Archive for February 14th, 2010

Heat Transfer in Mechanical Engineering, Part I, Conduction

Sunday, February 14th, 2010

     Last week we finished up our series on fluid mechanics with a look at fluid dynamics, which considers fluids that move.  This week we’ll talk about heat transfer, which is the study of how heat moves through vacuums, gases, liquids, and solid objects.

     Understanding heat transfer is important when designing insulating materials, because they’re responsible for conserving energy by keeping heat contained inside things, things like pipes, boilers, and steam turbines.  Done in reverse, the concepts of heat transfer can also be used to determine how to dissipate excess heat, like in automobile engines and electrical equipment, to keep them from overheating.

     In the most basic of terms, heat transfer takes place because heat always wants to travel from a place of higher temperature to a place of lower temperature.  Heat will continue to flow in this direction until temperatures reach equilibrium, and this is true whether we’re considering heat moving through gases, liquids, or solids.  For example, if you pull the plug on your refrigerator, the heat from the air in your kitchen will begin to flow through the walls of the refrigerator where it will get absorbed by the cold food and ice cubes.  Eventually the heat will stop flowing when the temperature of the stuff inside of the refrigerator equals the temperature of the air in the kitchen.

     Now, there are different means by which heat can be transferred.  These include conduction, convection, and radiation.  Heat transfer analysis can get complicated, especially if it involves a combination of these means.  For now, let’s focus on conduction.

     As its name implies, heat transfer by conduction occurs when heat is conducted through a material.  Let’s consider the simple conductive heat transfer problem shown in Figure 1. 

Figure 1 – Heat Flow Through A 3-Centimeter Thick Copper Plate

 

    Figure 1 shows a 3 centimeter (cm) copper plate.  One side of the plate has a temperature of 400 degrees Centigrade (°C), the other side that of 100°C.  For this example let’s say that the plate is 30cm high and 20cm wide.  So, how do you calculate the heat flow?

    Now remember, heat always flows from hot to cold, so we know that it’s going to flow from the 400°C side to the 100°C side of the plate.  But let’s get into a little more detail.  Conductive heat flow depends on this temperature difference and some other things, like the ability of the material itself to conduct heat.  As with other materials and processes commonly used, scientists have performed lab experiments to measure heat conducting ability for all sorts of materials and recorded them in resource materials under the heading, “thermal conductivity,” so this element of information is readily available to us if we only seek out the reference manuals.  But in addition to this thermal conductivity factor, heat flow also depends on the area of the material that it is flowing through, as well as the material’s thickness.  So with this said, we can calculate the heat flow in Figure 1 to be:

        Heat Flow  =  (The Thermal Conductivity of Copper) x

                                   (The Area That The Heat Is Flowing Through) x

                                   (The Difference In Temperature) / (The Plate Thickness)

     From reference manuals, we know that the thermal conductivity of copper is 370 Watts/meter °C.  The second part of the equation asks us to calculate the area through which our heat will be flowing, and we calculate this to be 20cm x 30cm, or 600cm2.  Now in order for the units to match those of the thermal conductivity constant, we have to convert the area and thickness from centimeters (cm) to units of meters (m).  Therefore, 600cm2 becomes 0.06m2, and 3cm becomes 0.03m.  So our completed equation becomes:

Heat Flow = (370 W/m °C) x (0.06m2) x (400°C – 100°C) / (0.03m)

= 222,000 Watts

     This means that 222,000 Watts of heat will flow from the 400°C side to the 100°C side.   “Watts” don’t just apply to light bulbs, as we can see in this example.  Here, the number of Watts represent how much heat energy is flowing in a given amount of time.  This heat energy flow will stop when the temperature on each side of the copper plate becomes the same.  

     That wraps things up for our discussion of heat transfer via conduction.  Next week we’ll consider heat transfer by convection, and the next time someone talks about their convection oven, you’ll know what they’re talking about.

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