Thermal resistance of pipe with eccentric lagging Solution

STEP 0: Pre-Calculation Summary
Formula Used
Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))))
rth = (1/(2*pi*ke*Le))*(ln((sqrt(((r2+r1)^2)-e^2)+sqrt(((r2-r1)^2)-e^2))/(sqrt(((r2+r1)^2)-e^2)-sqrt(((r2-r1)^2)-e^2))))
This formula uses 1 Constants, 2 Functions, 6 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
ln - The natural logarithm, also known as the logarithm to the base e, is the inverse function of the natural exponential function., ln(Number)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Eccentric Lagging Thermal Resistance - (Measured in Kelvin per Watt) - Eccentric Lagging Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow.
Eccentric Lagging Thermal Conductivity - (Measured in Watt per Meter per K) - Eccentric Lagging Thermal Conductivity is expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance.
Eccentric Lagging Length - (Measured in Meter) - Eccentric Lagging Length is the measurement or extent of something from end to end.
Radius 2 - (Measured in Meter) - Radius 2 is the radius of the second concentric circle or circle.
Radius 1 - (Measured in Meter) - Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle.
Distance Between Centers of Eccentric Circles - (Measured in Meter) - Distance Between Centers of Eccentric Circles is the distance between the centres of two circles that are eccentric to each other.
STEP 1: Convert Input(s) to Base Unit
Eccentric Lagging Thermal Conductivity: 15 Watt per Meter per K --> 15 Watt per Meter per K No Conversion Required
Eccentric Lagging Length: 7 Meter --> 7 Meter No Conversion Required
Radius 2: 12.1 Meter --> 12.1 Meter No Conversion Required
Radius 1: 4 Meter --> 4 Meter No Conversion Required
Distance Between Centers of Eccentric Circles: 1.4 Meter --> 1.4 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
rth = (1/(2*pi*ke*Le))*(ln((sqrt(((r2+r1)^2)-e^2)+sqrt(((r2-r1)^2)-e^2))/(sqrt(((r2+r1)^2)-e^2)-sqrt(((r2-r1)^2)-e^2)))) --> (1/(2*pi*15*7))*(ln((sqrt(((12.1+4)^2)-1.4^2)+sqrt(((12.1-4)^2)-1.4^2))/(sqrt(((12.1+4)^2)-1.4^2)-sqrt(((12.1-4)^2)-1.4^2))))
Evaluating ... ...
rth = 0.00165481550104387
STEP 3: Convert Result to Output's Unit
0.00165481550104387 Kelvin per Watt --> No Conversion Required
FINAL ANSWER
0.00165481550104387 โ‰ˆ 0.001655 Kelvin per Watt <-- Eccentric Lagging Thermal Resistance
(Calculation completed in 00.004 seconds)

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11 Other shapes Calculators

Inner surface temperature of pipe with eccentric lagging
Go Eccentric Lagging Inner Surface Temperature = (Eccentric Lagging Heat Flow Rate*((1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))))))+Eccentric Lagging Outer Surface Temperature
Outer surface temperature of pipe with eccentric lagging
Go Eccentric Lagging Outer Surface Temperature = Eccentric Lagging Inner Surface Temperature-(Eccentric Lagging Heat Flow Rate*((1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))))))
Heat flow rate through pipe with eccentric lagging
Go Eccentric Lagging Heat Flow Rate = (Eccentric Lagging Inner Surface Temperature-Eccentric Lagging Outer Surface Temperature)/((1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))))
Thermal conductivity for pipe with eccentric lagging
Go Eccentric Lagging Thermal Conductivity = (Eccentric Lagging Heat Flow Rate*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))))/(2*pi*Eccentric Lagging Length*(Eccentric Lagging Inner Surface Temperature-Eccentric Lagging Outer Surface Temperature))
Length of pipe with eccentric lagging
Go Eccentric Lagging Length = (Eccentric Lagging Heat Flow Rate*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))))/(2*pi*Eccentric Lagging Thermal Conductivity*(Eccentric Lagging Inner Surface Temperature-Eccentric Lagging Outer Surface Temperature))
Thermal resistance of pipe with eccentric lagging
Go Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))))
Heat flow through pipe in square section
Go Heat Flow Rate = (Inner Surface Temperature-Outer Surface Temperature)/((1/(2*pi*Length))*((1/(Inside Convection*Cylinder Radius))+((Length/Thermal Conductivity)*ln((1.08*Side of Square)/(2*Cylinder Radius)))+(pi/(2*External Convection*Side of Square))))
Inner surface temperature of pipe in square section
Go Inner Surface Temperature = (Heat Flow Rate*(1/(2*pi*Length))*((1/(Inside Convection*Cylinder Radius))+((Length/Thermal Conductivity)*ln((1.08*Side of Square)/(2*Cylinder Radius)))+(pi/(2*External Convection*Side of Square))))+Outer Surface Temperature
Outer surface temperature of pipe in square section
Go Outer Surface Temperature = Inner Surface Temperature-(Heat Flow Rate*(1/(2*pi*Length))*((1/(Inside Convection*Cylinder Radius))+((Length/Thermal Conductivity)*ln((1.08*Side of Square)/(2*Cylinder Radius)))+(pi/(2*External Convection*Side of Square))))
Thermal Resistance for Pipe in Square Section
Go Thermal Resistance = (1/(2*pi*Length))*((1/(Inside Convection*Cylinder Radius))+((Length/Thermal Conductivity)*ln((1.08*Side of Square)/(2*Cylinder Radius)))+(pi/(2*External Convection*Side of Square)))
Average Nusselt Number for Bingham Plastic Fluids from Isothermal Semi-Circular Cylinder
Go Average Nusselt Number = (1+(0.0023*Modified Prandtl Number))^(-1.23)* ((0.51)*((Modified Rayleigh Number)^(0.25)))+ Nusselt Number

