Numerical Solution of Heat Transfer Problems in Iron Smelting Furnaces: A Case Study of Ajaokuta Steel Complex

Heat transfer efficiency in blast furnace operations is fundamental to the economic viability of steel production at the Ajaokuta Steel Company in Kogi State, North Central Nigeria. This study develops a numerical model for solving the heat conduction equation governing temperature distribution within the furnace wall and refractory lining during smelting operations. The finite difference method is applied to discretise the two-dimensional heat equation using an implicit Crank-Nicolson scheme, which ensures numerical stability under large time steps. Material thermal properties including conductivity, specific heat capacity, and density are assigned based on published refractory data for magnesia-carbon bricks at elevated operating temperatures. Boundary conditions reflect the thermal loading profile documented in historical operational records from the complex. The numerical scheme is implemented using Python and validated against the analytical solution for simplified one-dimensional cases, yielding a maximum error of 0.6 percent. Simulation results reveal that heat flux through the furnace sidewall peaks during the charging phase, creating thermal stress concentrations in the lower tuyere zone. The model predicts that increasing lining thickness by 12 centimetres reduces outer shell temperature by approximately 34 degrees Celsius, lowering refractory wear rates. Findings support engineering recommendations for preventive maintenance scheduling and lining replacement cycles at the complex. Keywords: heat transfer, finite difference method, blast furnace, Ajaokuta Steel, Crank-Nicolson scheme.