Maximum Temperature in Solid Sphere 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%
✖Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface.ⓘ Radius of Sphere [R_s]			+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%

✖Maximum Temperature is defined as the highest possible or permissible value of temperature.ⓘ Maximum Temperature in Solid Sphere [T_max]

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Formula

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Maximum Temperature in Solid Sphere

Formula

`"T"_{"max"} = "T"_{"w"}+("q"_{"G"}*"R"_{"s"}^2)/(6*"k")`

Example

`"500K"="273K"+("100W/m³"*("11.775042m")^2)/(6*"10.18W/(m*K)")`

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Maximum Temperature in Solid Sphere Solution

STEP 0: Pre-Calculation Summary

Formula Used

Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)
T_max = T_w+(q_G*R_s^2)/(6*k)
This formula uses 5 Variables

Variables Used

Maximum Temperature - (Measured in Kelvin) - Maximum Temperature is defined as the highest possible or permissible value of temperature.
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.
Radius of Sphere - (Measured in Meter) - Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface.
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.

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
Radius of Sphere: 11.775042 Meter --> 11.775042 Meter No Conversion Required
Thermal Conductivity: 10.18 Watt per Meter per K --> 10.18 Watt per Meter per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

T_max = T_w+(q_G*R_s^2)/(6*k) --> 273+(100*11.775042^2)/(6*10.18)

Evaluating ... ...

T_max = 500.000023087367

STEP 3: Convert Result to Output's Unit

500.000023087367 Kelvin --> No Conversion Required

FINAL ANSWER

500.000023087367 ≈ 500 Kelvin <-- Maximum Temperature

(Calculation completed in 00.004 seconds)

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< 14 Steady State Heat Conduction with Heat Generation Calculators

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

Go 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))

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

Go 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)

Temperature Inside Solid Cylinder at given Radius Immersed in Fluid

Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)

Temperature at given Thickness x Inside Plane Wall Surrounded by Fluid

Go 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 Inside Solid Cylinder Immersed in Fluid

Go Maximum Temperature = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder*(2+(Convection Heat Transfer Coefficient*Radius of Cylinder)/Thermal Conductivity))/(4*Convection Heat Transfer Coefficient)

Maximum Temperature in Plane Wall Surrounded by Fluid with Symmetrical Boundary Conditions

Go Maximum Temperature of Plain Wall = (Internal Heat Generation*Wall Thickness^2)/(8*Thermal Conductivity)+(Internal Heat Generation*Wall Thickness)/(2*Convection Heat Transfer Coefficient)+Fluid Temperature

Temperature Inside Plane Wall at given Thickness x with Symmetrical Boundary Conditions

Go Temperature 1 = -(Internal Heat Generation*Wall Thickness^2)/(2*Thermal Conductivity)*(Thickness/Wall Thickness-(Thickness/Wall Thickness)^2)+Surface Temperature

Temperature Inside Solid Cylinder at given Radius

Go Temperature Solid Cylinder = Internal Heat Generation/(4*Thermal Conductivity)*(Radius of Cylinder^2-Radius^2)+Surface Temperature of wall

Temperature Inside Solid Sphere at given Radius

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

Surface Temperature of Solid Cylinder Immersed in Fluid

Go Surface Temperature of wall = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder)/(2*Convection Heat Transfer Coefficient)

Maximum Temperature in Solid Cylinder

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

Maximum Temperature in Solid Sphere

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

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

Go Location of Maximum Temperature = Wall Thickness/2

Maximum Temperature in Solid Sphere Formula

Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity)
T_max = T_w+(q_G*R_s^2)/(6*k)

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.

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.

How to Calculate Maximum Temperature in Solid Sphere?

Maximum Temperature in Solid Sphere calculator uses Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity) to calculate the Maximum Temperature, The Maximum temperature in solid sphere formula gives the value of maximum temperature when there is an internal heat generation source inside the sphere. Maximum Temperature is denoted by T_max symbol.

How to calculate Maximum Temperature in Solid Sphere using this online calculator? To use this online calculator for Maximum Temperature in Solid Sphere, enter Surface Temperature of wall (T_w), Internal Heat Generation (q_G), Radius of Sphere (R_s) & Thermal Conductivity (k) and hit the calculate button. Here is how the Maximum Temperature in Solid Sphere calculation can be explained with given input values -> 456.5064 = 273+(100*11.775042^2)/(6*10.18).

FAQ

What is Maximum Temperature in Solid Sphere?

The Maximum temperature in solid sphere formula gives the value of maximum temperature when there is an internal heat generation source inside the sphere and is represented as T_max = T_w+(q_G*R_s^2)/(6*k) or Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity). 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, Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface & 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.

How to calculate Maximum Temperature in Solid Sphere?

The Maximum temperature in solid sphere formula gives the value of maximum temperature when there is an internal heat generation source inside the sphere is calculated using Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Sphere^2)/(6*Thermal Conductivity). To calculate Maximum Temperature in Solid Sphere, you need Surface Temperature of wall (T_w), Internal Heat Generation (q_G), Radius of Sphere (R_s) & Thermal Conductivity (k). With our tool, you need to enter the respective value for Surface Temperature of wall, Internal Heat Generation, Radius of Sphere & Thermal Conductivity 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 Maximum Temperature?

In this formula, Maximum Temperature uses Surface Temperature of wall, Internal Heat Generation, Radius of Sphere & Thermal Conductivity. We can use 3 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)
Maximum Temperature = Surface Temperature of wall+(Internal Heat Generation*Radius of Cylinder^2)/(4*Thermal Conductivity)
Maximum Temperature = Fluid Temperature+(Internal Heat Generation*Radius of Cylinder*(2+(Convection Heat Transfer Coefficient*Radius of Cylinder)/Thermal Conductivity))/(4*Convection Heat Transfer Coefficient)

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