Thermal resistance of pipe with eccentric lagging Formula

Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))))
rth = (1/(2*pi*ke*Le))*(ln((sqrt(((r2+r1)^2)-e^2)+sqrt(((r2-r1)^2)-e^2))/(sqrt(((r2+r1)^2)-e^2)-sqrt(((r2-r1)^2)-e^2))))

What are eccentric circles?

Eccentric circles are circles that lie one inside the other and do not share the same center and do not intersect each other.

How to Calculate Thermal resistance of pipe with eccentric lagging?

Thermal resistance of pipe with eccentric lagging calculator uses Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))) to calculate the Eccentric Lagging Thermal Resistance, The Thermal resistance of pipe with eccentric lagging formula is defined as the thermal resistance offered by a pipe with eccentric lagging. Eccentric Lagging Thermal Resistance is denoted by rth symbol.

How to calculate Thermal resistance of pipe with eccentric lagging using this online calculator? To use this online calculator for Thermal resistance of pipe with eccentric lagging, enter Eccentric Lagging Thermal Conductivity (ke), Eccentric Lagging Length (Le), Radius 2 (r2), Radius 1 (r1) & Distance Between Centers of Eccentric Circles (e) and hit the calculate button. Here is how the Thermal resistance of pipe with eccentric lagging calculation can be explained with given input values -> 0.001655 = (1/(2*pi*15*7))*(ln((sqrt(((12.1+4)^2)-1.4^2)+sqrt(((12.1-4)^2)-1.4^2))/(sqrt(((12.1+4)^2)-1.4^2)-sqrt(((12.1-4)^2)-1.4^2)))).

FAQ

What is Thermal resistance of pipe with eccentric lagging?
The Thermal resistance of pipe with eccentric lagging formula is defined as the thermal resistance offered by a pipe with eccentric lagging and is represented as rth = (1/(2*pi*ke*Le))*(ln((sqrt(((r2+r1)^2)-e^2)+sqrt(((r2-r1)^2)-e^2))/(sqrt(((r2+r1)^2)-e^2)-sqrt(((r2-r1)^2)-e^2)))) or Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))). Eccentric Lagging Thermal Conductivity is expressed as amount of heat flows per unit time through a unit area with a temperature gradient of one degree per unit distance, Eccentric Lagging Length is the measurement or extent of something from end to end, Radius 2 is the radius of the second concentric circle or circle, Radius 1 is the distance from the center of the concentric circles to any point on the first/smallest concentric circle or the radius of the first circle & Distance Between Centers of Eccentric Circles is the distance between the centres of two circles that are eccentric to each other.
How to calculate Thermal resistance of pipe with eccentric lagging?
The Thermal resistance of pipe with eccentric lagging formula is defined as the thermal resistance offered by a pipe with eccentric lagging is calculated using Eccentric Lagging Thermal Resistance = (1/(2*pi*Eccentric Lagging Thermal Conductivity*Eccentric Lagging Length))*(ln((sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)+sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2))/(sqrt(((Radius 2+Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)-sqrt(((Radius 2-Radius 1)^2)-Distance Between Centers of Eccentric Circles^2)))). To calculate Thermal resistance of pipe with eccentric lagging, you need Eccentric Lagging Thermal Conductivity (ke), Eccentric Lagging Length (Le), Radius 2 (r2), Radius 1 (r1) & Distance Between Centers of Eccentric Circles (e). With our tool, you need to enter the respective value for Eccentric Lagging Thermal Conductivity, Eccentric Lagging Length, Radius 2, Radius 1 & Distance Between Centers of Eccentric Circles 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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