The shape of the analytical and numerical solutions is different because they represent the temperature at different locations in the reservoir. The analytical solution shows the average temperature of the reservoir, which decreases at a decreasing rate at all times. In contrast, the numerical solution shows the production well's temperature, which decreases at an increasing rate until the thermal front reaches the production well. Then the temperature continues to decrease, but at a decreasing rate. This temperature versus time pattern in the numerical solution is a classic example of thermal breakthrough. It seems that both solutions are valid, but they measure different aspects of the temperature.