Thermal Resistance for Pipe in Square Section Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)))
Rth = (1/(2*pi*L))*((1/(hi*R))+((L/k)*ln((1.08*a)/(2*R)))+(pi/(2*ho*a)))
This formula uses 1 Constants, 1 Functions, 7 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)
Variables Used
Thermal Resistance - (Measured in Kelvin per Watt) - Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow.
Length - (Measured in Meter) - Length is the measurement or extent of something from end to end.
Inside Convection - (Measured in Watt per Square Meter per Kelvin) - Inside Convection Heat Transfer Coefficient is the coefficient of convection heat transfer at the inside surface of the body or object or wall, etc.
Cylinder Radius - (Measured in Meter) - The Cylinder Radius is the radius of its base.
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.
Side of Square - (Measured in Meter) - Side of square is defined as the length of the sides of the square. In the square all four sides are equal and all four angles are 90 degrees.
External Convection - (Measured in Watt per Square Meter per Kelvin) - External Convection Heat Transfer Coefficient is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat in case of convective heat transfer.
STEP 1: Convert Input(s) to Base Unit
Length: 3 Meter --> 3 Meter No Conversion Required
Inside Convection: 12 Watt per Square Meter per Kelvin --> 12 Watt per Square Meter per Kelvin No Conversion Required
Cylinder Radius: 1.5 Meter --> 1.5 Meter No Conversion Required
Thermal Conductivity: 10 Watt per Meter per K --> 10 Watt per Meter per K No Conversion Required
Side of Square: 8 Meter --> 8 Meter No Conversion Required
External Convection: 9 Watt per Square Meter per Kelvin --> 9 Watt per Square Meter per Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Rth = (1/(2*pi*L))*((1/(hi*R))+((L/k)*ln((1.08*a)/(2*R)))+(pi/(2*ho*a))) --> (1/(2*pi*3))*((1/(12*1.5))+((3/10)*ln((1.08*8)/(2*1.5)))+(pi/(2*9*8)))
Evaluating ... ...
Rth = 0.0209399765751945
STEP 3: Convert Result to Output's Unit
0.0209399765751945 Kelvin per Watt --> No Conversion Required
FINAL ANSWER
0.0209399765751945 0.02094 Kelvin per Watt <-- Thermal Resistance
(Calculation completed in 00.004 seconds)

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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 for Pipe in Square Section Formula

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)))
Rth = (1/(2*pi*L))*((1/(hi*R))+((L/k)*ln((1.08*a)/(2*R)))+(pi/(2*ho*a)))

What is thermal resistance?

Thermal resistance is a heat property and a measurement of a temperature difference by which an object or material resists a heat flow. Thermal resistance is the reciprocal of thermal conductance.

How to Calculate Thermal Resistance for Pipe in Square Section?

Thermal Resistance for Pipe in Square Section calculator uses 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))) to calculate the Thermal Resistance, The Thermal Resistance for Pipe in Square Section formula is defined as the total thermal resistance offered by a section with a pipe in the square for heat transfer, with convection on either side. Thermal Resistance is denoted by Rth symbol.

How to calculate Thermal Resistance for Pipe in Square Section using this online calculator? To use this online calculator for Thermal Resistance for Pipe in Square Section, enter Length (L), Inside Convection (hi), Cylinder Radius (R), Thermal Conductivity (k), Side of Square (a) & External Convection (ho) and hit the calculate button. Here is how the Thermal Resistance for Pipe in Square Section calculation can be explained with given input values -> 0.02094 = (1/(2*pi*3))*((1/(12*1.5))+((3/10)*ln((1.08*8)/(2*1.5)))+(pi/(2*9*8))).

FAQ

What is Thermal Resistance for Pipe in Square Section?
The Thermal Resistance for Pipe in Square Section formula is defined as the total thermal resistance offered by a section with a pipe in the square for heat transfer, with convection on either side and is represented as Rth = (1/(2*pi*L))*((1/(hi*R))+((L/k)*ln((1.08*a)/(2*R)))+(pi/(2*ho*a))) or 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))). Length is the measurement or extent of something from end to end, Inside Convection Heat Transfer Coefficient is the coefficient of convection heat transfer at the inside surface of the body or object or wall, etc, The Cylinder Radius is the radius of its base, 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, Side of square is defined as the length of the sides of the square. In the square all four sides are equal and all four angles are 90 degrees & External Convection Heat Transfer Coefficient is the proportionality constant between the heat flux and the thermodynamic driving force for the flow of heat in case of convective heat transfer.
How to calculate Thermal Resistance for Pipe in Square Section?
The Thermal Resistance for Pipe in Square Section formula is defined as the total thermal resistance offered by a section with a pipe in the square for heat transfer, with convection on either side is calculated using 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))). To calculate Thermal Resistance for Pipe in Square Section, you need Length (L), Inside Convection (hi), Cylinder Radius (R), Thermal Conductivity (k), Side of Square (a) & External Convection (ho). With our tool, you need to enter the respective value for Length, Inside Convection, Cylinder Radius, Thermal Conductivity, Side of Square & External Convection 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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