More Useful Lumps (Part 2)

In our last post, we examined the case of lumped capacitance where the free-stream temperature was a function of time and presented the equation governing that situation. This time, we’ll look at some specific examples.

More Useful Lumps

All beginning heat transfer classes cover the topic of lumped capacitance calculations: the case where heat conduction within a body is fast enough that the entire body can be considered to be at a single temperature. 

This is a very useful tool for estimating heat transfer in some situations.   However, with just a little work, we can extend the tool to a broader application.

A Thermodynamics Class Project

In my graduate thermodynamics class last year we did a semester-long project developing a computer model of an internal combustion, spark ignition engine.  We started with a simple Otto cycle and through the course of the semester added more realistic effects until by the end of the semester we had a fairly reasonable computer model for an engine.

Keep Turning Up the Hot Water!

In the last two posts, we considered the cooling of the exit temperature of a hot water tank with a given flow rate and heat input rate, and thought about recharge times once the hot water withdrawal was stopped.  However, in real life you’d keep turning up the proportion of hot water as long as you could in order to keep your shower at a constant temperature.  Of course, the cooler the water came out from the hot water tank, the more you’d need to use, making it cool down even faster.

How Long Should I Wait to Shower?

Last post we talked about the temperature of a hot water tank as hot water is withdrawn, and also about the temperature while it is recharging.  With the expressions that we had for those processes, it is possible to calculate the time that it would take for the tank temperature to reach a certain point, and for the tank to recharge from that point. 

Who Used All the Hot Water?

You may have had the wonderful experience of starting a nice, hot shower, only to find that somebody has mostly drained the hot water heater tank.  This leaves you desperately turning the tap to more and more hot water while the shower gets cooler and cooler.  You lather, rinse, (no time for repeat) with feverish speed, but eventually wind up rinsing off in lukewarm (or ice-cold) water.  If so, this post is for you.

Convection Heat Transfer

Convection heat transfer describes the movement of heat between a solid surface and a moving fluid.  The basic equation of convective heat transfer, sometimes known as Newton’s law of cooling, is very straightforward:

                                   q″=h*(T_s-T_f)

Pressure Cookers at Altitude

Water boils at 212 deg F at sea level, of course, but the boiling temperature of pure water is a pretty strong function of the ambient pressure.   This figure shows the boiling temperature of water at different pressures.  Atmospheric pressure at sea level is around 14.7 psi, and that point is marked on the figure with a red circle. The standard operating pressure for pressure cookers is 15 lbs which means 15 psi above atmospheric pressure.  That point is marked with a green triangle in the figure.  You can see that the boiling temperature for water is around 250 deg F inside a pressure cooker operating at sea level.

How big is the heat flow?

Sometimes it is useful to have a ballpark idea of the size of a heat flow before even starting a more detailed heat transfer analysis.  It is also kind of fun to have a rough idea of the magnitude of different heat flows. To those ends, we present this figure:

Freezing water on a warm night

Everybody knows that water freezes at 32 deg F. 

Then how come frost (which is just ice that has come from the water vapor in the air) can sometimes be seen in the morning on nights when the temperature never got below 32 deg F?  

 Similarly, backpackers and desert dwellers occasionally report a film of ice on a puddle or bucket of water on not-quite-freezing nights.

The answer has to do with the nature of heat transfer.  Heat can move by conduction (movement through a solid, or a fluid at rest) by convection (movement between a solid and a flowing fluid) or by radiation (direct exchange of energy via electromagnetic waves).  The temperature of a surface depends on the temperatures of the surroundings plus the effects of all three modes of heat transfer.

From the ground...down (part 3)

Some people might think that we’ve already talked about this topic enough, but we know better. 

In the last two posts, we talked about how temperature fluctuations at the surface of the ground might affect the underground temperature, and specifically, how deeply those fluctuations might penetrate.

So, now imagine that there might be an application where it wasn’t the surface temperature nor the ground temperature that mattered, but the difference between the two.   (This actually is important for certain applications that propose to use that temperature difference to generate small amounts of electricity).