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

✖Surface Temperature of wall is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.ⓘ Surface Temperature of Wall [T_w]			+10% -10%
✖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 sphere any figure is the radius of a larger circle of the two concentric circles that form its boundary.ⓘ Outer Radius of Sphere [r₂]			+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%
✖The Inner Radius of sphere any figure is the radius of its cavity and the smaller radius among two concentric circles.ⓘ Inner Radius of Sphere [r₁]			+10% -10%

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

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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 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)
T = T_w+q_G/(6*k)*(r₂^2-r^2)+(q_G*r₁^3)/(3*k)*(1/r₂-1/r)
This formula uses 7 Variables

Variables Used

Temperature - (Measured in Kelvin) - Temperature is the degree or intensity of heat present in a substance or object.
Surface Temperature of Wall - (Measured in Kelvin) - Surface Temperature of wall is the temperature at or near a surface. Specifically, it may refer to as Surface air temperature, the temperature of the air near the surface of the earth.
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 Sphere - (Measured in Meter) - The Outer Radius of sphere any figure is the radius of a larger circle of the two concentric circles that form its boundary.
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.
Inner Radius of Sphere - (Measured in Meter) - The Inner Radius of sphere any figure is the radius of its cavity and the smaller radius among two concentric circles.

STEP 1: Convert Input(s) to Base Unit

Surface Temperature of Wall: 273 Kelvin --> 273 Kelvin No Conversion Required
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 Sphere: 2 Meter --> 2 Meter No Conversion Required
Radius: 4 Meter --> 4 Meter No Conversion Required
Inner Radius of Sphere: 6.320027 Meter --> 6.320027 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T = T_w+q_G/(6*k)*(r₂^2-r^2)+(q_G*r₁^3)/(3*k)*(1/r₂-1/r) --> 273+100/(6*10.18)*(2^2-4^2)+(100*6.320027^3)/(3*10.18)*(1/2-1/4)

Evaluating ... ...

T = 460.00000274085

STEP 3: Convert Result to Output's Unit

460.00000274085 Kelvin --> No Conversion Required

FINAL ANSWER

460.00000274085 ≈ 460 Kelvin <-- Temperature

(Calculation completed in 00.004 seconds)

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

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Shri Govindram Seksaria Institute of Technology and Science (SGSITS), Indore

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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 Sphere at given Radius between Inner and Outer Radius Formula

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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 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) 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 of Wall (T_w), Internal Heat Generation (q_G), Thermal Conductivity (k), Outer Radius of Sphere (r₂), Radius (r) & Inner Radius of Sphere (r₁) 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 -> 238.4648 = 273+100/(6*10.18)*(2^2-4^2)+(100*6.320027^3)/(3*10.18)*(1/2-1/4).

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 = T_w+q_G/(6*k)*(r₂^2-r^2)+(q_G*r₁^3)/(3*k)*(1/r₂-1/r) or 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). Surface Temperature of wall is the temperature at or near a surface. Specifically, it may refer to as 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 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 sphere any figure is the radius of a larger circle of the two concentric circles that form its boundary, Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated & The Inner Radius of sphere any figure is the radius of its cavity and 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 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). To calculate Temperature Inside Hollow Sphere at given Radius between Inner and Outer Radius, you need Surface Temperature of Wall (T_w), Internal Heat Generation (q_G), Thermal Conductivity (k), Outer Radius of Sphere (r₂), Radius (r) & Inner Radius of Sphere (r₁). With our tool, you need to enter the respective value for Surface Temperature of Wall, Internal Heat Generation, Thermal Conductivity, Outer Radius of Sphere, Radius & Inner Radius of Sphere 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 of Wall, Internal Heat Generation, Thermal Conductivity, Outer Radius of Sphere, Radius & Inner Radius of Sphere. 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 = 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))

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