Logarithmic mean temperature difference for single pass counter flow Calculator

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Heat exchanger

Basics of HMT

Conduction

Convection

Convective Mass Transfer

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Transverse Fin Heat Exchanger

✖Entry temperature of hot fluid is the temperature of the hot fluid at entry.ⓘ Entry Temperature of Hot Fluid [T1]			+10% -10%
✖Exit temperature of cold fluid is the temperature of the cold fluid at exit.ⓘ Exit Temperature of Cold Fluid [t2]			+10% -10%
✖Entry temperature of cold fluid is the temperature of the cold fluid at entry.ⓘ Entry Temperature of Cold Fluid [t1]			+10% -10%
✖Exit temperature of hot fluid is the temperature of the hot fluid at exit.ⓘ Exit Temperature of Hot Fluid [T2]			+10% -10%

✖Logarithmic Mean Temperature Difference is the log of the mean of the temperature values.ⓘ Logarithmic mean temperature difference for single pass counter flow [ΔT_m]

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Formula

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Logarithmic mean temperature difference for single pass counter flow

Formula

`"ΔT"_{"m"} = (("T1"-"t2")-("t1"-"T2"))/ln(("T1"-"t2")/("t1"-"T2"))`

Example

`"15.41695"=(("60K"-"25K")-("10K"-"5K"))/ln(("60K"-"25K")/("10K"-"5K"))`

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Logarithmic mean temperature difference for single pass counter flow Solution

STEP 0: Pre-Calculation Summary

Formula Used

Logarithmic Mean Temperature Difference = ((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)-(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))/ln((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))
ΔT_m = ((T1-t2)-(t1-T2))/ln((T1-t2)/(t1-T2))
This formula uses 1 Functions, 5 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 Temperature Difference - Logarithmic Mean Temperature Difference is the log of the mean of the temperature values.
Entry Temperature of Hot Fluid - (Measured in Kelvin) - Entry temperature of hot fluid is the temperature of the hot fluid at entry.
Exit Temperature of Cold Fluid - (Measured in Kelvin) - Exit temperature of cold fluid is the temperature of the cold fluid at exit.
Entry Temperature of Cold Fluid - (Measured in Kelvin) - Entry temperature of cold fluid is the temperature of the cold fluid at entry.
Exit Temperature of Hot Fluid - (Measured in Kelvin) - Exit temperature of hot fluid is the temperature of the hot fluid at exit.

STEP 1: Convert Input(s) to Base Unit

Entry Temperature of Hot Fluid: 60 Kelvin --> 60 Kelvin No Conversion Required
Exit Temperature of Cold Fluid: 25 Kelvin --> 25 Kelvin No Conversion Required
Entry Temperature of Cold Fluid: 10 Kelvin --> 10 Kelvin No Conversion Required
Exit Temperature of Hot Fluid: 5 Kelvin --> 5 Kelvin No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

ΔT_m = ((T1-t2)-(t1-T2))/ln((T1-t2)/(t1-T2)) --> ((60-25)-(10-5))/ln((60-25)/(10-5))

Evaluating ... ...

ΔT_m = 15.4169502710925

STEP 3: Convert Result to Output's Unit

15.4169502710925 --> No Conversion Required

FINAL ANSWER

15.4169502710925 ≈ 15.41695 <-- Logarithmic Mean Temperature Difference

(Calculation completed in 00.020 seconds)

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Logarithmic mean temperature difference for single pass counter flow

Go Logarithmic Mean Temperature Difference = ((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)-(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))/ln((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))

Mass flow rate of cold fluid

Go Mass Flow Rate of Cold Fluid = (Effectiveness of Heat Exchanger*Smaller Value/Specific heat of cold fluid)*(1/((Exit Temperature of Cold Fluid-Entry Temperature of Cold Fluid)/(Entry Temperature of Hot Fluid-Entry Temperature of Cold Fluid)))

Specific heat of cold fluid

Go Specific heat of cold fluid = (Effectiveness of Heat Exchanger*Smaller Value/Mass Flow Rate of Cold Fluid)*(1/((Exit Temperature of Cold Fluid-Entry Temperature of Cold Fluid)/(Entry Temperature of Hot Fluid-Entry Temperature of Cold Fluid)))

