Temperature Inside Solid Sphere at given 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%
✖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%
✖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%

✖Temperature 2 is the degree or intensity of heat present in a substance or object.ⓘ Temperature Inside Solid Sphere at given Radius [t₂]

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Formula

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Temperature Inside Solid Sphere at given Radius

Formula

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

Example

`"473.8049K"="273K"+"100W/m³"/(6*"10.18W/(m*K)")*(("11.775042m")^2-("4m")^2)`

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Temperature Inside Solid Sphere at given Radius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2)
t₂ = T_w+q_G/(6*k)*(R_s^2-r^2)
This formula uses 6 Variables

Variables Used

Temperature 2 - (Measured in Kelvin) - Temperature 2 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.
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.
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.

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
Radius of Sphere: 11.775042 Meter --> 11.775042 Meter No Conversion Required
Radius: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

t₂ = T_w+q_G/(6*k)*(R_s^2-r^2) --> 273+100/(6*10.18)*(11.775042^2-4^2)

Evaluating ... ...

t₂ = 473.804869190838

STEP 3: Convert Result to Output's Unit

473.804869190838 Kelvin --> No Conversion Required

FINAL ANSWER

473.804869190838 ≈ 473.8049 Kelvin <-- Temperature 2

(Calculation completed in 00.010 seconds)

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Home » Physics » Heat and Mass Transfer » Conduction » Steady State Heat Conduction with Heat Generation » Temperature Inside Solid Sphere at given Radius

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Created by Ravi Khiyani

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

Ravi Khiyani has created this Calculator and 200+ more calculators!

Verified by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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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

Temperature Inside Solid Sphere at given Radius Formula

Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2)
t₂ = T_w+q_G/(6*k)*(R_s^2-r^2)

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 thermal conductivity?

The thermal conductivity of a material is a measure of its ability to conduct heat. It is generally denoted by the symbol ‘k’ but can also be denoted by ‘λ’ and ‘κ’.

How to Calculate Temperature Inside Solid Sphere at given Radius?

Temperature Inside Solid Sphere at given Radius calculator uses Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2) to calculate the Temperature 2, The Temperature inside solid sphere at given radius formula gives the value of temperature at the desired radius inside the sphere which is provided with an internal heat generation source. Temperature 2 is denoted by t₂ symbol.

How to calculate Temperature Inside Solid Sphere at given Radius using this online calculator? To use this online calculator for Temperature Inside Solid Sphere at given Radius, enter Surface Temperature of wall (T_w), Internal Heat Generation (q_G), Thermal Conductivity (k), Radius of Sphere (R_s) & Radius (r) and hit the calculate button. Here is how the Temperature Inside Solid Sphere at given Radius calculation can be explained with given input values -> 473.8049 = 273+100/(6*10.18)*(11.775042^2-4^2).

FAQ

What is Temperature Inside Solid Sphere at given Radius?

The Temperature inside solid sphere at given radius formula gives the value of temperature at the desired radius inside the sphere which is provided with an internal heat generation source and is represented as t₂ = T_w+q_G/(6*k)*(R_s^2-r^2) or Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2). 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, Radius of Sphere is a line segment extending from the center of a sphere to the circumference or bounding surface & Radius is the radial distance to the point or plane up to which the value of the desired variable will be calculated.

How to calculate Temperature Inside Solid Sphere at given Radius?

The Temperature inside solid sphere at given radius formula gives the value of temperature at the desired radius inside the sphere which is provided with an internal heat generation source is calculated using Temperature 2 = Surface Temperature of wall+Internal Heat Generation/(6*Thermal Conductivity)*(Radius of Sphere^2-Radius^2). To calculate Temperature Inside Solid Sphere at given Radius, you need Surface Temperature of wall (T_w), Internal Heat Generation (q_G), Thermal Conductivity (k), Radius of Sphere (R_s) & Radius (r). With our tool, you need to enter the respective value for Surface Temperature of wall, Internal Heat Generation, Thermal Conductivity, Radius of Sphere & Radius and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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