# A Study of Scrap Heating by Burners: Part II—Numerical Modeling

- First Online:

DOI: 10.1007/s11663-012-9752-1

- Cite this article as:
- Mandal, K. & Irons, G.A. Metall and Materi Trans B (2013) 44: 196. doi:10.1007/s11663-012-9752-1

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## Abstract

A computational fluid dynamics code was developed to model the heating of a bed of porous steel scrap by combustion gases from a burner. The code accounted for nonuniform void fraction in the bed; turbulent, non-Darcian flow, heat transfer from the gas to the scrap; and radiation. The measured bed porosity values were used in the code. Because steel scrap pieces are very irregular in shape and size, the effective particle diameter was fitted to measurements made in a 1-m^{3} capacity furnace, as reported in part I. It was found that the lower porosity of the scrap was the most beneficial in increasing the efficiency of heat transfer to the scrap bed because the interfacial area is larger. The effect of particle size was much smaller. It was found that the configurations that increased the residence time or path length of the gases increased the efficiency. The measured porosity of the bed approached unity at the walls, so this provided an easy path for the gas to short-circuit the bed, which limited the effectiveness of decreasing the porosity to increase heat-transfer efficiency. Similarly, simulations of nonuniform scrap distributions reduced efficiency of heat transfer due to short circuiting. The implications of the findings for industrial operations are discussed.

### Nomenclature

### Abbreviations

- Re
_{P} pore Reynolds number

- Re
Reynolds number

### Subscript

- f
fluid

- s
solid

### Greek

*β*thermal expansion coefficient

*φ*local porosity

*φ*_{∞}porosity from the far away from the boundary or wall

*σ*Stefan–Boltzmann constant

*σ*_{k}*k–ε*model constant*σ*_{ε}*k–ε*model constant*ρ*Fluid density

*ε*dissipation rate of turbulent kinetic energy

*μ*fluid viscosity

*μ*_{eff}effective fluid viscosity

*μ*_{l}laminar fluid viscosity

*μ*_{T}turbulent fluid viscosity

*ν*_{f}kinematic viscosity of the fluid

- Δ
*P* pressure gradient

- Δ
*T* temperature difference between the local and reference temperatures

### Roman

- a
parameter

- b
parameter

*A*_{S}surface area

*C*specific heat

*C*_{P(gas)}specific heat of gas

*C*_{P(R)}specific heat of refractory

*C*_{μ}*k–ε*model constant*C*_{k}porous media

*k–ε*model constant*d*_{P}particle diameter

*E*emissivity

*F*drag coefficient or Geometric factor

*g*acceleration due to gravity

*G*_{K}volumetric rate of turbulent production

*h*_{v}volumetric heat transfer coefficient

*h*_{fS}heat transfer coefficient between fluid and solid

*K*permeability

*K*_{eff}effective thermal conductivity

*K*_{s}thermal conductivity of solid

*K*_{r}radiative conductivity

*K*_{f}thermal conductivity of fluid

*K*_{feff}effective thermal conductivity of fluid

*K*_{seff}effective thermal conductivity of solid

*k*turbulent kinetic energy

*L*characteristic length

*q*^{r}heat flux due to radiation

*S*_{K}source term in turbulent kinetic energy equation

*S*_{ε}source term in the dissipation rate of turbulent kinetic energy equation

*t*time

*T*_{S}solid temperature

*T*_{f}fluid temperature

*T*_{flame}flame temperature

*T*_{exhaust}exhaust gas temperature

*T*_{ambient}ambient temperature

*u*_{f}fluid velocity in

*x*-direction*v*_{f}fluid velocity in

*y*-direction*V*_{d}Darcy velocity

*V*_{P}pore velocity

*w*_{f}fluid velocity in

*z*-direction