Paul, the direct answer to your question is “no”; using 200 °F (93 °F) water to heat wort with a copper coil heat exchanger is not going to hurt your efficiency. The important factor is the wort temperature measured at the outlet of your heater, not the temperature of the heating medium.
Heat transfer rate is defined by the following simplified equation:
q = UAΔt/d
Where “U” is the overall heat transfer coefficient, “A” is area, “Δt” is the temperature difference between the heating medium and the product being heated, and “d” is the thickness of the heating surface. This basic equation is used in all sorts of engineering applications from home insulation to food processing to power plant operation. There are a few important take home points that are very helpful to brewing since heat exchangers are used for mash and wort heating, water heating, wort boiling, wort cooling, and fermenter control.
The easiest ways to increase the overall rate of heat transfer are to increase the heat transfer area and/or increase the temperature of the heating medium. In the case of HERMS mashing, you can increase the heating area by using a longer heating coil or by changing the diameter of the tube (tube area = πr2L, where r is the tube radius and L is the tube length). At home it is not practical to use tubing that is greater than 1⁄2 inch (1.25 cm) in diameter because anything larger is difficult to bend without purchasing special tools, and extending the tube length is limited since the tube coil needs to fit in your hot liquor tank.
If area is effectively maxed out, the next variable to play with is temperature. The challenge with this is that water can only be heated to 212 °F (100 °C) before it begins to boil. This limitation can be overcome by using pressurized hot water systems, hot oil systems, hot glycol systems, or steam systems. Pressurizing water above atmospheric pressure increases the boiling point and is really simple in principle, but has several challenges related to safety and practicality. Steam systems are the norm for commercial breweries, but very uncommon at home because of cost.
I don’t know of any homebrewers using hot oil or hot glycol systems, but these two heating media can be heated well above 212 °F (100 °C) and used in the same fashion as the water in your hot liquor tank. In fact, if these high temperature fluids are pumped through a coil submerged in a kettle they can be used for wort boiling. Commercial hot oil and pressurized water brewhouses were fairly common from the 1950s through the 1970s, but were replaced by steam systems. Although this solution requires another vessel and pump, the design is really pretty simple and may be of interest to some.
The third approach is to focus on the U-Value. So what is the U-Value? It’s a term with multiple components that essentially describes the resistance to heat flow of the heat transfer surface. In the case of a heat exchanger tube, the primary components of the U-Value include:
• The thermal conductivity of the heating surface.
• The convective heat transfer coefficient on the product side of the tube.
• The convective heat transfer coefficient on the utility side of the tube (hot water, oil, etc.).
The U-Value is adversely affected by fouling at the heat transfer surface, and the take home message is that a dirty heat exchanger performs less effectively than a clean heat exchanger by reducing the convective heat transfer coefficient. Soils on the wort side and mineral deposits on the utility side are examples of fouling that brewers must address to prevent progressive reductions in heating rate.
The thermal conductivity of the heating surface is a material property and copper conducts heat at a rate roughly 17 times greater than stainless steel (assuming the same material thickness). Although stainless steel has many advantages over copper, thermal conductivity is not one of them. As long as you use cleaning chemicals that are compatible with copper, you will get a very long service life from your heating and cooling coils. The bottom line with this topic is that material selection directly influences the U-Value.
Finally, there is the convective heat transfer coefficient. The most effective means of increasing this value is with liquid turbulence at the heating surfaces. With a HERMS the wort is pumped through the heat exchange coil. Turbulence can be increased inside the tube by increasing flow rate for a given tube size or by reducing the tube size for a given flow rate. Turbulent flow is defined by the Reynold’s number, where Re = ρvd/µ and Re>4,000 is defined as turbulent; ρ = density, v = velocity, d = diameter, and µ = viscosity.
In your HERMS, the hot water in your hot liquor tank moves very little, and the movement that is present is entirely due to natural convection. Stirring the water will significantly increase the U-Value by changing the convective heat transfer coefficient on the water side of the tube. Water tanks can be stirred with a simple mixer or by pumping the water in the tank and returning the water at an angle that causes movement. In the case of a tube-in-tube heat exchanger, such as a wort cooler where a copper tube is surrounded by a hose, the water side convective heat transfer coefficient can be affected by playing with the Reynold’s number.
At the end of the day, what matters to the enzyme system in the mash is temperature. How you change the temperature affects heating rate, and as long as you don’t increase the mash temperature by heating wort from the mash to very high temperatures you will be in good shape.