The Calculation of Transient and Steady State Heat Transfer in Refractory Linings under various Conditions
The heat transfer analysis of multi-layer plates in both transient and steady state conditions is particularly important for many pyro-processing industries. Knowing the temperature profile through the different layers is important for design and operational trouble-shooting. In one dimensional (1D) models steady state is the most common condition evaluated. In many cases, simplifying assumptions are made when undertaking a heat transfer analysis. Incorrect assumptions can lead to poor or the wrong selection of materials which in turn can lead to excess heat loss, refractory failure, overheating of vessels, too low shell temperatures or poor lining design with increased capital costs. Knowledge of temperature profiles in the transient regime can be particularly useful when considering drying of materials and thermal shocks caused by rapid changes or cycling of temperatures.
Heat transfer theory is generally well understood. It is possible to predict temperature profiles under various conditions with reasonable accuracy. Most simple software used by engineers or technicians is a 1D model under steady state conditions. Refractory linings are generally composed of multiple layers of varying insulating materials and a dense abrasion resistant hot face layer. When the layer is flat or thin (thickness < 5% of the radius of curvature), conduction heat flow, Q, through each layer is well defined by Q = /Δx A ΔT, where is the average thermal conductivity of the layer material, Δx its thickness, A the area for heat transfer and ΔT the temperature difference across the layer. However, convection is generally applied to one or both sides by using some simplified correlations are used to account for wind and other flow effects. Complications occur where the thermal conductivity is a function of temperature, gas composition and pressure.
A 1D transient model that allows the user to rapidly account for many of the temperature, velocity, gas composition and pressure dependency properties encountered in refractory lined process vessels is an extremely useful tool. This approach is simpler than having to use a 2D or 3D analysis which requires more expensive software and longer times for someone to develop the numerical model.
A 1D transient heat transfer program, P-Thermal, has been developed that quickly allows the user to analysis various conditions and scenarios which can lead to a better understanding of transient heating conditions and more efficient processes. P-Thermal takes into account various gas compositions, varying thermal conductivity of the gas and refractory material, gas pressure and velocity. The graphical output allows the user to quickly evaluate not only interface temperatures between layers but temperatures at multiple points through the lining thickness.