Chemical-based enhanced oil recovery (EOR) techniques utilize the injection of chemicals, such as solutions of polymers, alkali, and surfactants, into oil reservoirs for incremental recovery. The injection of a polymer increases the viscosity of the injected fluid and alters the water-to-oil mobility ratio which in turn improves the volumetric sweep efficiency. This research study aims to investigate strategies that would help intensify oil recovery with the polymer solution injection. For that purpose, we utilize a lab-scale, cylindrical heavy oil reservoir model. Furthermore, a dynamic mathematical black oil model is developed based on cylindrical physical model of homogeneous porous medium. The experiments are carried out by injecting classic and novel partially hydrolyzed polyacrylamide solutions (concentration: 0.1-0.5 wt %) with 1 wt % brine into the reservoir at pressures in the range, 1.03-3.44 MPa for enhanced oil recovery. The concentration of the polymer solution remains constant throughout the core flooding experiment and is varied for other subsequent experimental setup. Periodic pressure variations between 2.41 and 3.44 MPa during injection are found to increase the heavy oil recovery by 80% original-oil-in-place (OOIP). This improvement is approximately 100% more than that with constant pressure injection at the maximum pressure of 3.44 MPa. The experimental oil recoveries are in fair agreement with the model calculated oil production with a RMS% error in the range of 5-10% at a maximum constant pressure of 3.44 MPa.