###### Abstract  
The term \"travelling fire\" is used to label fires which burn locally and move across the floor over a period of time in large compartments. Through experimental and numerical campaigns and while observing the travelling fire events, it became clear that such fires imply a transient heating of the surrounding structure. The necessity to better characterize the thermal impact generated on the structure by a travelling fire motivated the development of an analytical model allowing to capture, in a simple manner, the multidimensional transient heating of a structure considering the effect of the ventilation. This paper first presents the basic assumptions of a new analytical model which is based on the virtual solid flame concept; a comparison of the steel temperatures measured during a travelling fire test in a steel-framed building with the ones obtained analytically is then presented. The limitations inherent to the analyticity of the model are also discussed. This paper suggests that the developed analytical model can allow for both an acceptable representation of the travelling fire in terms of fire spread and steel temperatures while not being computationally demanding, making it potentially desirable for pre-design. t 2021 9283. [[https://doi.org/10.3390/app11199263](https://doi.org/10.3390/app11199263)]([https://doi.org/10.3390/app11199263](https://doi.org/10.3390/app11199263))  
Academic Editors: [PERSON], [PERSON] and [PERSON]  
Received: 6 September 2021  
Accepted: 22 September 2021  
Published: 6 October 2021  
**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. **Published:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. field is divided in two regions: the near field and the far field. The ventilation conditions are not accounted for in this methodology and the near field temperature applies along the full height of the compartment. In 2015, [PERSON] [1] developed a simple method to determine the thermal action of a spreading fire for the design of structures: this model is based on the idea of repetitious heat release rate parametric curves acting with required time offset in neighbouring parts of a structure. In 2016, [PERSON] et al. [8] developed models for localised fires to predict the radiative heat flux to a structural element (the analytical model being detailed by [PERSON] et al. [9]). This methodology allows evaluating the heat fluxes in three dimensions and a transient heating of a structural element. However, in this model, localised fires are assumed to remain in given locations and do not reflect the possible travelling nature of the fire. In 2020, [PERSON] et al. [10] proposed a new travelling fire framework (\"ETFM\") considering a mobile version of Hasemi model--a localised fire model--and a smoke layer computed by the \"FIRM\" zone model [11]. A limitation of the ETFM framework is the limited applicability of [PERSON]'s localised fire model which is applicable only if the fire impacts the ceiling. The above mentioned limitations motivated the development of a new analytical model allowing to determine the heat fluxes capturing the transient heating of a structure, both along the direction followed by the fire and along the height of the enclosure whilst taking into account the influence of the ventilation boundary conditions. The present paper describes this development. First, this paper presents the basic assumptions of the analytical model. The fire representation is based on the virtual solid flame concept developed in the frame of the \"LOCAFI\" project [8,9]. The fire is represented as a rectangular volume with a basis given by the burning bands which evolve as a function of time. Contrarily to the LOCAFI model where the virtual solid flame has a conical shape, it is here considered as (a succession of) parallelepiped rectangles.