Many stakeholders involved in heat treating try to find answers as to why their products are discharged 100-300°F below the furnace setpoint temperature. We shall only consider continuous annealing furnaces used in metal heating for the purposes of this article.

The purpose of annealing is to heat up the product to a predefined temperature, soak it at this temperature for a specified amount of time and then cool it to a lower temperature consistent with material specifications. This is a controlled process where careful application of time, temperature and atmosphere (for gas-fired furnaces) is critical.

By controlling these variables, the internal atomic microstructure of the product is also altered. The physics of the heating process is just as interesting as the physics of the metallurgical interactions occurring in the product. It is this microstructure that determines the final mechanical properties of the material. This is what you sell to the customer. I hope by now it is clear that the temperature of the product is the most critical control variable. Let’s keep this in mind.

As opposed to batch furnaces, continuous furnaces (Fig. 1) constantly feed the product to a furnace divided into several zones of control. This type of heating reaches steady-state, and large variations in furnace temperature are not common, especially with modern temperature control and process automation. However, most control problems arise because the focus of control is on the furnace and not the product to be heated – in this case, a metal strip/sheet. While this article touches on existing control and modern control technologies to address this issue, the goal is to simply explain the physics behind the difference in strip and furnace temperature, which industry experts refer to as the “final temperature head.”


What does the physics tell us?

Today, many furnaces in the industry control only to the furnace temperature. There is a general assumption that the product and the furnace will assume the same temperature. Therefore, the furnace setpoint is set to the desired strip temperature. This is not true in most practical heating applications, and many people wonder why there is a variation between the strip and the furnace. Here comes the physics: thermal inertia.

Thermal inertia is the degree of slowness with which the temperature of a body approaches that of its surroundings. It depends on the body’s absorptivity, specific heat, thermal conductivity, geometry, etc. Alternatively, it is defined as the measure of responsiveness of a material to changes in temperature. Materials with high specific heat possess a high thermal inertia and vice versa.

Many alloy grades have differing thermal-inertia values. Given that the product to be heated possesses different values of thermal conductivity, diffusivity, emissivity, specific heat and geometry or surface area, the time to reach the furnace temperature is reduced.

Not only does the physics prove this, but many years of combined experience between experts in this industry also prove that equal temperature of furnace and strip is not to be assumed in practical heat-treating applications.

In the widely consulted and industry-accepted book Industrial Furnaces, professor Trinks advises that “Strip temperature is almost never the same as furnace temperature, following firing rates more closely than furnace temperature” [Trinks 134]. The latter part of his statement is very true, especially for direct-fired or open furnaces where flames are “seen” by the heat sink (product).


How then can we proactively address this issue?

First, we can apply the physics to set up the furnace. An example of this is discussed here for continuous annealing of titanium sheet (Fig. 2). This is mostly beneficial where the control process relies heavily on operator experience or the current control method is not productive.

Second, a growing research area across many leading companies is the development of a strip temperature control that focuses on the strip temperature and optimizes line speed for maximum productivity. Many advanced control techniques have been applied, such as PID with advanced tuning methods, model predictive control, intelligent control and many others. Some of these results have proven to be very efficient and productive. We show some modern control methods in the section after “Example of Furnace Physics.”


Example of Furnace Physics

We wish to anneal a titanium alloy sheet (cp = 0.40 BTU/poundm/°F, density = 278 poundm/feet3) 0.07 inches thick, 1,000 feet long and 42 inches wide in a continuous furnace that uses a medium-velocity gas burner with good air/fuel ratio control (assume heat-transfer coefficient, h, of 20 BTU/feet2/°F/hour). We desire strip temperature of 1400°F (initial strip temperature of 70°F), and we wish to run at a speed of 30 feet/minute. We can simply use the thermodynamic energy equation to evaluate this problem by using the following approach (below).

