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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-(Given radius)^2))+Outer surface temperature+((ln(Given 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 = ((qG/(4*k))*((r₂)^2-(r)^2))+To+((ln(r/r₂)/ln(r₂/r₁))*((qG/(4*k))*((r₂)^2-(r₁)^2)+(To-Ti)))
This formula uses 1 Functions, 7 Variables
Functions Used
ln - Natural logarithm function (base e), ln(Number)
Variables Used
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. (Measured in Watt Per Cubic Metre)
Thermal Conductivity - Thermal Conductivity is the rate at which heat passes through a specified material, expressed as the amount of heat that flows per unit time through a unit area with a temperature gradient of one degree per unit distance. (Measured in Watt per Meter per K)
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. (Measured in Meter)
Given radius - Given radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated. (Measured in Meter)
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). (Measured in Kelvin)
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. (Measured in Meter)
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). (Measured in Kelvin)
STEP 1: Convert Input(s) to Base Unit
Internal heat generation: 100 Watt Per Cubic Metre --> 100 Watt Per Cubic Metre No Conversion Required
Thermal Conductivity: 10 Watt per Meter per K --> 10 Watt per Meter per K No Conversion Required
Outer Radius of Cylinder: 10 Meter --> 10 Meter No Conversion Required
Given radius: 4 Meter --> 4 Meter No Conversion Required
Outer surface temperature: 6 Kelvin --> 6 Kelvin No Conversion Required
Inner Radius of Cylinder: 1 Meter --> 1 Meter No Conversion Required
Inner surface temperature: 10 Kelvin --> 10 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = ((qG/(4*k))*((r₂)^2-(r)^2))+To+((ln(r/r₂)/ln(r₂/r₁))*((qG/(4*k))*((r₂)^2-(r₁)^2)+(To-Ti))) --> ((100/(4*10))*((10)^2-(4)^2))+6+((ln(4/10)/ln(10/1))*((100/(4*10))*((10)^2-(1)^2)+(6-10)))
Evaluating ... ...
T = 119.101607888359
STEP 3: Convert Result to Output's Unit
119.101607888359 Kelvin --> No Conversion Required
FINAL ANSWER
119.101607888359 Kelvin <-- Temperature
(Calculation completed in 00.016 seconds)

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Temperature at given thickness x inside plane wall surrounded by fluid
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 Go
Temperature inside solid cylinder at given radius immersed in fluid
temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Radius)^2)+Fluid temperature+(Internal heat generation*Cylinder Radius/(2*Convection heat transfer coefficient)) Go
Maximum temperature inside solid cylinder immersed in fluid
maximum_temperature = Fluid temperature+(((Internal heat generation*Cylinder Radius)/(4*Convection heat transfer coefficient))*(2+(Convection heat transfer coefficient*Cylinder Radius/Thermal Conductivity))) Go
Temperature inside plane wall at given thickness x with symmetrical boundary conditions
temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface temperature Go
Maximum temperature in plane wall surrounded by fluid with symmetrical boundary conditions
maximum_temperature = (Internal heat generation*(Wall thickness)^2/(8*Thermal Conductivity))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature Go
Temperature inside solid cylinder at given radius
temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Given radius)^2)+Surface temperature Go
Maximum temperature in solid sphere
maximum_temperature = Surface temperature+((Internal heat generation*(Radius of Sphere)^2)/(6*Thermal Conductivity)) Go
Maximum temperature in solid cylinder
maximum_temperature = Surface temperature+((Internal heat generation*(Cylinder Radius)^2)/(4*Thermal Conductivity)) Go
Maximum temperature in plane wall with symmetrical boundary conditions
maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity)) Go
Location of maximum temperature in plane wall with symmetrical boundary conditions
location_of_maximum_temperature = Wall thickness/2 Go

Temperature inside hollow cylinder at given radius between inner and outer radius Formula

temperature = ((Internal heat generation/(4*Thermal Conductivity))*((Outer Radius of Cylinder)^2-(Given radius)^2))+Outer surface temperature+((ln(Given 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 = ((qG/(4*k))*((r₂)^2-(r)^2))+To+((ln(r/r₂)/ln(r₂/r₁))*((qG/(4*k))*((r₂)^2-(r₁)^2)+(To-Ti)))

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-(Given radius)^2))+Outer surface temperature+((ln(Given 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 (qG), Thermal Conductivity (k), Outer Radius of Cylinder (r₂), Given radius (r), Outer surface temperature (To), Inner Radius of Cylinder (r₁) & Inner surface temperature (Ti) 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 -> 119.1016 = ((100/(4*10))*((10)^2-(4)^2))+6+((ln(4/10)/ln(10/1))*((100/(4*10))*((10)^2-(1)^2)+(6-10))).

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 = ((qG/(4*k))*((r₂)^2-(r)^2))+To+((ln(r/r₂)/ln(r₂/r₁))*((qG/(4*k))*((r₂)^2-(r₁)^2)+(To-Ti))) or temperature = ((Internal heat generation/(4*Thermal Conductivity))*((Outer Radius of Cylinder)^2-(Given radius)^2))+Outer surface temperature+((ln(Given 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 the rate at which heat passes through a specified material, expressed as the amount of heat that 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, Given 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-(Given radius)^2))+Outer surface temperature+((ln(Given 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 (qG), Thermal Conductivity (k), Outer Radius of Cylinder (r₂), Given radius (r), Outer surface temperature (To), Inner Radius of Cylinder (r₁) & Inner surface temperature (Ti). With our tool, you need to enter the respective value for Internal heat generation, Thermal Conductivity, Outer Radius of Cylinder, Given 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, Given radius, Outer surface temperature, Inner Radius of Cylinder & Inner surface temperature. We can use 10 other way(s) to calculate the same, which is/are as follows -
  • maximum_temperature = Surface temperature+((Internal heat generation*(Wall thickness)^2)/(8*Thermal Conductivity))
  • location_of_maximum_temperature = Wall thickness/2
  • maximum_temperature = Surface temperature+((Internal heat generation*(Cylinder Radius)^2)/(4*Thermal Conductivity))
  • maximum_temperature = Surface temperature+((Internal heat generation*(Radius of Sphere)^2)/(6*Thermal Conductivity))
  • temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Given radius)^2)+Surface temperature
  • temperature = (Internal heat generation/(4*Thermal Conductivity))*((Cylinder Radius)^2-(Radius)^2)+Fluid temperature+(Internal heat generation*Cylinder Radius/(2*Convection heat transfer coefficient))
  • temperature = -(((Internal heat generation*(Wall thickness)^2)/(2*Thermal Conductivity))*((Thickness/Wall thickness)-(Thickness/Wall thickness)^2))+Surface 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
  • maximum_temperature = (Internal heat generation*(Wall thickness)^2/(8*Thermal Conductivity))+(Internal heat generation*Wall thickness/(2*Convection heat transfer coefficient))+Fluid temperature
  • maximum_temperature = Fluid temperature+(((Internal heat generation*Cylinder Radius)/(4*Convection heat transfer coefficient))*(2+(Convection heat transfer coefficient*Cylinder Radius/Thermal Conductivity)))
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