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Temperature inside hollow sphere at given radius between inner and outer radius Solution

STEP 0: Pre-Calculation Summary
Formula Used
temperature = Surface temperature+((Internal heat generation/(6*Thermal Conductivity))*((Outer Radius)^2-(Given radius)^2))+(((Internal heat generation*(Inner Radius)^3)/(3*Thermal Conductivity))*((1/Outer Radius)-(1/Given radius)))
T = Tw+((qG/(6*k))*((router)^2-(r)^2))+(((qG*(rinner)^3)/(3*k))*((1/router)-(1/r)))
This formula uses 6 Variables
Variables Used
Surface temperature - Surface temperature is the temperature at or near a surface. Specifically, it may refer to: Surface air temperature, the temperature of the air near the surface of the earth. .. (Measured in Kelvin)
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 - Outer Radius is the radius of the larger of the two concentric circles that form its boundary. (Measured in Centimeter)
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)
Inner Radius - Inner Radius of any figure is the radius of its cavity. It is the smaller radius among two concentric circles. (Measured in Centimeter)
STEP 1: Convert Input(s) to Base Unit
Surface temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
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: 10 Centimeter --> 0.1 Meter (Check conversion here)
Given radius: 4 Meter --> 4 Meter No Conversion Required
Inner Radius: 5 Centimeter --> 0.05 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
T = Tw+((qG/(6*k))*((router)^2-(r)^2))+(((qG*(rinner)^3)/(3*k))*((1/router)-(1/r))) --> 300+((100/(6*10))*((0.1)^2-(4)^2))+(((100*(0.05)^3)/(3*10))*((1/0.1)-(1/4)))
Evaluating ... ...
T = 273.3540625
STEP 3: Convert Result to Output's Unit
273.3540625 Kelvin --> No Conversion Required
FINAL ANSWER
273.3540625 Kelvin <-- Temperature
(Calculation completed in 00.031 seconds)

10+ Steady state heat conduction with heat generation Calculators

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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 sphere at given radius between inner and outer radius Formula

temperature = Surface temperature+((Internal heat generation/(6*Thermal Conductivity))*((Outer Radius)^2-(Given radius)^2))+(((Internal heat generation*(Inner Radius)^3)/(3*Thermal Conductivity))*((1/Outer Radius)-(1/Given radius)))
T = Tw+((qG/(6*k))*((router)^2-(r)^2))+(((qG*(rinner)^3)/(3*k))*((1/router)-(1/r)))

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 sphere at given radius between inner and outer radius?

Temperature inside hollow sphere at given radius between inner and outer radius calculator uses temperature = Surface temperature+((Internal heat generation/(6*Thermal Conductivity))*((Outer Radius)^2-(Given radius)^2))+(((Internal heat generation*(Inner Radius)^3)/(3*Thermal Conductivity))*((1/Outer Radius)-(1/Given radius))) to calculate the Temperature, The Temperature inside hollow sphere at given radius between inner and outer radius formula gives the value of temperature along with the thickness of the hollow sphere provided with an internal heat generation source. Temperature is denoted by T symbol.

How to calculate Temperature inside hollow sphere at given radius between inner and outer radius using this online calculator? To use this online calculator for Temperature inside hollow sphere at given radius between inner and outer radius, enter Surface temperature (Tw), Internal heat generation (qG), Thermal Conductivity (k), Outer Radius (router), Given radius (r) & Inner Radius (rinner) and hit the calculate button. Here is how the Temperature inside hollow sphere at given radius between inner and outer radius calculation can be explained with given input values -> 273.3541 = 300+((100/(6*10))*((0.1)^2-(4)^2))+(((100*(0.05)^3)/(3*10))*((1/0.1)-(1/4))) .

FAQ

What is Temperature inside hollow sphere at given radius between inner and outer radius?
The Temperature inside hollow sphere at given radius between inner and outer radius formula gives the value of temperature along with the thickness of the hollow sphere provided with an internal heat generation source and is represented as T = Tw+((qG/(6*k))*((router)^2-(r)^2))+(((qG*(rinner)^3)/(3*k))*((1/router)-(1/r))) or temperature = Surface temperature+((Internal heat generation/(6*Thermal Conductivity))*((Outer Radius)^2-(Given radius)^2))+(((Internal heat generation*(Inner Radius)^3)/(3*Thermal Conductivity))*((1/Outer Radius)-(1/Given radius))) . Surface temperature is the temperature at or near a surface. Specifically, it may refer to: Surface air temperature, the temperature of the air near the surface of the earth. , 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, Outer Radius is the radius of the larger of the two concentric circles that form its boundary, Given radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated & Inner Radius of any figure is the radius of its cavity. It is the smaller radius among two concentric circles.
How to calculate Temperature inside hollow sphere at given radius between inner and outer radius?
The Temperature inside hollow sphere at given radius between inner and outer radius formula gives the value of temperature along with the thickness of the hollow sphere provided with an internal heat generation source is calculated using temperature = Surface temperature+((Internal heat generation/(6*Thermal Conductivity))*((Outer Radius)^2-(Given radius)^2))+(((Internal heat generation*(Inner Radius)^3)/(3*Thermal Conductivity))*((1/Outer Radius)-(1/Given radius))) . To calculate Temperature inside hollow sphere at given radius between inner and outer radius, you need Surface temperature (Tw), Internal heat generation (qG), Thermal Conductivity (k), Outer Radius (router), Given radius (r) & Inner Radius (rinner). With our tool, you need to enter the respective value for Surface temperature, Internal heat generation, Thermal Conductivity, Outer Radius, Given radius & Inner Radius 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 Surface temperature, Internal heat generation, Thermal Conductivity, Outer Radius, Given radius & Inner Radius. 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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