Heat flow rate through pipe with eccentric lagging Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))))
Qe = (Tie-Toe)/((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, 8 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 Heat Flow Rate - (Measured in Watt) - Eccentric lagging Heat Flow Rate is the amount of heat that is transferred per unit of time in some material. Heat is the flow of thermal energy driven by thermal non-equilibrium.
Eccentric Lagging Inner Surface Temperature - (Measured in Kelvin) - Eccentric Lagging Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc.
Eccentric Lagging Outer Surface Temperature - (Measured in Kelvin) - Eccentric Lagging Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc).
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 Inner Surface Temperature: 25 Kelvin --> 25 Kelvin No Conversion Required
Eccentric Lagging Outer Surface Temperature: 20 Kelvin --> 20 Kelvin No Conversion Required
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
Qe = (Tie-Toe)/((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))))) --> (25-20)/((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 ... ...
Qe = 3021.48487057679
STEP 3: Convert Result to Output's Unit
3021.48487057679 Watt --> No Conversion Required
FINAL ANSWER
3021.48487057679 3021.485 Watt <-- Eccentric Lagging Heat Flow Rate
(Calculation completed in 00.020 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

Heat flow rate through pipe with eccentric lagging Formula

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)))))
Qe = (Tie-Toe)/((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 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 (joules per second). Heat is the flow of thermal energy driven by thermal non-equilibrium

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 Heat flow rate through pipe with eccentric lagging?

Heat flow rate through pipe with eccentric lagging calculator uses 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))))) to calculate the Eccentric Lagging Heat Flow Rate, The Heat flow rate through pipe with eccentric lagging formula is defined as the rate of heat flow through a pipe with eccentric lagging without convection. Eccentric Lagging Heat Flow Rate is denoted by Qe symbol.

How to calculate Heat flow rate through pipe with eccentric lagging using this online calculator? To use this online calculator for Heat flow rate through pipe with eccentric lagging, enter Eccentric Lagging Inner Surface Temperature (Tie), Eccentric Lagging Outer Surface Temperature (Toe), 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 Heat flow rate through pipe with eccentric lagging calculation can be explained with given input values -> 3021.485 = (25-20)/((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 Heat flow rate through pipe with eccentric lagging?
The Heat flow rate through pipe with eccentric lagging formula is defined as the rate of heat flow through a pipe with eccentric lagging without convection and is represented as Qe = (Tie-Toe)/((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 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))))). Eccentric Lagging Inner Surface Temperature is the temperature at the inner surface of the wall either plane wall or cylindrical wall or spherical wall, etc, Eccentric Lagging Outer surface temperature is the temperature at the outer surface of the wall (either plane wall or cylindrical wall or spherical wall, etc), 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 Heat flow rate through pipe with eccentric lagging?
The Heat flow rate through pipe with eccentric lagging formula is defined as the rate of heat flow through a pipe with eccentric lagging without convection is calculated using 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))))). To calculate Heat flow rate through pipe with eccentric lagging, you need Eccentric Lagging Inner Surface Temperature (Tie), Eccentric Lagging Outer Surface Temperature (Toe), 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 Inner Surface Temperature, Eccentric Lagging Outer Surface Temperature, 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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