dti = tpi - tsi = inlet primary and secondary fluid temperature difference (oF, oC)
dto = tpo - tso = outlet primary and secondary fluid temperature difference (oF, oC)
For counter flow:
dti = tpi - tso = inlet primary and outlet secondary fluid temperature difference (oF, oC)
dto = tpo - tsi = outlet primary and inlet secondary fluid temperature difference (oF, oC)
The Logarithmic Mean Temperature Difference is always less than the Arithmetic Mean Temperature Difference.
An easier but less accurate way to calculate the mean temperature difference is the
AMTD can be expressed as:
AMTD = (tpi + tpo) / 2 - (tsi + tso) / 2 (2)
AMTD = Arithmetic Mean Temperature Difference (oF, oC)
tpi = primary inlet temperature (oF, oC)
tpo = primary outlet temperature (oF, oC)
tsi = secondary inlet temperature (oF, oC)
tso = secondary outlet temperature (oF, oC)
A linear increase in the secondary fluid temperature makes it more easy to do manual calculations. AMTD will in general give a satisfactory approximation for the mean temperature difference when the smallest of the inlet or outlet temperature differences is more than half the greatest of the inlet or outlet temperature differences.
When heat is transferred as a result of a change of phase like condensation or evaporation the temperature of the primary or secondary fluid remains constant. The equations can then be simplified by setting
tp1 = tp2
ts1 = ts2
The calculator below can be used to calculate Arithmetic and Logarithmic Mean Temperature Difference of counter-flow an parallel-flow heat exchangers.
Hot water at 80 oC heats air from from a temperature of 0 oC to 20 oC in a parallel flow heat exchanger. The water leaves the heat exchanger at 60 oC.
Arithmetic Mean Temperature Difference can be calculated as
AMTD = ((80 oC) + (60 oC)) / 2 - ((0 oC) + (20 oC)) / 2
= 60 oC
Logarithmic Mean Temperature Difference can be calculated as
LMTD = ((60 oC) - (20 oC)) - ((80 oC) - (0 oC))) / ln(((60 oC) - (20 oC)) / ((80 oC) - (0 oC)))
= 57.7 oC
Steam at 2 bar gauge heats water from 20 oC to 50 oC. The saturation temperature of steam at 2 bar gauge is 134 oC.
Note! that steam condenses at a constant temperature. The temperature on the heat exchangers surface on the steam side is constant and determined by the steam pressure.
Arithmetic Mean Temperature Difference can be calculated like
AMTD = ((134 oC) + (134 oC)) / 2 - ((20 oC) + (50 oC)) / 2
= 99 oC
Log Mean Temperature Difference can be calculated like
LMTD = ((134 oC) - (20 oC) - ((134 oC) - (50 oC))) / ln(((134 oC) - (20 oC)) / ((134 oC) - (50 oC)))
= 98.24 oC
Heat loss from pipes, tubes and tanks - with and without insulation - foam, fiberglass, rockwool and more.
Heat transfer and heat loss from buildings and technical applications - heat transfer coefficients and insulation methods to reduce energy consumption.
Thermodynamics of steam and condensate systems.
Work, heat and energy systems.
Heat transfer when steam condensates.
Conductive heat transfer takes place in a solid if there is a temperature gradient.
Heat transfer between a solid and a moving fluid is called convection. This is a short tutorial about convective heat transfer.
Latent and sensible cooling and heating equations - imperial units.
Heat loss from uninsulated copper pipes - dimensions ranging 1/2 - 4 inches.
The heat emission from a radiator or a heating panel depends on the temperature difference between the radiator and the surrounding air.
Overall heat transfer coefficients in common heat exchanger designs - tubular, plate or spiral.
Average overall heat transmission coefficients for fluid and surface combinations like Water to Air, Water to Water, Air to Air, Steam to Water and more.
Basic equations for heat transfer - selecting criteria for heaters and coolers in ventilations systems.
The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
Walls or heat exchangers - calculate overall heat transfer coefficients.
Saturated Steam Table with steam properties as specific volume, density, specific enthalpy and specific entropy.
Steam consumption and condensate generation when heating liquid or gas flows
Steam radiators and steam convectors - heating capacities and temperature coefficients.
Heat transfer coefficients for steam and hot water coils submerged in oil tanks.
Introduction to temperature - including Celsius, Fahrenheit, Kelvin and Rankine definitions - and an online temperature converter.
Heat loss through common building elements due to transmission, R-values and U-values - imperial and SI units.
Definition and examples of calculation of weighted average bed temperature in adiabatic reactors.
Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!
We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.
Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.