## Logarithmic Mean Area of Cylinder Solution

STEP 0: Pre-Calculation Summary
Formula Used
Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder)
Amean = (Ao-Ai)/ln(Ao/Ai)
This formula uses 1 Functions, 3 Variables
Functions Used
ln - Natural logarithm function (base e), ln(Number)
Variables Used
Logarithmic Mean Area - (Measured in Square Meter) - Logarithmic mean area tells us what should be the area of a conducting wall in terms of the area of a cylindrical surface so that their heat resistances are same .
Outer Area of Cylinder - (Measured in Square Meter) - Outer area of Cylinder gives the area of the outer part of the Cylinder.
Inner Area of Cylinder - (Measured in Square Meter) - The Inner area of Cylinder gives the area of the inner part of the Cylinder.
STEP 1: Convert Input(s) to Base Unit
Outer Area of Cylinder: 12 Square Meter --> 12 Square Meter No Conversion Required
Inner Area of Cylinder: 8 Square Meter --> 8 Square Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Amean = (Ao-Ai)/ln(Ao/Ai) --> (12-8)/ln(12/8)
Evaluating ... ...
Amean = 9.86521384950573
STEP 3: Convert Result to Output's Unit
9.86521384950573 Square Meter --> No Conversion Required
9.86521384950573 9.865214 Square Meter <-- Logarithmic Mean Area
(Calculation completed in 00.004 seconds)
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## Credits

Created by Vaibhav Mishra
DJ Sanghvi College of Engineering (DJSCE), Mumbai
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## < 17 Basics of Heat Transfer Calculators

Log Mean Temperature Difference for Counter Current Flow
Log Mean Temperature Difference = ((Outlet Temperature of Hot Fluid-Inlet Temperature of Cold Fluid)-(Inlet Temperature of Hot Fluid-Outlet Temperature of Cold Fluid))/ln((Outlet Temperature of Hot Fluid-Inlet Temperature of Cold Fluid)/(Inlet Temperature of Hot Fluid-Outlet Temperature of Cold Fluid))
Log Mean Temperature Difference for CoCurrent Flow
Log Mean Temperature Difference = ((Outlet Temperature of Hot Fluid-Outlet Temperature of Cold Fluid)-(Inlet Temperature of Hot Fluid-Inlet Temperature of Cold Fluid))/ln((Outlet Temperature of Hot Fluid-Outlet Temperature of Cold Fluid)/(Inlet Temperature of Hot Fluid-Inlet Temperature of Cold Fluid))
Logarithmic Mean Area of Cylinder
Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder)
Equivalent Diameter when Flow in Rectangular Duct
Equivalent Diameter = (4*Length of Rectangular Section*Breadth of Rectangle)/(2*(Length of Rectangular Section+Breadth of Rectangle))
Internal Diameter of Pipe given Heat Transfer Coefficient for Gas in Turbulent Motion
Internal Diameter of Pipe = ((16.6*Specific Heat Capacity*(Mass Velocity)^0.8)/(Heat Transfer Coefficient for Gas))^(1/0.2)
Heat Transfer from Stream of Gas flowing in Turbulent Motion
Heat Transfer Coefficient = (16.6*Specific Heat Capacity*(Mass Velocity)^0.8)/(Internal Diameter of Pipe^0.2)
Colburn Factor using Chilton Colburn Analogy
Colburn's j-factor = Nusselt Number/((Reynolds Number)*(Prandtl Number)^(1/3))
Heat Transfer Coefficient based on Temperature Difference
Heat Transfer Coefficient = Heat Transfer/Overall Temperature Difference
Equivalent Diameter of Non-Circular Duct
Equivalent Diameter = (4*Cross Sectional Area of Flow)/Wetted Perimeter
Heat Transfer Coefficient given Local Heat Transfer Resistance of Air Film
Heat Transfer Coefficient = 1/((Area)*Local Heat Transfer Resistance)
Local Heat Transfer Resistance of Air-Film
Local Heat Transfer Resistance = 1/(Heat Transfer Coefficient*Area)
Wetted Perimeter = Cross Sectional Area of Flow/Hydraulic Radius
Hydraulic Radius = Cross Sectional Area of Flow/Wetted Perimeter
Reynolds Number given Colburn Factor
Reynolds Number = (Colburn's j-factor/0.023)^((-1)/0.2)
J-Factor for Pipe Flow
Colburn's j-factor = 0.023*(Reynolds Number)^(-0.2)
Colburn J-Factor given Fanning Friction Factor
Colburn's j-factor = Fanning Friction Factor/2
Fanning Friction Factor given Colburn J-Factor
Fanning Friction Factor = 2*Colburn's j-factor

## Logarithmic Mean Area of Cylinder Formula

Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder)
Amean = (Ao-Ai)/ln(Ao/Ai)

## Why do we calculate Logarithmic Mean Area ?

If heat transfer is taking place from a cylinder, so if we want to find out the area of slab for the same amount of heat transfer then log mean area is used, as heat transfer area in case of cylinder is continuously varying from inner radius to outer radius, so the utility of log mean area is to deduce a constant area for the same amount of heat transfer.

## How to Calculate Logarithmic Mean Area of Cylinder?

Logarithmic Mean Area of Cylinder calculator uses Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder) to calculate the Logarithmic Mean Area, Logarithmic mean area of Cylinder tells us what should be the area of a conducting wall in terms of the area of a cylindrical surface so that their heat resistances are same. Logarithmic Mean Area is denoted by Amean symbol.

How to calculate Logarithmic Mean Area of Cylinder using this online calculator? To use this online calculator for Logarithmic Mean Area of Cylinder, enter Outer Area of Cylinder (Ao) & Inner Area of Cylinder (Ai) and hit the calculate button. Here is how the Logarithmic Mean Area of Cylinder calculation can be explained with given input values -> 9.865214 = (12-8)/ln(12/8).

### FAQ

What is Logarithmic Mean Area of Cylinder?
Logarithmic mean area of Cylinder tells us what should be the area of a conducting wall in terms of the area of a cylindrical surface so that their heat resistances are same and is represented as Amean = (Ao-Ai)/ln(Ao/Ai) or Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder). Outer area of Cylinder gives the area of the outer part of the Cylinder & The Inner area of Cylinder gives the area of the inner part of the Cylinder.
How to calculate Logarithmic Mean Area of Cylinder?
Logarithmic mean area of Cylinder tells us what should be the area of a conducting wall in terms of the area of a cylindrical surface so that their heat resistances are same is calculated using Logarithmic Mean Area = (Outer Area of Cylinder-Inner Area of Cylinder)/ln(Outer Area of Cylinder/Inner Area of Cylinder). To calculate Logarithmic Mean Area of Cylinder, you need Outer Area of Cylinder (Ao) & Inner Area of Cylinder (Ai). With our tool, you need to enter the respective value for Outer Area of Cylinder & Inner Area of Cylinder 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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