A Second-Order Mixed Finite Element Method for Convection-Radiation Flows in Furnaces with Burners

We present a class of simplified approximations for modelling heat transfer in a two-dimensional furnace with inclusions. The governing equations are the well-established thermal incompressible Navier–Stokes equations subject to the Boussinesq approximation for modelling the change in density. Simplified P_N-approximations are carried out for the radiative transfer which is coupled with convection. A Taylor–Hood finite elements technique has been adopted to solve the equations using triangular meshes. The Galerkin-characteristics method is accounted for the dominant advection. Numerical results are presented under the operation of different burners and comparisons between simulations without radiation and with radiation are discussed. Results show that the temperature on the sides of the furnace is not equal. This is due to the fact that the unsteady convection-radiation heat draws the unstable heat flow towards the sides at the chosen time. The effect of higher value of Reynolds number as far as heat transfer is concerned, is that an additional mechanism of heat transfer in the azimuthal and radial directions becomes available and higher. This is commonly termed “eddy transport” and is intense, providing much better transfer of energy across the flow at a given position than in lower value of Reynolds number. Another difference worth noting is the extent of the thermal entrance region in which the transverse temperature distribution becomes fully developed. This region is relatively short in operation with 7 and 9 burners (precisely because of the intense turbulent transverse transport of energy), whereas it tends to be long under the operation of 1 and 3 burners.