Aortic dissection causes splitting of the aortic wall layers, allowing blood to enter a ‘false lumen’ (FL). For type B dissection, a significant predictor of patient outcomes is patency or thrombosis of the FL. Yet, no methods are currently available to assess the chances of FL thrombosis. In this study, we present a new computational model that is capable of predicting thrombus formation, growth and its effects on blood flow under physiological conditions. Predictions of thrombus formation and growth are based on fluid shear rate, residence time and platelet distribution, which are evaluated through convection–diffusion–reaction transport equations. The model is applied to a patient-specific type B dissection for which multiple follow-up scans are available. The predicted thrombus formation and growth patterns are in good qualitative agreement with clinical data, demonstrating the potential applicability of the model in predicting FL thrombosis for individual patients. Our results show that the extent and location of thrombosis are strongly influenced by aortic dissection geometry that may change over time. The high computational efficiency of our model makes it feasible for clinical applications. By predicting which aortic dissection patient is more likely to develop FL thrombosis, the model has great potential to be used as part of a clinical decision-making tool to assess the need for early endovascular intervention for individual dissection patients.