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

✖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.ⓘ Internal Heat Generation [q_G]			+10% -10%
✖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.ⓘ Thermal Conductivity [k]			+10% -10%
✖The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.ⓘ Outer Radius of Cylinder [r_o]			+10% -10%
✖Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated.ⓘ Radius [r]			+10% -10%
✖Outer Surface Temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).ⓘ Outer Surface Temperature [T_o]			+10% -10%
✖The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.ⓘ Inner Radius of Cylinder [r_i]			+10% -10%
✖Inner Surface Temperature is the temperature at the inner surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).ⓘ Inner Surface Temperature [T_i]			+10% -10%

✖Temperature is the degree or intensity of heat present in a substance or object.ⓘ Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius [T]

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

STEP 0: Pre-Calculation Summary

Formula Used

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))
T = q_G/(4*k)*(r_o^2-r^2)+T_o+ln(r/r_o)/ln(r_o/r_i)*(q_G/(4*k)*(r_o^2-r_i^2)+(T_o-T_i))
This formula uses 1 Functions, 8 Variables

Functions Used

ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)

Variables Used

Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Internal Heat Generation - (Measured in Watt Per Cubic Meter) - 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.
Thermal Conductivity - (Measured in Watt per Meter per K) - 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.
Outer Radius of Cylinder - (Measured in Meter) - The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder.
Radius - (Measured in Meter) - Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated.
Outer Surface Temperature - (Measured in Kelvin) - Outer Surface Temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).
Inner Radius of Cylinder - (Measured in Meter) - The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder.
Inner Surface Temperature - (Measured in Kelvin) - Inner Surface Temperature is the temperature at the inner surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).

STEP 1: Convert Input(s) to Base Unit

Internal Heat Generation: 100 Watt Per Cubic Meter --> 100 Watt Per Cubic Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required
Outer Radius of Cylinder: 30.18263 Meter --> 30.18263 Meter No Conversion Required
Radius: 4 Meter --> 4 Meter No Conversion Required
Outer Surface Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Inner Radius of Cylinder: 2.5 Meter --> 2.5 Meter No Conversion Required
Inner Surface Temperature: 10 Kelvin --> 10 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = q_G/(4*k)*(r_o^2-r^2)+T_o+ln(r/r_o)/ln(r_o/r_i)*(q_G/(4*k)*(r_o^2-r_i^2)+(T_o-T_i)) --> 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))

Evaluating ... ...

T = 459.999983082048

STEP 3: Convert Result to Output's Unit

459.999983082048 Kelvin --> No Conversion Required

FINAL ANSWER

459.999983082048 ≈ 460 Kelvin <-- Temperature

(Calculation completed in 00.020 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Mechanical » Steady State Heat Conduction with Heat Generation » Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius

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< Steady State Heat Conduction with Heat Generation Calculators

Maximum Temperature in Solid Cylinder

LaTeX Go Maximum Temperature = Surface Temperature of Wall+(Internal Heat Generation*Radius of Cylinder^2)/(4*Thermal Conductivity)

Maximum Temperature in Solid Sphere

LaTeX Go Maximum Temperature = Surface Temperature of Wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)

Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

LaTeX Go Maximum Temperature = Surface Temperature+(Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)

Location of Maximum Temperature in Plane Wall with Symmetrical Boundary Conditions

LaTeX Go Location of Maximum Temperature = Wall Thickness/2

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

LaTeX Go

What is 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.

What is steady state conduction?

Steady-state conduction is the form of conduction that happens when the temperature difference(s) driving the conduction are constant.

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

Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius calculator 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 calculate 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 calculate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius using this online calculator? To use this online calculator 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. Here is how the Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius calculation can be explained with given input values -> 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)).

FAQ

What is Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius?

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 and is represented as T = q_G/(4*k)*(r_o^2-r^2)+T_o+ln(r/r_o)/ln(r_o/r_i)*(q_G/(4*k)*(r_o^2-r_i^2)+(T_o-T_i)) or 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)). 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, 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, The Outer Radius of Cylinder is a straight line from the center to the Cylinder's base to outer surface of the Cylinder, Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated, Outer Surface Temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc), The Inner Radius of Cylinder is a straight line from the center to the Cylinder's base to inner surface of the Cylinder & Inner Surface Temperature is the temperature at the inner surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).

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

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 is calculated using 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 calculate Temperature Inside Hollow Cylinder at given Radius between Inner and Outer Radius, you need 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). With our tool, you need to enter the respective value for Internal Heat Generation, Thermal Conductivity, Outer Radius of Cylinder, Radius, Outer Surface Temperature, Inner Radius of Cylinder & Inner Surface Temperature 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 Temperature?

In this formula, Temperature uses Internal Heat Generation, Thermal Conductivity, Outer Radius of Cylinder, Radius, Outer Surface Temperature, Inner Radius of Cylinder & Inner Surface Temperature. We can use 2 other way(s) to calculate the same, which is/are as follows -

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)

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