Mass flow rate of hot fluid

Go Mass Flow Rate of Hot Fluid = (Effectiveness of Heat Exchanger*Smaller Value/Specific heat of hot fluid)*(1/((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Hot Fluid-Entry Temperature of Cold Fluid)))

Specific heat of hot water

Go Specific heat of hot fluid = (Effectiveness of Heat Exchanger*Smaller Value/Mass Flow Rate of Hot Fluid)*(1/((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Hot Fluid-Entry Temperature of Cold Fluid)))

Heat transfer surface area for unit length of matrix in storage type heat exchanger

Go Surface Area = (Location factor*Specific heat of fluid*Mass Flowrate)/(Convective Heat Transfer Coefficient*Distance from Point to YY Axis)

Convective heat transfer coefficient of storage type heat exchanger

Go Convective Heat Transfer Coefficient = (Location factor*Specific heat of fluid*Mass Flowrate)/(Surface Area*Distance from Point to YY Axis)

Specific heat of fluid in storage type heat exchanger

Go Specific heat of fluid = (Convective Heat Transfer Coefficient*Surface Area*Distance from Point to YY Axis)/(Location factor*Mass Flowrate)

Mass Flowrate of Fluid in Storage type Heat Exchanger

Go Mass Flowrate = (Convective Heat Transfer Coefficient*Surface Area*Distance from Point to YY Axis)/(Specific heat of fluid*Location factor)

Location factor at distance X of heat exchanger

Go Location factor = (Convective Heat Transfer Coefficient*Surface Area*Distance from Point to YY Axis)/(Specific heat of fluid*Mass Flowrate)

Convective heat transfer coefficient of storage type heat exchanger given time factor

Go Convective Heat Transfer Coefficient = (Time Factor*Specific heat of matrix material*Mass of Solid)/(Surface Area*Total Time Taken)

Heat transfer surface area for unit length given time factor

Go Surface Area = (Time Factor*Specific heat of matrix material*Mass of Solid)/(Convective Heat Transfer Coefficient*Total Time Taken)

Time factor of storage type heat exchanger

Go Time Factor = (Convective Heat Transfer Coefficient*Surface Area*Total Time Taken)/(Specific heat of matrix material*Mass of Solid)

Time taken for storage type heat exchanger

Go Total Time Taken = (Time Factor*Specific heat of matrix material*Mass of Solid)/(Surface Area*Convective Heat Transfer Coefficient)

Mass of solid per unit length of matrix

Go Mass of Solid = (Convective Heat Transfer Coefficient*Surface Area*Total Time Taken)/(Time Factor*Specific heat of matrix material)

Specific heat of matrix material

Go Specific heat of matrix material = (Convective Heat Transfer Coefficient*Surface Area*Total Time Taken)/(Time Factor*Mass of Solid)

Entry temperature of cold fluid

Go Entry Temperature of Cold Fluid = Entry Temperature of Hot Fluid-(Heat exchanged/(Effectiveness of Heat Exchanger*Smaller Value))

Entry temperature of hot fluid

Go Entry Temperature of Hot Fluid = (Heat exchanged/(Effectiveness of Heat Exchanger*Smaller Value))+Entry Temperature of Cold Fluid

Heat exchanged NTU method

Go Heat exchanged = Effectiveness of Heat Exchanger*Smaller Value*(Entry Temperature of Hot Fluid-Entry Temperature of Cold Fluid)

Overall heat transfer coefficient given LMTD

Go Overall Heat Transfer Coefficient = Heat exchanged/(Correction Factor*Area*Logarithmic Mean Temperature Difference)

Logarithmic mean temperature difference

Go Logarithmic Mean Temperature Difference = Heat exchanged/(Correction Factor*Overall Heat Transfer Coefficient*Area)

Correction factor in heat exchanger

Go Correction Factor = Heat exchanged/(Overall Heat Transfer Coefficient*Area*Logarithmic Mean Temperature Difference)

Area of heat exchanger

Go Area = Heat exchanged/(Overall Heat Transfer Coefficient*Logarithmic Mean Temperature Difference*Correction Factor)

Heat exchanged

Go Heat exchanged = Correction Factor*Overall Heat Transfer Coefficient*Area*Logarithmic Mean Temperature Difference

Capacity Ratio

Go Heat capacity ratio = Minimum heat capacity/Maximum heat capacity

Logarithmic mean temperature difference for single pass counter flow Formula

What is Heat exchanger?

