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 = (Ti-To)/((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 = (Ti-To)/((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)

Credits

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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!
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Amrita School of Engineering (ASE), Vallikavu
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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
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 = (Ti-To)/((r2-r1)/(4*pi*k*r1*r2))

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 (Ti), Outer Surface Temperature (To), 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 = (Ti-To)/((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 (Ti), Outer Surface Temperature (To), 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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