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Last post we talked about the temperature of a hot water tank as hot water is withdrawn, and also about the temperature while it is recharging.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.