When measuring the temperature rise of an unheated quench tank, the equation used to determine the size of a quench tank is:

Where M_{m} is the mass of the metal, C_{pm} is the specific heat of the metal, and ΔT_{m} is the decrease in the temperature of the metal being quenched. Similar nomenclature is used for the quenchant. Typical values for specific heat at 20°C are as follows:

- Steel 0.17 cal/gm/°C (0.17 BTU/lb/°F)
- Aluminum 0.23 cal/gm/°C (0.23 BTU/lb/°F)
- Quench Oil 0.50 cal/gm/°C (0.50 BTU/lb/°F)
- Polymer Quenchant 0.95 cal/gm/°C (0.95 BTU/lb/°F)
- Water 1.0 cal/gm/°C (1.0 BTU/lb/°F)

For batch operations, the tank size is determined by solving for M_{q}, once the other known values are substituted into the equation, and the allowable temperature rise is established.

In a continuous operation, a constant influx of heat from the parts is occurring. This absorbed heat from the parts initially heats the quench oil. If the heat input from the hot parts is equal to the heat recovered by tank losses and heat exchanger, then the quenchant temperature will maintain a steady state temperature. In this case, the operating temperature is controlled as a function of the pounds per hour of workload, and the amount lost through the tank or recovered via the heat exchanger (Figure 1).

In this case, the equation above is modified, to replace M_{m} to be the pounds per hour instead of pounds quenched at one time. The units then become BTU/hr for the heat that needs to be removed from the system. Your heat exchanger supplier can get much more in depth with the calculation of the heat exchanger, and properly size the heat exchanger, pumps, and filters needed for the heat exchanger installation. However, this method will give a quality estimate of the size of heat exchanger needed.

For most continuous furnaces, the initial loads heat the oil to the desired operating temperature, and the heat exchangers remove the balance of the heat. The heat exchanger is sized (plus safety margin) to remove the heat of the weight per hour.

### Example

A parts manufacturer of widgets is designing a quench tank for an existing furnace they are modifying for use. The parts weigh 2.5 pounds each and are SAE 1060 forgings. It is desired to quench into a polymer quenchant to reduce smoke and fumes. The austenitizing temperature is 1,600°F, and the bath temperature is initially 100°F. The production rate is 5,000 lbs/hour. It is desired that the operating temperature of the quenchant should be 125°F. The parts should exit the quench tank at 160°F, which is approximately the martensite finish temperature of SAE 1060.

Using the equation

Where Q is the heat load in BTU/hr and substituting:

This is the heat that must be removed from the quench tank by the heat exchanger and heat losses from the surface and shell of the quench tank.

Instead of using heaters to heat the quench tank to the desired operating temperature of 125°F, the initial parts are used to heat the quench tank up to the operating temperature. We will assume that we want the tank to get to operating temperature within 30 minutes. So, using a similar equation

we can determine the size of the quench tank. In 30 minutes, approximately 2,500 pounds will be quenched, or 468,000 BTU/hr (936,000 BTU/hr/2). Using this value of Q, and solving for M_{q}:

The specific gravity of a dilute concentration of polymer is approximately that of water, and if water weighs 8.33 lbs/gal, then the quench tank size would be 2,366 gallons. Adding an additional 10 percent as a safety factor yields a tank size of 2,600 gallons. The heat exchanger would be sized for 936,000 BTU/hr or 78 refrigeration tons. The temperature of the quench tank can be controlled by using a thermocouple, temperature controller, and proportional valve on the return line of the heat exchanger.

### Conclusions

In this brief column, I have illustrated a quick method for determining the size of a continuous furnace quench tank, assuming the basic information of alloy, production rate, and quenchant are known. Further, this calculation also determines the necessary heat exchanger size.