Psychrometric analysis of the performance of portable air conditioners and air coolers


The use of portable air conditioners to reduce the temperature and make occupants more comfortable in the summer and in emergencies is a concept which is well understood. Most people would agree that if the temperature in their office is much over 24 deg C then they will begin to feel uncomfortably hot. However, relating comfort to temperature alone can be very misleading.


Most of us would be familiar with the idea that hot humid days feel hotter and make us less comfortable. Quantifying this effect and relating it to the use of air conditioners, dehumidifiers and evaporative coolers requires a deeper understanding of the physics and in particular air psychrometry.


A myth to dispel is that our bodies sense temperature. We do not, we sense the rate of heat transfer.

A couple of examples to prove this:-

    1. Put a piece of polystyrene and a metal spoon in your freezer for a while. When they have both had time to reach your freezer temperature of about -5 deg C take them out and see which feels colder. The metal spoon will transfer heat to your finders very quickly through conduction and feel very cold whereas the polystyrene will not, due to the low heat content and good insulating properties.

    2. Inside a sauna the air becomes very dry due to the electric heating. This dry air at over 100 deg C is hot but does not burn. Add a ladle of water which increases the humidity in the sauna and the effect is instant. The temperature has not changed but the rate of heat transfer has increased dramatically and it feels much hotter.


What temperature is comfortable?

We can feel comfortable and able to work in quite a wide range of summer temperatures even up to 30 Deg C, provided we control the rate of heat transfer from our skin. If we are cold then we can add layers of clothing to reduce the heat loss. If we feel too hot then as well as reducing the temperature we can take other steps to improve the skins ability to shed heat.


The ability of skin to shed heat depends on the rate of evaporation of moisture from the surface. If we sweat and it does not evaporate then we feel hot and sticky and our clothes become damp which further worsens the situation. Reducing humidity and/or increasing air movement across the skin increases evaporation rates.


Some understanding of the science is needed if we are to determine the best approach to creating comfortable living conditions, particularly where limitations on the ideal use of sufficient temporary air conditioning exist. A better understanding is also needed if comfortable conditions are to be achieved as efficiently as possible.


Technical analysis & definitions

Relative humidity

Air can contain varying amounts of moisture held invisibly but there is a maximum. This figure is higher if the temperature is higher and vice versa. More than this maximum and the water appears as visible water droplets making a visible cloud. Relative humidity is the term used to describe the amount of water present in the air expressed as a percentage of the maximum.

The upper row of data in the following table shows the amount of water which 1 m3 of air holds at varying relative humidity. The lower row is the temperature to which this air would need to be reduced for that moisture to begin to condense out. It should be noted that any cooling of air with 100% relative humidity will result is condensing some of the water vapour. At 50 deg C and 70% humidity 1 cubic mt of air has 58.1gm of water in it and if cooled to below 43 deg C that water will begin to condense out.


Table of relative humidity and water of air



Apparent temperature

The apparent temperature is a good measure of the temperature sensed by humans and so is the temperature of most interest to us. A temperature of 24 deg C measured by a thermometer (dry bulb) will be about equal to the apparent temperature when the relative humidity is 50%. If the relative humidity is 0% (dry air) then the apparent temperature will be 21 deg C and relative humidity of 100% would give an apparent temperature of 27 deg C. The apparent temperature is therefore a measure of the rate of heat transfer from the skin which will take place.


Sensible cooling and latent cooling

To understand the process of cooling a room with air conditioning it is necessary to understand the difference between sensible heat and latent heat.

If an air conditioner cooled the air in the room without condensing out any moisture in the process then only sensible cooling takes place and all of the cooling capacity of the air conditioner would go to reducing the air temperature, as measured by a thermometer.

Sensible cooling heat flow becomes:-

Qs (KW) = Specific heat of air x density of air (KG/cubic mt) x volume per hour (cubic mt/hr) x Delta t (deg K) /3600

Where:-    Specific heat of air is can be taken as 1.005KJ/KG.deg K
                   Density of air at the temperatures we are dealing with can be taken as 1.2 KG/cubic mt
                   Volume of fresh air is taken to be, perhaps, 3 air changes per hour in the room (min 10 lt/person/hr)
                   Delta t is amount by which the room temperature is below that of the fresh air supply

If the air conditioner is reducing the humidity of the air then the mass of water vapour which is being condensed needs the latent heat of vaporization to be removed and then the liquid needs to be cooled to the condensate temperature.

