# Improvement of Radiant Heat Efficiency of the
## 1 Introduction  
Additive manufacturing (AM) has emerged as a breakthrough processing technology owing to its various advantages, such as ease of fabrication of complex geometry parts, improvement of expensive raw materials' yield [1; 2; 3; 4; 5]. AM has a short lead time, but not always. AM parts (made from the AM process) can be applied in diverse fields and contribute in various ways to the system to which they belong. For example, the total performance of the system is increased by high-performance AM parts, while lightweight AM parts can reduce energy consumption [6; 7; 8; 9; 10]. The final product of the continuous annealing process is a finished cold-rolled steel strip. In this process, the strips are annealed in a reheating furnace, with an atmosphere stabilized and maintained without chemical change. This type of annealing is done in a continuous annealing line (CAL), commonly referred to as CAL in the steelmaking industry. POSCO has been searching processes that could reduce fuel consumption by applying AM because of the implementation of stricter regulations on the air environment [11]. The CAL consumesa large amount of fuel to maintain pre-set heat treatment temperatures (approximately 800-1000 \({}^{\circ}\)C). Depending on the size of the CAL, approximately 100-500 radiant tubes are in operation in the CAL, and about 300 million m\({}^{3}\) of coke oven gas (COG) and liquefied natural gas (LNG) are consumed every year. Radiant heat is continuously released from the outside surface of radiant tubes, whereas combustion heat is charged and then continuously released through the inside surface radiant tubes. A radiant tube (RT) consists of a burner, recuperator, and tube made of either high-temperature steel or nickel-based alloys. In the burner, the fuel (LNG or COG) ignites and quickly enters the inlet of the RT. The generated high-temperature heat in the tube is transmitted by radiation from the outer surface of the tube to the steel strip. Lastly, the heat is exhausted through the outlet. The hot exhaust gas recovered by the recuperator is then used to reheat the cold air flowing through the burner RTs appear in diverse shapes: double P, straight, W, and U [12]. Many studies have focused on improving the radiant heat efficiency of the burner and reheating system of the RT. [PERSON] et al. in 2010 argued that increasing fuel efficiency depends on an effective reheating of the cold air flowing through the burner [12]. Thus, they emphasized on the importance of RT designs that can use internal air preheating technologies, such as plug-in recovery, and regenerative and recuperative burners. [PERSON] et al. in 2015 used a double regenerative RT burner to improve the unstable combustion, gas pressure, and flow changes that often occur in conventional burners [13]. They reported that using low heat gases capable of burning at lower temperatures could reduce fuel costs, thus increasing fuel efficiency. [PERSON] et al. in 2006 tried to find the best operating conditions of RT in terms of optimum equivalence ratio, thermal power, and lower pollutant emissions [14]. They introduced a self-induced exhaust gas recirculation mechanism and reduced NOx emissions by up to 50%, for a wide range of thermal power and equivalence ratios, compared to the original burner design without compromising the thermal efficiency, CO emissions, and surface temperature uniformity of the RT. This paper presents a way to improve the radiant heat efficiency of W-type RT in CAL using AM. The RT surface area was increased by printing a series of honeycomb patterns on the RT surface. A three-dimensional (3D) elastic-thermal finite element (FE) analysis was carried out to calculate the time-integrated radiation per unit area (hereafter, referred to as radiant heat (J/s) and determine the appropriate dimensions (width, length, and thickness) of the honeycomb printed on the RT surface. An RT is large (the size of a straight tube is \(\Phi\)190 \(\times\) 2000 mm) and has a curved surface.