This research aims to achieving the effective cooling parameter on the runout table (ROT) of strip steel in hot rolling process. The 2dimensional transient heat conduction is developed including the external force convection and heat source due to translational motion. The material property, boundary, and initial condition are defined and bounded to model geometry. The strip velocity, cooling water temperature, and external fluid velocity are chosen for the influent parameters during cooling process at ROT. To find the optimality of cooling operating requirement, simulation study is conducted throughout this research. To reach the objective of optimal cooling consumption at ROT, temperature distribution in the strip steel during cooling governs by the form of heat transfer equation. To solve 2dimensional transient heat conduction by numerical methods, the backward difference formula (BDF) applies to discretization of partial differentiation equation (PDE). The parallel sparse direct linear solver (PARDISO) and conjugate gradients method are comparatively applied to computation in linear algebraic equation. The simulation studies are divided into 12 case studies with three variations subjected to cooling conditions at ROT. From simulation results, the range of such three variations can be identified in relation to economic cooling system and desired quality of products.
Recently, advanced material processing technology must have become suitable for low cost of production, high productivity, and better quality of product. Manufacturing process of steel making is a long distance process. Slap products are passed to several machines to gain the desired size of product such as roughing mill machine, finishing rolling mill. After finishing rolling stand, the steel strip type is defined at this stage. Mechanical and physical properties of steel strip are controlled for the desired product quality. Temperature is one of the main parameters to control the product properties. After finishing stand process, the next process of the strip steel will arrive to runout table (ROT) as depicted in Figure
Layout of hot rolling process of strip steel production.
This research is an extension of the previous research [
The mathematical model [
Mathematical model of heat conduction in strip at runout table in rectangular coordinate can be formulated to describe the thermal behavior. The physical system is modeled in twodimensional heat transfer equation of moving strip. The transient analysis of heat transfer of moving strip can be described by (
The differential equation needs to be solved by numerical methods. The heat conduction occurs on the slap surface. The convection heat transfer applied the force convection and natural convection using water and air, respectively. At runout table, conduction of heat transfer in strip surface can be set to boundary conditions by (
Boundary condition at inlet region is
Backward difference formula (BDF) is applied to estimate the first and second order derivative equation as shown in (
The update time derivative of model can be calculated to the specification of time stepping interval. Based on implicit time stepping method, the iterative solution can be formulated by using the finite difference methods. Since
Forward time derivative for
In simulation, we set boundary and condition of 2D heat transfer model as illustrated in Figure
2D heat conduction transfer in transient analysis,
strip dimension
steel type AISI 4340,
convective cooling by water at total plate length 47 m with average heat transfer coefficient
initial value for strip temperature 1148 K,
no heat source
no heat flux generation at all boundaries,
strip velocity:
external fluid velocity:
temperature of cooling water:
Boundary and condition setting.
This research utilized the Comsol Multiphysics software to build the model and solve with the numerical methods as in [
Case of simulation studied on changing three variables.
Case study  Strip velocity 
Fluid velocity 
Cooling water temperature 

1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



11 



12 



At runout table of cooling process of strip steel, we specify the strip temperature at entrance ROT and exist ROT indicated in Table
Output of surface temperature at ROT.
Case study no.  Entrance ROT temperature 
Reference at exit ROT temperature 
Actual surface temperature 
True error  Percent relative error 

1  1148  793  754.31  38.69  0.048789407 
2  1148  793  720.7  72.3  0.091172762 
3  1148  793  458.85  334.15  0.421374527 
4  1148  793  455.25  337.75  0.42591425 
5  1148  793  679.96  113.04  0.142547289 
6  1148  793  455.25  337.75  0.42591425 
7  1148  793  679.96  113.04  0.142547289 
8  1148  793  503.6  289.4  0.364943253 
9  1148  793  441.85  351.15  0.442812106 
10  1148  793  440.4  352.6  0.444640605 
11  1148  793  375.32  417.68  0.526708701 
12  1148  793  378.7  414.3  0.522446406 
Temperature of strip using the parallel sparse direct linear solver (PARDISO).
Temperature of strip using conjugate gradients method.
This research aims to study the effective cooling parameters at ROT of strip steel in hot rolling process. The desired quality of product must be achieved. In cooling process, the efficiency at ROT must be optimal to the customer requirement of strip steel grade. To find the optimal operating variables of ROT’s cooling process, we develop the 2dimensional transient heat transfer of strip steel developed by using mathematical model. Boundary and initial condition are bounded valuable by considering the practical conditions. Numerical solution is applied to solve the mathematical model built using a Comsol Multiphysics software by heat transfer module. Backward difference formula (BDF) applies to discretization of partial differentiation equation (PDE). The parallel sparse direct linear solver (PARDISO) and conjugate gradients method are comparisons for computation of linear algebraic equation. There are three variables useful for each simulation of case studies such as strip velocity, external fluid velocity, and temperature of cooling water, respectively. From the simulation results, the minimum percent relative error of strip surface temperature compared to strip temperature from finishing stand is the case study number 1 as depicted in Table
The work described in this paper was partially supported by the Danieli Far East Co. LTD, Thailand, and Science and Technology Research Institute (STRI), KMUTNB, Thailand.