Latent cooling heat flow becomes:-

Ql (KW) = 2465 KJ/KG of condensate x Litres/hour of condensate /3600

Where 2465KJ/KG is the energy needed to condense moisture in the air to produce 1 KG (1Litre) of condensate.

Clearly under conditions where a portable air conditioner is producing condensate a proportion of it's cooling capacity is used for latent cooling and the remainder achieves sensible cooling. The more humid the atmospheric conditions, the more condensate is produced and hence a lower proportion the machine cooling capacity is available for sensible cooling.


Cooling load calculation

A 30 sq mt room with volume of 72 cubic mt has 4 people in it and 4 air changes per hour of fresh air at 30 deg and relative humidity of 70%. It is required to achieve 24 deg C with relative humidity of 60% to provide comfortable working conditions.

From the table above it can be seen that each cubic mt of fresh air will need to have the water content reduced by 21.3gm minus 13.1gm = 8.2gm.

Mass (KG) of condensate produced = 72 cubic mt x 4 ach x 8.2gm/1000 = 2.3KG

Ql (KW) to condense this water vapour = 2465KJ/KG x 2.3KG/3600 = 1.6KW

Qs (KW) = 1.005KJ/KG.K x 1.2 KG/cubic mt x 72 cubic mt x 4 ach x 6 deg C/3600 = 0.6 KW

If we estimate that electrical, solar and other gains total 2KW then this needs to be added to the sensible cooling load to give a total cooling load of 4.4KW of which 2.6KW is sensible cooling. The Apparent temperature would have been reduced from approx 31.5 deg C to 24.5 deg C which is a good indication of the improvement in working conditions which will be felt by the occupants.


Dehumidification by portable air conditioners

The temperature drop across most portable air conditioners is 12 -15 deg C depending on design and fan speed setting and humidity. The outlet air discharged from the machine is the mean temperature. The heat is given up to a finned heat exchanged as the air passes over it and moisture is condensed out on the coil and collected in a drip tray, for disposal. Not all the air passing over the evaporator coil is cooled equally so some is taken to a lower temperature than the final outlet air temperature but we can draw some conclusions from analysis using this discharge temperature.

Using the performance of a 3.8KW monobloc model with 12 deg K temp drop and 450cubic mt/hr air flow, for analysis let's look at the rate at which condensate is removed from the air when the machine is first turned on with a single pipe to the window. This is as described in applications example no 1 showing a room with opening windows.


Example 1 - humid weather

A humid day with outside temp of 22 deg C and relative humidity of 70% and room air at 25 deg C and 70% relative humidity allowing for incidental gains and occupation.

When the portable unit is switched on moisture content of room air is 16.1gm/cubic mt. If outlet air is 100% humidity at 13 deg C, then it will have a moisture content of 11.3gm/cubic mt.

Condensate collection rate = (16.1gm-11.3gm) x 450 cubic mt/hr = 2160gm or 2.1 litre per hr


Example 2 - average temperature & humidity

Average day with outside temp of 22 deg C and relative humidity of 50% and room air at 25 deg C and 50% relative humidity allowing for incidental gains and occupation.

When the portable unit is switched on moisture content of room air is 11.5gm/cubic mt. If outlet air is 100% humidity at 13 deg C, then it will have a moisture content of 11.3gm/cubic mt.

Condensate collection rate = (11.5gm-11.3gm) x 450 cubic mt/hr = 90gm or 0.09 litre/hr


Example 3 - hot weather & average humidity

A humid day with outside temp of 30 deg C and relative humidity of 50% and room air at 33 deg C and 50% relative humidity allowing for incidental gains and occupation.

When the portable unit is switched on moisture content of room air is 18.0gm/cubic mt. If outlet air is 100% humidity at 21 deg C, then it will have a moisture content of 18.4gm/cubic mt.

Condensate collection rate = (18.0gm-18.4gm) x 450 cubic mt/hr = no condensate collected


Conclusion: A portable monobloc air conditioner installed with a single pipe cannot reduce the relative humidity to below 50% but will reduce higher relative humidities towards 50%.


Portable air conditioning hire, by Aircon Hire, the air conditioner hire specialists -
serving London and South East England.


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