat Generation*Inner Radius of Sphere^3)/(3*Thermal Conductivity)*(1/Outer Radius of Sphere-1/Radius)

Can the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius be negative?

Yes, the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius, measured in Temperature can be negative.

Which unit is used to measure Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius is usually measured using the Kelvin[K] for Temperature. Celsius[K], Fahrenheit[K], Rankine[K] are the few other units in which Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius can be measured.

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Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Formula

​GoTemperature at given Thickness x Inside Plane Wall Surrounded by Fluid Formula

​GoTemperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Formula

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Example

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Solution

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius Formula Elements

Other Formulas to find Temperature

Other formulas in Steady State Heat Conduction with Heat Generation category

How to Evaluate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

FAQs on Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius

Variable Name

GoTemperature at given Thickness x Inside Plane Wall Surrounded by Fluid Formula

GoTemperature Inside Hollow Sphere at given Radius between Inner and Outer Radius Formula