Refractory Lining Heat Loss, Interface Temperatures, and Shell Temperature

A furnace or boiler lining is a series of resistances, and the whole design lives at the interfaces rather than at the shell. Per unit area each layer adds its thickness over its conductivity, the outer film adds one over its coefficient, the flux is the total temperature drop over the total resistance, and every interface is the hot face less the flux times the resistance ahead of it. A 4.5 in hot face at 2,100 degF over 2.5 in of insulating firebrick and 2 in of block, in 90 degF air, passes 336 BTU/hr/sq ft and lands the shell at 258 degF. The trap worth carrying is that INSULATING THE OUTSIDE OF A FURNACE MAKES THE INSIDE HOTTER: adding block insulation to cut heat loss raises every interface behind the hot face, because less heat is now escaping, and on that same wall the block sees 1,480 degF on its hot face. A lining improved that way can put a layer above its service temperature, and the failure does not appear at commissioning -- it appears months later as a shell hot spot where the backup has shrunk and opened a path. Note which face the limit applies to: a layer's service temperature is a limit on its HOT face, the interface ahead of it, not the cooler one behind. The shell carries two limits pulling opposite ways. One is the personnel and structural limit, which wants it cool. The other applies on flue gas service, where the casing must stay ABOVE the acid dew point, roughly 250 to 300 degF depending on the fuel's sulphur, or sulphuric acid condenses on the inside and corrodes it -- so over-insulating a flue gas casing to save energy is a corrosion failure, the opposite of the usual advice. Conductivities are entered because refractory k varies strongly with temperature and product, and using one value across a 2,000 degF drop is the largest approximation here. One-dimensional and steady state: it does not address dry-out schedules, expansion joints, corners, penetrations, anchors and their thermal bridges, gas-side radiation, slag attack, or spalling. The refractory and insulation manufacturers' data and the furnace or boiler designer govern.

one-dimensional steady-state plane-wall conduction: each layer contributes thickness / conductivity and the outer film one / coefficient, the flux is the total temperature drop over the total resistance, and each interface temperature is the hot face less the flux times the resistance ahead of it; the shell is the ambient plus the flux times the film resistance.

A steady-state series-resistance solve with every interface reported against its own layer's service limit, and the shell against both a personnel limit and, on flue gas service, an acid dew point. Conductivities are ENTERED because refractory k varies strongly with temperature and with the specific product. It does not address transient heating and dry-out schedules, thermal expansion and joints, corners, arches, penetrations, anchors and the thermal bridge each anchor makes, gas-side convection and radiation, slag or chemical attack, or spalling.

A sum of resistances and one division; no manufacturer conductivity table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: hot_face_f, ambient_f, film_coeff_btu_hr_ft2_f, layer1_thickness_in, layer1_k, layer1_limit_f, layer2_thickness_in, layer2_k, layer2_limit_f, layer3_thickness_in, layer3_k, layer3_limit_f, shell_limit_f, acid_dew_point_f, total_resistance, flux_btu_hr_ft2, interface1_f, interface2_f, shell_temp_f, layer3_hot_face_f

• Conductivities are entered refractory k varies strongly with mean temperature; one value across a 2,000 degF drop is the largest approximation herethe refractory manufacturer's k-versus-temperature curve
• One-dimensional and steady state no transient, corner, penetration, or anchor bridgingthe furnace or boiler designer
• Not a lining design material selection, dry-out, and expansion joints are separatethe refractory manufacturer and the applicable code