<p>A novel theoretical model has been developed to determine the temperature field in functionally graded thermoelectric materials or devices by combining the finite difference method with the Thomas algorithm. Using the model, a theoretical analysis was performed on an Al-doped ZnO-based functionally graded thermoelectric device with material properties varying according to the power, exponential, and sigmoidal functions. The thermoelectric efficiency was evaluated and optimized as a function of current density, with results indicating that the power law distribution yields the highest efficiency. Additionally, a new mathematical model has been formulated to account for the influence of porosity on thermoelectric properties, considering porosity volume fractions ranging from 0 to 0.5. The model enables an in-depth investigation of the effects of porosity on thermoelectric efficiency and figure-of-merit for Al-doped ZnO-based functionally graded thermoelectric devices. The findings reveal that, for a fully dense Al-doped ZnO device, the maximum efficiency was 0.0024 at a current density of 17 A/cm², while the figure-of-merit reached 0.053 at 200&#xa0;°C. The optimal porosity volume fraction has been identified as between 0 and 0.1, demonstrating the potential of controlled porosity to enhance device performance. The present work establishes a strong theoretical foundation for analyzing and optimizing porous functionally graded thermoelectric devices.</p>