The use of mathematical models to predict the thermal resistance of polymer-based, intumescent coatings are reviewed and their limitations are discussed. A mathematical model is derived to describe the developing temperature profile across an intumescent coating when exposed to a radiant heat source. The model includes the effects of: the endothermic and exothermic reactions; convective heat transfer as degradation gases are transported through the coating; radiation heat transfer across the developing porous solid; and the increase in thermal resistance as gases are formed and the coating expands. The model predictions are compared with experimental data from the heating of epoxy-based and vinyl acetate-based intumescent coatings in a cone calorimeter. A sensitivity analysis is performed to show the effect of the thermal characteristics of the coating on the thermal resistance of the material. The application of the model to newly developed intumescent coatings is discussed.

The Modeling of Heat Transfer across Intumescent Polymer Coatings

Response of steel beam–columns exposed to fire

Bench-scale cone calorimetry is often used to evaluate the fire performance of intumescent-type coatings. During the tests, the coating geometry inflates. These thick, block-shaped specimens expose their perimeter side surfaces to both the heat source and the surroundings, unlike the typical thin, plate-shaped samples used in flammability tests. We assessed the thermal boundaries of block-shaped specimens using plain steel solids with several thicknesses. The heat transmitted through the exposed boundaries in convection and radiation modes was determined by four sub-defining functions: non-linear irradiance, convective loss, and radiant absorption into and radiant emission from solids. The individual functions were methodically derived and integrated into numerical calculations. The predictions were verified by physical measurements of the metals under different heating conditions. The results demonstrate that (1) considering absorptivity, being differentiated from emissivity, led to accurate predictions of time-temperature relationships for all stages from transient, through steady, and to cooling states; (2) the determined values for the geometric view factor and the fluid dynamic coefficient of convection can be generalized for engineering applications; (3) the proposed process provides a practical solution for the determination of optical radiative properties (absorptivity and emissivity) for use in engineering; and (4) the heat transmitted through the side surfaces of block specimens should be included in energy balance, particularly in the quantification of a heat loss mechanism. This paper outlines a comprehensive heat transfer model for cone calorimetry testing, providing insights into the mechanism of complex heat transmission generated on the test samples and quantifying their individual contributions.

Thermal Boundaries in Cone Calorimetry Testing

Performance of beam-to-column joints in fire—A review

Numerical investigation of the lateral–torsional buckling of beams with slender cross sections for the case of fire

http://www.ipb.pt/~ppiloto/pdf/jcsr_mesquita.pdf

Experimental and numerical research on the critical temperature of laterally unrestrained steel I beams

Experimental investigation of the fire resistance of partially encased beams

An investigation of two different intumescent coatings used in steel fire protection has been performed to evaluate their efficiency. A set of experimental tests is presented. They were conducted in a cone calorimeter, considering different thicknesses and heat fluxes. Among other quantities, the steel temperature and the intumescence thickness variation were measured. A numerical model for the paint decomposition is also presented. Based on the intumescence experimental value, the model is able to provide a reasonably good prediction of the steel temperature evolution.

/pdf/decomposition-of-intumescent-coatings-comparison-between-a-5ft7xa9647.pdf

Decomposition of Intumescent Coatings: Comparison between a Numerical Method and Experimental Results

The use of intumescent coatings plays an important role in the fire protection of structural elements. When submitted to elevated temperatures an intumescent coating undergoes thermochemical reactions that promote a higher thermal protection. To evaluate the behaviour of an intumescent coating, a set of experimental tests made on coated steel plates are performed in a cone calorimeter. These tests are performed with different heat fluxes and intumescent thicknesses. A simple and an advanced model, based in the Finite Difference Method, are presented and applied to determine the intumescent surface temperature evolution, considering the initial thickness and the intumescence variation. The intumescence effective thermal conductivity is estimated by solving the inverse heat transfer problem, considering the temperature in the steel equal to the experimental measured values. When the intumescence thickness variation is taken into account in the numerical model a higher thermal conductivity is expected, when compared with the constant thickness model.

/pdf/an-experimental-study-of-intumescent-fire-protection-5361oxgtc4.pdf

An experimental study of intumescent fire protection coatings

Valorization of industrial low-value side-streams are of great interest, contributing to boosts in the circular economy. In this context, lignin side-streams of the pulp and paper industry were oxypropylated to produce biobased polyols and tested in the synthesis of rigid polyurethane (RPU) foams. E. globulus lignins, namely a lignin isolated from an industrial Kraft black liquor and depolymerized lignins obtained as by-products of an oxidation process, were used. RPU foams, synthesized with 100% lignin-based polyols and using a 1.1 NCO/OH ratio, were characterized concerning apparent density, morphology, thermal conductivity, thermal stability, and heat release rate (HRR). Foams containing the lignin-based polyols presented densities varying from 44.7 to 112.2 kg/m3 and thermal conductivity in the range of 37.2–49.0 mW/mK. For the reference foam (sample produced with 100% wt. Daltofoam TP 32015 polyol), values of 70.9 kg/m3 and 41.1 mW/mK were obtained, respectively. The achieved results point out the viability of using the generated lignin-based polyols at 100% content in RPU foams, mainly when depolymerized lignins are used. Moreover, fire retardancy was favored when the lignin-based polyols were introduced. The proposed strategies can contribute to establishing the integrated pulp and paper biorefinery concept where material synthesis (polyols and RPU foams) can be combined with chemical production (vanillin and syringaldehyde).

https://www.mdpi.com/1996-1073/14/13/3825/pdf

L.M.R. Mesquita

Papers

Experimental and numerical research on the critical temperature of laterally unrestrained steel I beams

Experimental investigation of the fire resistance of partially encased beams

Decomposition of Intumescent Coatings: Comparison between a Numerical Method and Experimental Results

An experimental study of intumescent fire protection coatings

Valorization of Lignin Side-Streams into Polyols and Rigid Polyurethane Foams—A Contribution to the Pulp and Paper Industry Biorefinery