We have now predetermined the amount of heat that needs to be transferred into the product to meet design specifications based on the desired temperature. We can now apply the generalized combined heat-transfer model to determine the mean temperature head (average difference between the furnace and product temperature).

This means that we need to set the furnace 78°F (1400 + 78 = 1478°F) above the desired strip temperature to account for thermal-inertial effects. This value represents the mean temperature head and not the final temperature head, but it is good for close approximation. This temperature head is low, which is good, because we are assuming a moderate heat-transfer coefficient value.

Actual values for most traditional combustion applications are around 8-15 BTU/feet2/hour/°F. The values are much higher (>40) for modern high-velocity burners that exit POC gases at >300 feet/second. Interested readers should refer to The Heating of Steel by M.H Mawhinney for a review of finding the actual final head temperature. If we used a traditional burner with velocity less than 300 feet/second, the heat-transfer coefficient will be in the range of 2-12, which would give a temperature head of 130-310°F and lead to a much less-efficient process.

This method works best if:

  • Circulation is greater due to high-velocity burners.
  • Pyrometer measurements are reliable to a reasonable degree.
  • Furnace has higher temperature-holding capability.


Existing and Modern Control Technology

Due to the large thermal inertia of various products in addition to new products evolving in the market, conventional methods of controlling strip temperature through the furnace are becoming more obsolete and unproductive. Even PID control algorithms struggle to meet the demands of changing product dimensions in the furnace (transitions) and large inertias that introduce delays and increase dynamic response time.

The concept of controlling the material temperature using advanced and or intelligent control is one of many interests of the author, and he wishes to write more on the topic and any innovative solutions developed in the coming years.

The control scheme in Figure 3 shows a classical approach to controlling strip temperature in a continuous furnace. Separate PID loops are used for the strip, temperature and fuel input control. This is more common because the strip control is just an addition to the already existing furnace temperature control. A starting temperature is needed for the furnace, and, based on the control logic, the furnace is adjusted to meet strip temperature. Logic to limit the furnace temperature may be included to account for newly developed products with tighter furnace temperature requirements.

An improvement on the classical approach is the use of advanced methods such as predictive control (Fig. 4). In the simplest type of predictive control, the system is smarter in the way that it anticipates the strip dimensions and speed ahead of time and adjusts the furnace parameters in real time. This allows the system to be proactive and reduce the complexity arising from the changing product dimensions in the furnace. The benefits are increased productivity and better fuel consumption and overall quality product.

In a slightly complex form of this control, a process model pre-calculates the strip temperature for a given time period and uses an optimization function to minimize the error between the setpoint and actual temperature. This is done at each time step and is very efficient, but it needs good computational power. This type of control is known as model predictive control (MPC), which is a form of optimal control.

Since we live in the world of artificial intelligence, some model predictive controllers use a data-driven or machine-learning model instead of the process model. This is especially useful where there is not enough information to describe the physical process.

More research in advanced product temperature control and intelligent control systems has been conducted in this area. The future is bright for product temperature control in industrial process-heating applications, especially in metal heating.



The purpose of this article is to explain the physics surrounding the observed delta between furnace and strip temperature in industrial- and process-heating applications. Understanding the physics behind this phenomenon allows product and process engineers to own their process by properly setting up the furnace. A simple way of predetermining the required difference is demonstrated.

Modern ways of directly controlling product temperature are presented to give the reader an understanding of the different automation, control methods and systems available to help process and product engineers focus on satisfying tight customer requirements.

Click here to listen to the author discuss this article with Industrial Heating Editor Reed Miller in a podcast.

For more information: Contact Louis Ayisi, process control engineer, Allegheny Technologies Inc., Specialty Rolled Products, 100 River Road, Brackenridge, PA 15014; tel: 978-798-8135; e-mail:; web:



1. KATA Steel, Steel Factory,

2. Kawasaki Steel 21st Century Foundation, An Introduction to Iron and Steel Processing, 3C (5) “Continuous Annealing,” 2002