Friday, June 21, 2019

Unizor - Physics4Teens - Energy - Heat Transfer - Convection

Notes to a video lecture on

Heat Transfer - Convection

As in a case of conduction, we start with a statement: heat is a form of internal energy that is related to molecular movement.
However, while heat transfer during the process of conduction occurs between molecules oscillating around their relatively fixed positions and transferring their internal energy by "shaking" the neighboring molecules, convection occurs when molecules are free to travel in different directions and carry their internal energy with them.

In other words, conduction is a pure transfer of energy on a micro level from one oscillating molecule in a relatively fixed position to another such molecule, while convectionoccurs when molecules freely fly away from their positions, carrying their internal energy with themselves, thus transferring energy on a macro level.

It should be noted that, when dealing with solid objects, conduction is a prevailing way of heat transfer, while in liquids and gases the main way of heat transfer is convection. It does not mean that conduction does not occur in liquids or gases, it does, but it does not constitute the major way of heat transfer. Much more heat is transferred through the mechanism of convection

Here are a few examples of heat transfer through convection:
(a) heating up water in a pot; heat is carried from hot bottom of a pot up by hot (fast moving with high kinetic energy) molecules;
(b) circulation of air in the atmosphere from hot places to cold;
(c) circulation of water in oceans from hot places to cold.

Describing convectionmathematically is not a simple task.
While in case of conduction we can use a relatively simple Fourier's Law of Thermal Conduction
q(x) = −k·dT(x)/dx
that describes the heat flow as a function of how fast the temperature between the layers of conducting material changes (dT(x)/dx) and properties of the material itself (conductivity coefficient k), the process of convection is significantly more complex, described by convection-diffusion differential equations that are beyond the scope of this course.

However, for practical purposes we can use a similar formula that puts the amount of heat transferred by convectionprocess in a liquid or gas during a unit of time through a unit of area as proportional to a difference of temperatures between the layers of liquid or gas and a convective heat transfer coefficient h that depends on the physical properties of this liquid or gas:
q = −h·(T2−T1)

This formula puts amount of heat q going through a layer of a unit area of liquid or gas during a unit of time as proportional to a difference of temperatures between bounding surfaces of this layer T2−T1 and some physical properties of liquid or gas expressed in convective heat transfer coefficient h that, in turn, depend on such properties as viscositydensity, the type of flow (turbulent or laminar) etc.

Consider an example.
A round steam pipe of temperature 100°C goes through a room with air temperature 25°C. We have to calculate the amount of heat from the pipe to select an air conditioner required to neutralize the heat from a pipe and keep the room temperature at that level.
Assume that the pipe's length is 4m, diameter 0.2m and the convective heat transfer coefficient of air is 40J/(sec·m²·°C). As we know, J/sec is a unit called "watt", so we will use W instead of J/sec.

The heat transfer per unit of time through a unit of area of a pipe is, therefore,
q = 40·(100−25) = 3000(W/m²)
The pipe's area is
A = π·0.2·4 = 2.512(m²)
Therefore, the pipe is producing the following amount of heat:
Q = 3000·2.512 = 7536(W)

So, we need an air conditioner that can extract 7536W of heat from the room to maintain stable temperature of 25°C.
Usually, the power of air conditioners is measured in BTU/hr (1 watt = 3.41 BTU/hr). So we need an air conditioner of approximately 2200 BTU/hr - a relatively small one.

Another example.
Outside temperature is 40°C, inside a room we want temperature 25°C. The glass wall between a room and outside air has an area of 20m². What kind of air conditioner is needed to maintain the room temperature at 25°C, assuming the convective heat transfer coefficient of air is 40W/(m²·°C)?

Q = 40·(40−25)·20 = 12000(W)
This is equivalent to about 3500 BTU/hr.

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