Heat Flow Rate through Spherical Wall Calculator

✖Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.ⓘ Inner Surface Temperature [T_i]			+10% -10%
✖Outer Surface Temperature is the temperature at the outer surface of the wall either plane wall or cylindrical wall or spherical wall, etc.ⓘ Outer Surface Temperature [T_o]			+10% -10%
✖Radius of 2nd Concentric Sphere is the distance from the center of the concentric spheres to any point on the second concentric sphere or radius of the second sphere.ⓘ Radius of 2nd Concentric Sphere [r₂]			+10% -10%
✖Radius of 1st Concentric Sphere is the distance from the center of the concentric spheres to any point on the first concentric sphere or radius of the first sphere.ⓘ Radius of 1st Concentric Sphere [r₁]			+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%

✖Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.ⓘ Heat Flow Rate through Spherical Wall [Q]

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Heat Flow Rate through Spherical Wall Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere))
Q = (T_i-T_o)/((r₂-r₁)/(4*pi*k*r₁*r₂))
This formula uses 1 Constants, 6 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Heat Flow Rate - (Measured in Watt) - Heat Flow Rate is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium.
Inner Surface Temperature - (Measured in Kelvin) - Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.
Outer Surface Temperature - (Measured in Kelvin) - Outer Surface Temperature is the temperature at the outer surface of the wall either plane wall or cylindrical wall or spherical wall, etc.
Radius of 2nd Concentric Sphere - (Measured in Meter) - Radius of 2nd Concentric Sphere is the distance from the center of the concentric spheres to any point on the second concentric sphere or radius of the second sphere.
Radius of 1st Concentric Sphere - (Measured in Meter) - Radius of 1st Concentric Sphere is the distance from the center of the concentric spheres to any point on the first concentric sphere or radius of the first sphere.
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

Inner Surface Temperature: 305 Kelvin --> 305 Kelvin No Conversion Required
Outer Surface Temperature: 300 Kelvin --> 300 Kelvin No Conversion Required
Radius of 2nd Concentric Sphere: 6 Meter --> 6 Meter No Conversion Required
Radius of 1st Concentric Sphere: 5 Meter --> 5 Meter No Conversion Required
Thermal Conductivity: 2 Watt per Meter per K --> 2 Watt per Meter per K No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

Q = (T_i-T_o)/((r₂-r₁)/(4*pi*k*r₁*r₂)) --> (305-300)/((6-5)/(4*pi*2*5*6))

Evaluating ... ...

Q = 3769.91118430775

STEP 3: Convert Result to Output's Unit

3769.91118430775 Watt --> No Conversion Required

FINAL ANSWER

3769.91118430775 ≈ 3769.911 Watt <-- Heat Flow Rate

(Calculation completed in 00.004 seconds)

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Credits

Created by Sai Venkata Phanindra Chary Arendra

Vallurupalli Nageswara Rao Vignana Jyothi Institute of Engineering and Technology (VNRVJIET), Hyderabad

Sai Venkata Phanindra Chary Arendra has created this Calculator and 100+ more calculators!

Verified by Sanjay Krishna

Amrita School of Engineering (ASE), Vallikavu

Sanjay Krishna has verified this Calculator and 200+ more calculators!

< Conduction in Sphere Calculators

Total Thermal Resistance of Spherical wall of 3 Layers without Convection

LaTeX Go Sphere Thermal Resistance = (Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity of 1st Body*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)+(Radius of 3rd Concentric Sphere-Radius of 2nd Concentric Sphere)/(4*pi*Thermal Conductivity of 2nd Body*Radius of 2nd Concentric Sphere*Radius of 3rd Concentric Sphere)+(Radius of 4th Concentric Sphere-Radius of 3rd Concentric Sphere)/(4*pi*Thermal Conductivity of 3rd Body*Radius of 3rd Concentric Sphere*Radius of 4th Concentric Sphere)

Total Thermal Resistance of Spherical Wall of 2 Layers without Convection

LaTeX Go Sphere Thermal Resistance Without Convection = (Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity of 1st Body*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)+(Radius of 3rd Concentric Sphere-Radius of 2nd Concentric Sphere)/(4*pi*Thermal Conductivity of 2nd Body*Radius of 2nd Concentric Sphere*Radius of 3rd Concentric Sphere)

Total Thermal Resistance of Spherical Wall with Convection on Both Side

LaTeX Go Sphere Thermal Resistance = 1/(4*pi*Radius of 1st Concentric Sphere^2*Inner Convection Heat Transfer Coefficient)+(Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)+1/(4*pi*Radius of 2nd Concentric Sphere^2*External Convection Heat Transfer Coefficient)

Convection Resistance for Spherical Layer

LaTeX Go Thermal Resistance of Sphere Without Convection = 1/(4*pi*Radius of Sphere^2*Convection Heat Transfer Coefficient)

Heat Flow Rate through Spherical Wall Formula

LaTeX Go

What is heat flow rate?

The rate of heat flow is the amount of heat that is transferred per unit of time in some material, usually measured in watt. Heat is the flow of thermal energy driven by thermal non-equilibrium

How to Calculate Heat Flow Rate through Spherical Wall?

Heat Flow Rate through Spherical Wall calculator uses Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)) to calculate the Heat Flow Rate, The Heat Flow Rate through Spherical Wall formula is the rate of heat flow through a spherical wall when inner and outer surface temperatures, radii, and thermal conductivity of the material of the wall are known. Heat Flow Rate is denoted by Q symbol.

How to calculate Heat Flow Rate through Spherical Wall using this online calculator? To use this online calculator for Heat Flow Rate through Spherical Wall, enter Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Concentric Sphere (r₂), Radius of 1st Concentric Sphere (r₁) & Thermal Conductivity (k) and hit the calculate button. Here is how the Heat Flow Rate through Spherical Wall calculation can be explained with given input values -> 3769.911 = (305-300)/((6-5)/(4*pi*2*5*6)).

FAQ

What is Heat Flow Rate through Spherical Wall?

The Heat Flow Rate through Spherical Wall formula is the rate of heat flow through a spherical wall when inner and outer surface temperatures, radii, and thermal conductivity of the material of the wall are known and is represented as Q = (T_i-T_o)/((r₂-r₁)/(4*pi*k*r₁*r₂)) or Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)). Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc, Outer Surface Temperature is the temperature at the outer surface of the wall either plane wall or cylindrical wall or spherical wall, etc, Radius of 2nd Concentric Sphere is the distance from the center of the concentric spheres to any point on the second concentric sphere or radius of the second sphere, Radius of 1st Concentric Sphere is the distance from the center of the concentric spheres to any point on the first concentric sphere or radius of the first sphere & 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 Heat Flow Rate through Spherical Wall?

The Heat Flow Rate through Spherical Wall formula is the rate of heat flow through a spherical wall when inner and outer surface temperatures, radii, and thermal conductivity of the material of the wall are known is calculated using Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((Radius of 2nd Concentric Sphere-Radius of 1st Concentric Sphere)/(4*pi*Thermal Conductivity*Radius of 1st Concentric Sphere*Radius of 2nd Concentric Sphere)). To calculate Heat Flow Rate through Spherical Wall, you need Inner Surface Temperature (T_i), Outer Surface Temperature (T_o), Radius of 2nd Concentric Sphere (r₂), Radius of 1st Concentric Sphere (r₁) & Thermal Conductivity (k). With our tool, you need to enter the respective value for Inner Surface Temperature, Outer Surface Temperature, Radius of 2nd Concentric Sphere, Radius of 1st Concentric Sphere & Thermal Conductivity 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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