Adsorption cooling systems (ACS) are considered as potential alternatives to traditional vapor compression air conditioning systems in heavy-duty vehicles. In ACS, adsorber bed heat exchangers (ABHEx) replace compressors and their appropriate design directly impacts the ACS performance. During operation, ABHEx undergo a large temperature swing to derive a refrigerant in ACS and their response time affects the dynamic behavior of ACS. In this study, a detailed three dimensional non-equilibrium model is developed to study the effects of heat and mass transfer in annular and longitudinal finned tube adsorber beds filled with zeolite-13x particles. The effects of fin height and spacing are studied on the system operating parameters to identify an optimum fin geometry. The simulation results show that a decrease in fin spacing leads to a decrease in the coefficient of performance (COP) and an increase in the specific cooling power (SCP), and no optimum value is observed for them in a specific fin spacing. However, variations of the total cooling power (TCP) maximize at a certain fin spacing. For longitudinal finned tube ABHEx, the optimum averaged fin spacing shifts from 5.4 to 6.8 mm for the adsorber beds with 10, 15, and 20 mm fin heights, while the optimum fin spacing of annular finned tube ABHEx changes from 5.0 to 6.4 mm. Furthermore, the results show that under similar dimensions and operating conditions, an ACS with annular finned tube ABHEx provides a 10% higher total cooling power than that with a longitudinal finned tube ABHEx at the optimum fin spacing. Using the ACS with optimized ABHEx in a truck would annually save about 370 L of fuel consumption and decreases greenhouse emissions by up to 738 kg CO2e.