Heat transfer between concentric spheres given both radii Calculator

✖Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.ⓘ Effective Thermal Conductivity [k_Eff]			+10% -10%
✖Inside Radius is a straight line from the centre to the inner circumference of a circle or sphere.ⓘ Inside Radius [r1]			+10% -10%
✖Outer Radius is a straight line from the centre to the outer circumference of a circle or sphere.ⓘ Outer Radius [r2]			+10% -10%
✖Temperature Difference is the measure of the hotness or the coldness of an object.ⓘ Temperature Difference [ΔT]			+10% -10%

✖Heat transfer is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings.ⓘ Heat transfer between concentric spheres given both radii [q]

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Formula

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Heat transfer between concentric spheres given both radii

Formula

`"q" = (4*pi*"k"_{"Eff"}*"r1"*"r2"*"ΔT")/("r2"-"r1")`

Example

`"72.88495W"=(4*pi*"10W/(m*K)"*"0.01m"*"0.02m"*"29K")/("0.02m"-"0.01m")`

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Heat transfer between concentric spheres given both radii Solution

STEP 0: Pre-Calculation Summary

Formula Used

Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius)
q = (4*pi*k_Eff*r1*r2*ΔT)/(r2-r1)
This formula uses 1 Constants, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Heat transfer - (Measured in Watt) - Heat transfer is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings.
Effective Thermal Conductivity - (Measured in Watt per Meter per K) - Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference.
Inside Radius - (Measured in Meter) - Inside Radius is a straight line from the centre to the inner circumference of a circle or sphere.
Outer Radius - (Measured in Meter) - Outer Radius is a straight line from the centre to the outer circumference of a circle or sphere.
Temperature Difference - (Measured in Kelvin) - Temperature Difference is the measure of the hotness or the coldness of an object.

STEP 1: Convert Input(s) to Base Unit

Effective Thermal Conductivity: 10 Watt per Meter per K --> 10 Watt per Meter per K No Conversion Required
Inside Radius: 0.01 Meter --> 0.01 Meter No Conversion Required
Outer Radius: 0.02 Meter --> 0.02 Meter No Conversion Required
Temperature Difference: 29 Kelvin --> 29 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

q = (4*pi*k_Eff*r1*r2*ΔT)/(r2-r1) --> (4*pi*10*0.01*0.02*29)/(0.02-0.01)

Evaluating ... ...

q = 72.8849495632832

STEP 3: Convert Result to Output's Unit

72.8849495632832 Watt --> No Conversion Required

FINAL ANSWER

72.8849495632832 ≈ 72.88495 Watt <-- Heat transfer

(Calculation completed in 00.004 seconds)

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Home » Physics » Heat and Mass Transfer » Convection » Free convection » Effective Thermal Conductivity and Heat Transfer » Heat transfer between concentric spheres given both radii

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 8 Effective Thermal Conductivity and Heat Transfer Calculators

Effective thermal conductivity for annular space between concentric cylinders

Go Effective Thermal Conductivity = Heat Transfer per Unit Length*((ln(Outside Diameter/Inside Diameter))/(2*pi)*(Inside Temperature-Outside Temperature))

Heat transfer per unit length for annular space between concentric cylinders

Go Heat Transfer per Unit Length = ((2*pi*Effective Thermal Conductivity)/(ln(Outside Diameter/Inside Diameter)))*(Inside Temperature-Outside Temperature)

Effective thermal conductivity for space between two concentric spheres

Go Effective Thermal Conductivity = Heat transfer/((pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length))

Heat transfer between concentric spheres given both diameters

Go Heat transfer = (Effective Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length)

Effective thermal conductivity

Go Effective Thermal Conductivity = (Heat transfer*(Outer Radius-Inside Radius))/(4*pi*Inside Radius*Outer Radius*Temperature Difference)

Heat transfer between concentric spheres given both radii

Go Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius)

Effective thermal conductivity given Prandtl number

Go Effective Thermal Conductivity = 0.386*Thermal Conductivity of Liquid*(((Prandtl Number)/(0.861+Prandtl Number))^0.25)*(Rayleigh Number(t))^0.25

Effective Thermal Conductivity given Rayleigh Number based on Turbulence

Go Effective Thermal Conductivity = Thermal Conductivity of Liquid*0.74*((Prandtl Number/(0.861+Prandtl Number))^0.25)*Rayleigh Number(t)^0.25

Heat transfer between concentric spheres given both radii Formula

Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius)
q = (4*pi*k_Eff*r1*r2*ΔT)/(r2-r1)

What is convection

Convection is the process of heat transfer by the bulk movement of molecules within fluids such as gases and liquids. The initial heat transfer between the object and the fluid takes place through conduction, but the bulk heat transfer happens due to the motion of the fluid.
Convection is the process of heat transfer in fluids by the actual motion of matter.
It happens in liquids and gases.
It may be natural or forced.
It involves a bulk transfer of portions of the fluid.

How to Calculate Heat transfer between concentric spheres given both radii?

Heat transfer between concentric spheres given both radii calculator uses Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius) to calculate the Heat transfer, The Heat transfer between concentric spheres given both radii formula is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings. Heat transfer is denoted by q symbol.

How to calculate Heat transfer between concentric spheres given both radii using this online calculator? To use this online calculator for Heat transfer between concentric spheres given both radii, enter Effective Thermal Conductivity (k_Eff), Inside Radius (r1), Outer Radius (r2) & Temperature Difference (ΔT) and hit the calculate button. Here is how the Heat transfer between concentric spheres given both radii calculation can be explained with given input values -> 72.88495 = (4*pi*10*0.01*0.02*29)/(0.02-0.01).

FAQ

What is Heat transfer between concentric spheres given both radii?

The Heat transfer between concentric spheres given both radii formula is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings and is represented as q = (4*pi*k_Eff*r1*r2*ΔT)/(r2-r1) or Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius). Effective Thermal Conductivity is the rate of heat transfer through a unit thickness of the material per unit area per unit temperature difference, Inside Radius is a straight line from the centre to the inner circumference of a circle or sphere, Outer Radius is a straight line from the centre to the outer circumference of a circle or sphere & Temperature Difference is the measure of the hotness or the coldness of an object.

How to calculate Heat transfer between concentric spheres given both radii?

The Heat transfer between concentric spheres given both radii formula is defined as the movement of heat across the border of the system due to a difference in temperature between the system and its surroundings is calculated using Heat transfer = (4*pi*Effective Thermal Conductivity*Inside Radius*Outer Radius*Temperature Difference)/(Outer Radius-Inside Radius). To calculate Heat transfer between concentric spheres given both radii, you need Effective Thermal Conductivity (k_Eff), Inside Radius (r1), Outer Radius (r2) & Temperature Difference (ΔT). With our tool, you need to enter the respective value for Effective Thermal Conductivity, Inside Radius, Outer Radius & Temperature Difference 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 Heat transfer?

In this formula, Heat transfer uses Effective Thermal Conductivity, Inside Radius, Outer Radius & Temperature Difference. We can use 1 other way(s) to calculate the same, which is/are as follows -

Heat transfer = (Effective Thermal Conductivity*pi*(Inside Temperature-Outside Temperature))*((Outside Diameter*Inside Diameter)/Length)

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