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Birla Institute of Technology & Science (BITS), Pilani
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## Log Mean Temperature Difference for Counter Current Flow Solution

STEP 0: Pre-Calculation Summary
Formula Used
lmtd = ((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))
LMTD = ((Tho-Tci)-(Thi-Tco))/ln((Tho-Tci)/(Thi-Tco))
This formula uses 1 Functions, 4 Variables
Functions Used
ln - Natural logarithm function (base e), ln(Number)
Variables Used
Outlet Temperature of Hot Fluid - Outlet Temperature of Hot Fluid is the temperature at which the hot fluid exits the heat exchanger. (Measured in Kelvin)
Inlet Temperature of Cold Fluid - Inlet Temperature of Cold Fluid is the temperature at which the cold fluid enters the heat exchanger (Measured in Kelvin)
Inlet Temperature of Hot Fluid - Inlet Temperature of Hot Fluid is the temperature at which the hot fluid enters the heat exchanger. (Measured in Kelvin)
Outlet Temperature of Cold Fluid - Outlet Temperature of Cold Fluid is the temperature at which the cold fluid exits the heat exchanger. (Measured in Kelvin)
STEP 1: Convert Input(s) to Base Unit
Outlet Temperature of Hot Fluid: 20 Kelvin --> 20 Kelvin No Conversion Required
Inlet Temperature of Cold Fluid: 5 Kelvin --> 5 Kelvin No Conversion Required
Inlet Temperature of Hot Fluid: 35 Kelvin --> 35 Kelvin No Conversion Required
Outlet Temperature of Cold Fluid: 10 Kelvin --> 10 Kelvin No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
LMTD = ((Tho-Tci)-(Thi-Tco))/ln((Tho-Tci)/(Thi-Tco)) --> ((20-5)-(35-10))/ln((20-5)/(35-10))
Evaluating ... ...
LMTD = 19.5761518897122
STEP 3: Convert Result to Output's Unit
19.5761518897122 Kelvin --> No Conversion Required
19.5761518897122 Kelvin <-- Log Mean Temperature Difference
(Calculation completed in 00.000 seconds)

## < 10+ Heat Transfer Calculators

Heat Exchanger Effectiveness
heat_exchanger_effectiveness = if(Mass of hot fluid*Specific Heat Capacity of Hot Fluid>Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) { Mass of hot fluid*Specific Heat Capacity of Hot Fluid*(inlet_temperature_hot_fluid-outlet_temperature_hot_fluid)/(Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(inlet_temperature_hot_fluid-inlet_temperature_cold_fluid)) } else { Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(inlet_temperature_cold_fluid-outlet_temperature_cold_fluid)/(Mass of hot fluid*Specific Heat Capacity of Hot Fluid*(inlet_temperature_hot_fluid-inlet_temperature_cold_fluid)) } Go
Number of Transfer Units in a Heat Exchanger
number_of_transfer_units = if(Mass of hot fluid*Specific Heat Capacity of Hot Fluid>Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) { overall_heat_transfer_coefficient/(area*Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) } else { overall_heat_transfer_coefficient/(area*Mass of hot fluid*Specific Heat Capacity of Hot Fluid) } Go
Log Mean Temperature Difference for Counter Current Flow
lmtd = ((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)) Go
Log Mean Temperature Difference for CoCurrent Flow
lmtd = ((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)) Go
Heat Transfer Through Plane Wall or Surface
heat_rate = -Thermal Conductivity*Original cross sectional area*(Outside Temperature-Inside Temperature)/Width Go
Heat Transfer in a Heat Exchanger using cold fluid properties
heat = Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(Inlet Temperature of Cold Fluid-Outlet Temperature of Cold Fluid) Go
Heat Transfer in a Heat Exchanger using overall heat transfer coefficient
heat = Overall Heat Transfer Coefficient*Area*(Outside Temperature-Inside Temperature) Go
Critical Radius of Insulation of a Hollow Sphere
critical_radius_of_insulation = 2*Thermal Conductivity of Insulation/External convection heat transfer coefficient Go
Critical Radius of Insulation of a Cylinder
critical_radius_of_insulation = Thermal Conductivity of Insulation/External convection heat transfer coefficient Go
Total Emmisive power of radiating body
power_per_area = (Emissivity*(Temperature)^4)*[Stefan-BoltZ] Go

### Log Mean Temperature Difference for Counter Current Flow Formula

lmtd = ((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))
LMTD = ((Tho-Tci)-(Thi-Tco))/ln((Tho-Tci)/(Thi-Tco))

## Log Mean Temperature Difference for Counter Current Flow

The Log Mean Temperature Difference for Counter Current Flow in is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger.

