Logarithmic Mean Area of Cylinder Calculator

✖Outer area of Cylinder gives the area of the outer part of the Cylinder.ⓘ Outer Area of Cylinder [A_o]			+10% -10%
✖The Inner area of Cylinder gives the area of the inner part of the Cylinder.ⓘ Inner Area of Cylinder [A_i]			+10% -10%

✖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 .ⓘ Logarithmic Mean Area of Cylinder [A_mean]

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Formula

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Logarithmic Mean Area of Cylinder

Formula

`"A"_{"mean"} = ("A"_{"o"}-"A"_{"i"})/ln("A"_{"o"}/"A"_{"i"})`

Example

`"9.865214m²"=("12m²"-"8m²")/ln("12m²"/"8m²")`

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Download Basics of Heat Transfer Formulas PDF

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)
A_mean = (A_o-A_i)/ln(A_o/A_i)
This formula uses 1 Functions, 3 Variables

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

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

A_mean = (A_o-A_i)/ln(A_o/A_i) --> (12-8)/ln(12/8)

Evaluating ... ...

A_mean = 9.86521384950573

STEP 3: Convert Result to Output's Unit

9.86521384950573 Square Meter --> No Conversion Required

FINAL ANSWER

9.86521384950573 ≈ 9.865214 Square Meter <-- Logarithmic Mean Area

(Calculation completed in 00.004 seconds)

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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

Go 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

Go 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

Go 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

Go 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

Go 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

Go Heat Transfer Coefficient = (16.6*Specific Heat Capacity*(Mass Velocity)^0.8)/(Internal Diameter of Pipe^0.2)

Colburn Factor using Chilton Colburn Analogy

Go Colburn's j-factor = Nusselt Number/((Reynolds Number)*(Prandtl Number)^(1/3))

Heat Transfer Coefficient based on Temperature Difference

Go Heat Transfer Coefficient = Heat Transfer/Overall Temperature Difference

Equivalent Diameter of Non-Circular Duct

Go Equivalent Diameter = (4*Cross Sectional Area of Flow)/Wetted Perimeter

Heat Transfer Coefficient given Local Heat Transfer Resistance of Air Film

Go Heat Transfer Coefficient = 1/((Area)*Local Heat Transfer Resistance)

Local Heat Transfer Resistance of Air-Film

Go Local Heat Transfer Resistance = 1/(Heat Transfer Coefficient*Area)

Wetted Perimeter given Hydraulic Radius

Go Wetted Perimeter = Cross Sectional Area of Flow/Hydraulic Radius

Hydraulic Radius

Go Hydraulic Radius = Cross Sectional Area of Flow/Wetted Perimeter

Reynolds Number given Colburn Factor

Go Reynolds Number = (Colburn's j-factor/0.023)^((-1)/0.2)

J-Factor for Pipe Flow

Go Colburn's j-factor = 0.023*(Reynolds Number)^(-0.2)

Colburn J-Factor given Fanning Friction Factor

Go Colburn's j-factor = Fanning Friction Factor/2

Fanning Friction Factor given Colburn J-Factor

Go 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)
A_mean = (A_o-A_i)/ln(A_o/A_i)

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 A_mean 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 (A_o) & Inner Area of Cylinder (A_i) 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 A_mean = (A_o-A_i)/ln(A_o/A_i) 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 (A_o) & Inner Area of Cylinder (A_i). 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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