DT097

DT097Heat Transfer

Richard KellyReference: Physics, Cutnell & Johnson 9th Ed.

Conduction is the process whereby heat is transferred directly through a material, with any bulk motion of the

material playing no role in the transfer.

Conduction

Materials that conduct heat well are referred to as Thermal Conductors. E.g. metals

Materials that conduct heat poorly arereferred to as Thermal Insulators. E.g. wood, glass, polystyrene

Thermal Conductors and Insulators

Heat is conducted through the bar when the ends of he bar are maintained at different temperatures.

The heat flows from the warmer to the cooler end.

Twice as much heat flows through two identical bars as through one.

1. Q is proportional to the time t during which conduction takes place (). Moreheat flows in longer time periods.

2. Q is proportional to the temperature difference ∆T between the ends of the bar(Q ∆T ). A larger difference causes more heat to flow. No heat flows when bothends have the same temperature and T= 0 C.

3. Q is proportional to the cross-sectional area A of the bar (). Look at the two identical bars (insulated sides not shown) placed between the warmer and cooler bodies. Clearly, twice as much heat flows through two bars as through one, because the cross-sectional area has been doubled.

4. Q is inversely proportional to the length L of the bar (). Greater lengths of material conduct less heat.

The amount of heat Q conducted through the bar from

the warmer end to the cooler end depends on a number of factors:

For thermal insulation in buildings, engineers use the concept of thermal resistance, denoted by R. The thermal resistance R of a slab of material with area

A is defined so that the heat current Q through the slab is Q

These proportionalities can be stated together as Q(AT )t/L. With the aid of a proportionality constant k, this result, which

is called the thermal conductivitycan be expressed as:

Since k =QL/(tA∆T )

the SI unit for thermal conductivity is

or

The SI unit of power is the joule per second (J/s), or watt (W), so the thermal conductivity is also given in units of

• Different materials have different thermal conductivities

• Because metals are such good thermal conductors, they have large thermal conductivities.

• In comparison, liquids and gases generally have small thermal

• conductivities. • In fact, in most fluids the heat transferred by

conduction is negligible compared to that transferred by convection when there are strong convection currents.

• Air, for instance, with its small thermal conductivity, is an excellent thermal insulator when confined to small spaces where no appreciable convection currents can be established.

• Styrofoam derives its fine insulating properties in part from the small dead-air spaces within them, as Figure 13.9 illustrates.

U-Values

Thermal transmittance, also known as U-value, is the rate of heat transfer or heat loss, in watts, through one square metre of the buildings fabric, divided by the difference in temperature across that element of the structure’s fabric.

It is expressed in watts per square metre per degree Kelvin, (W/m^2K).

Well-insulated parts of a building have a low thermal transmittance whereas poorly-insulated parts of a building have a high thermal transmittance.

U-values are a rating of energy efficiency. They are used to rate and compare windows, exterior doors, skylights and all other exterior building components, including exterior walls.

U-values are also the standard used in the building regulations for specifying the minimum energy efficiency values for all of these components.

The rate of heat loss, Q, through a building element can be determined from:

(Watts) Where A is the area of the element in square

metres is the difference in temperature between

both sides of the element

Using U-values

Convection

Convection is the process in which heat is carried from place

to place by the bulk movement of a fluid.

When part of a fluid is warmed, such as the air above a fire, the volume of that part of the fluid expands, and the density decreases.

According to Archimedes’ principle the surrounding cooler and denser fluid exerts a buoyant force on the warmer fluid and pushes it upward.

As warmer fluid rises, the surrounding cooler fluid replaces it. This cooler fluid, in turn, is warmed and pushed upward.

Thus, a continuous flow is established, which carries along heat. Whenever heat is transferred by the bulk movement of a gas or

a liquid, the heat is said to be transferred by convection.

The fluid flow itself is called a convection current.

Hot water radiators are frequently used in homes, and a cooling coil is a major component of a refrigerator. The locations of these heating and cooling devices are different because each is designed to maximize the production of convection currents.

Where should the heating unit and the cooling coil be located?

(a) Heating unit near the floor of the room and cooling coil near the top of the refrigerator

(b) Heating unit near the ceiling of the room and cooling coil near the bottom of the refrigerator

Heating and Cooling by Convection

An important goal for the heating system is to distribute heat throughout a room.

The analogous goal for the cooling coil is to remove heat from all of the space within a refrigerator. In each case, the heating or cooling device must be positioned so that convection makes the goal achievable.

Answer (a) is correct. The air above the radiator is heated, like the air

above a fire. Buoyant forces from the surrounding cooler air push the warm air upward. Cooler air near the ceiling is displaced downward and then warmed by the radiator, causing the convection current illustrated in Figure 13.3a.

Within the refrigerator, air in contact with the top-mounted coil is cooled, its volume decreases, and its density increases. The surrounding warmer and less dense air cannot provide sufficient buoyant force to support the cooler air, which sinks downward. In the process, warmer air near the bottom of the refrigerator is displaced upward and is then cooled by the coil, establishing the convection current shown in Figure 13.3b.

Air is a mixture of gases, including nitrogen, oxygen, and water vapour.

The total pressure of the mixture is the sum of the partial pressures of the component gases.

The partial pressure of a gas is the pressure it would exert if it alone occupied the entire volume at the same temperature as the mixture.

The partial pressure of water vapour in air depends on weather conditions. It can be as low as zero or as high as the equilibrium vapour pressure of water at the given temperature.

Humidity

Surface Condensation

To provide an indication of how much water vapour is in the air, weather forecasters usually give the relative humidity.

If the relative humidity is too low, the air contains such a small amount of water vapour that skin and mucous membranes tend to dry out. If the relative humidity is too high, especially on a hot day, we become very uncomfortable and our skin feels “sticky.”

Under such conditions, the air holds so much water vapour that the water exuded by sweat glands cannot evaporate efficiently.

The relative humidity is defined as the ratio (expressed as a percentage) of the actual partial pressure of water vapour in the air to the equilibrium vapour pressure at a given temperature.

Relative Humidity

Moisture movement within the materials making up a structure leading to local accumulations sufficient to cause problems: Rot Corrosion Frost damage Wetting of insulation Staining of internal surfaces Damage to equipment within the building

The term in the denominator on the right of the previous equation is given by the vaporization curve of water and is the pressure of the water vapour in equilibrium with the liquid.

At a given temperature, the partial pressure of the water vapour in the air cannot exceed this value. If it did, the vapour would not be in equilibrium with the liquid and would condense as dew or rain to re-establish equilibrium.

When the partial pressure of the water vapour equals the equilibrium vapour pressure of water at a given temperature, the relative humidity is 100%. In such a situation, the vapour is said to be saturated because it is present in the maximum amount, as it would be above a pool of liquid at equilibrium in a closed container. If the relative humidity is less than 100%, the water vapour is said to be unsaturated.

Ventilating cavity - partial cavity fill

Unventilated

Ventilated

Dew Point

When air containing a given amount of water vapour is cooled, a temperature is reached in which the partial pressure of the vapour equals the equilibrium vapour pressure.

This temperature is known as the dew point. The diagram shows that if the partial pressure

of water vapour is 3.2 x10^3 Pa, the dew point is 25 C.

This partial pressure would correspond to a relative humidity of 100%, if the ambient temperature were equal to the dew-point temperature.

Hence, the dew point is the temperature below which water vapour in the air condenses in the form of liquid drops (dew or fog).

The closer the actual temperature is to the dew point, the closer the relative humidity is to 100%.