A heat exchanger is a system used to transfer heat between two or more fluids. Heat exchangers are used in both cooling and heating processes. The fluids may be separated by a solid wall to prevent mixing or they may be in direct contact. They are widely used in space heating, refrigeration, air conditioning, power stations, chemical plants, petrochemical plants, petroleum refineries, natural-gas processing, and sewage treatment. The classic example of a heat exchanger is found in an internal combustion engine in which a circulating fluid known as engine coolant flows through radiator coils and air flows past the coils, which cools the coolant and heats the incoming air. Another example is the heat sink, which is a passive heat exchanger that transfers the heat generated by an electronic or a mechanical device to a fluid medium, often air or a liquid coolant.

How to Calculate Logarithmic mean temperature difference for single pass counter flow?

Logarithmic mean temperature difference for single pass counter flow calculator uses Logarithmic Mean Temperature Difference = ((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)-(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))/ln((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid)) to calculate the Logarithmic Mean Temperature Difference, The Logarithmic mean temperature difference for single pass counter flow formula is defined as the log of mean difference of temperature values of the fluids flowing in counter in single pass. Logarithmic Mean Temperature Difference is denoted by ΔT_m symbol.

How to calculate Logarithmic mean temperature difference for single pass counter flow using this online calculator? To use this online calculator for Logarithmic mean temperature difference for single pass counter flow, enter Entry Temperature of Hot Fluid (T1), Exit Temperature of Cold Fluid (t2), Entry Temperature of Cold Fluid (t1) & Exit Temperature of Hot Fluid (T2) and hit the calculate button. Here is how the Logarithmic mean temperature difference for single pass counter flow calculation can be explained with given input values -> 15.41695 = ((60-25)-(10-5))/ln((60-25)/(10-5)).

FAQ

What is Logarithmic mean temperature difference for single pass counter flow?

The Logarithmic mean temperature difference for single pass counter flow formula is defined as the log of mean difference of temperature values of the fluids flowing in counter in single pass and is represented as ΔT_m = ((T1-t2)-(t1-T2))/ln((T1-t2)/(t1-T2)) or Logarithmic Mean Temperature Difference = ((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)-(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))/ln((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid)). Entry temperature of hot fluid is the temperature of the hot fluid at entry, Exit temperature of cold fluid is the temperature of the cold fluid at exit, Entry temperature of cold fluid is the temperature of the cold fluid at entry & Exit temperature of hot fluid is the temperature of the hot fluid at exit.

How to calculate Logarithmic mean temperature difference for single pass counter flow?

The Logarithmic mean temperature difference for single pass counter flow formula is defined as the log of mean difference of temperature values of the fluids flowing in counter in single pass is calculated using Logarithmic Mean Temperature Difference = ((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)-(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid))/ln((Entry Temperature of Hot Fluid-Exit Temperature of Cold Fluid)/(Entry Temperature of Cold Fluid-Exit Temperature of Hot Fluid)). To calculate Logarithmic mean temperature difference for single pass counter flow, you need Entry Temperature of Hot Fluid (T1), Exit Temperature of Cold Fluid (t2), Entry Temperature of Cold Fluid (t1) & Exit Temperature of Hot Fluid (T2). With our tool, you need to enter the respective value for Entry Temperature of Hot Fluid, Exit Temperature of Cold Fluid, Entry Temperature of Cold Fluid & Exit Temperature of Hot Fluid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Logarithmic Mean Temperature Difference?

In this formula, Logarithmic Mean Temperature Difference uses Entry Temperature of Hot Fluid, Exit Temperature of Cold Fluid, Entry Temperature of Cold Fluid & Exit Temperature of Hot Fluid. We can use 1 other way(s) to calculate the same, which is/are as follows -

Logarithmic Mean Temperature Difference = Heat exchanged/(Correction Factor*Overall Heat Transfer Coefficient*Area)

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