## How to Calculate Log Mean Temperature Difference for Counter Current Flow?

Log Mean Temperature Difference for Counter Current Flow calculator uses lmtd = ((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)) to calculate the Log Mean Temperature Difference, The Log Mean Temperature Difference for Counter Current Flow in is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger. Log Mean Temperature Difference and is denoted by LMTD symbol.

How to calculate Log Mean Temperature Difference for Counter Current Flow using this online calculator? To use this online calculator for Log Mean Temperature Difference for Counter Current Flow, enter Outlet Temperature of Hot Fluid (Tho), Inlet Temperature of Cold Fluid (Tci), Inlet Temperature of Hot Fluid (Thi) and Outlet Temperature of Cold Fluid (Tco) and hit the calculate button. Here is how the Log Mean Temperature Difference for Counter Current Flow calculation can be explained with given input values -> 19.57615 = ((20-5)-(35-10))/ln((20-5)/(35-10)).

### FAQ

What is Log Mean Temperature Difference for Counter Current Flow?
The Log Mean Temperature Difference for Counter Current Flow in is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger and is represented as LMTD = ((Tho-Tci)-(Thi-Tco))/ln((Tho-Tci)/(Thi-Tco)) or lmtd = ((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)). Outlet Temperature of Hot Fluid is the temperature at which the hot fluid exits the heat exchanger, Inlet Temperature of Cold Fluid is the temperature at which the cold fluid enters the heat exchanger, Inlet Temperature of Hot Fluid is the temperature at which the hot fluid enters the heat exchanger and Outlet Temperature of Cold Fluid is the temperature at which the cold fluid exits the heat exchanger.
How to calculate Log Mean Temperature Difference for Counter Current Flow?
The Log Mean Temperature Difference for Counter Current Flow in is used to determine the temperature driving force for heat transfer in flow systems, most notably in heat exchangers. The LMTD is a logarithmic average of the temperature difference between the hot and cold streams at each end of the exchanger is calculated using lmtd = ((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)). To calculate Log Mean Temperature Difference for Counter Current Flow, you need Outlet Temperature of Hot Fluid (Tho), Inlet Temperature of Cold Fluid (Tci), Inlet Temperature of Hot Fluid (Thi) and Outlet Temperature of Cold Fluid (Tco). With our tool, you need to enter the respective value for Outlet Temperature of Hot Fluid, Inlet Temperature of Cold Fluid, Inlet Temperature of Hot Fluid and Outlet Temperature of Cold 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 Log Mean Temperature Difference?
In this formula, Log Mean Temperature Difference uses Outlet Temperature of Hot Fluid, Inlet Temperature of Cold Fluid, Inlet Temperature of Hot Fluid and Outlet Temperature of Cold Fluid. We can use 10 other way(s) to calculate the same, which is/are as follows -
• heat_rate = -Thermal Conductivity*Original cross sectional area*(Outside Temperature-Inside Temperature)/Width
• critical_radius_of_insulation = Thermal Conductivity of Insulation/External convection heat transfer coefficient
• critical_radius_of_insulation = 2*Thermal Conductivity of Insulation/External convection heat transfer coefficient
• power_per_area = (Emissivity*(Temperature)^4)*[Stefan-BoltZ]
• number_of_transfer_units = if(Mass of hot fluid*Specific Heat Capacity of Hot Fluid>Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) { overall_heat_transfer_coefficient/(area*Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) } else { overall_heat_transfer_coefficient/(area*Mass of hot fluid*Specific Heat Capacity of Hot Fluid) }
• lmtd = ((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))
• lmtd = ((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))
• heat_exchanger_effectiveness = if(Mass of hot fluid*Specific Heat Capacity of Hot Fluid>Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid) { Mass of hot fluid*Specific Heat Capacity of Hot Fluid*(inlet_temperature_hot_fluid-outlet_temperature_hot_fluid)/(Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(inlet_temperature_hot_fluid-inlet_temperature_cold_fluid)) } else { Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(inlet_temperature_cold_fluid-outlet_temperature_cold_fluid)/(Mass of hot fluid*Specific Heat Capacity of Hot Fluid*(inlet_temperature_hot_fluid-inlet_temperature_cold_fluid)) }
• heat = Overall Heat Transfer Coefficient*Area*(Outside Temperature-Inside Temperature)
• heat = Mass of Cold Fluid*Specific Heat Capacity of Cold Fluid*(Inlet Temperature of Cold Fluid-Outlet Temperature of Cold Fluid)
Where is the Log Mean Temperature Difference for Counter Current Flow calculator used?
Among many, Log Mean Temperature Difference for Counter Current Flow calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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