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Purpose The purpose of the study is to present a simplified model to replace the complicated foaming simulations for investigating the liquid polyurethane behavior just before solidification. Design/methodology/approach This model is inspired from the traveling heater method of crystallization because of the low injection velocity. Besides, the heat generated during the reaction is considered as a heat source function in the energy equation. Findings Various distributions of the heat generation function inside the geometry have been studied to choose the most realistic one. Effect of parameters such as the soil material and porosity on the temperature distribution and flow field are examined for different values of heat flux on the boundaries. Results show an almost linear dependency of pressure drop to the velocity, a uniform velocity profile and an expected temperature distribution compared to literature, which approves the suggested model. Originality/value A new model is presented in this study for foaming which replaces a heat generation function (exponential) in the source term of the energy equation instead of the heat produced at the exit boundary (the solid–liquid interface), and the traveling method is used instead of moving the geometry; besides, the growth ratio has been neglected; therefore, this model has been validated by a foaming simulation to confirm the suggested simplified idea.