The current study involves compiling and validating an extensive mathematical model of a small heat exchanger with offset strip fins. Compact heat exchanger functions as a cooler when the compressor is running. Here, ambient air is used as the coolant for compact heat exchangers. An exchanger with a compact design has its pressure drop and heat transfer coefficient calculated. The mass flow rate, temperature, and pressure of hot and cold fluids are examples of inlet operating parameters. The pressure drop at the heat exchanger outlet, effectiveness, and heat transfer coefficient are the output parameters. Pressure drop is calculated using the Fanning friction factor, often known as the "f" factor, while heat transfer coefficient is calculated using the Colburn "j" factor. We compared our mathematical model with the research observations for the "j" and "f" components, using the dimensions of the London and Kays plate-fin heat exchangers. The London and Kays conclusions are restricted to certain geometry, thus we derived the "j" and "f" factor for a variety of fin shapes using the correlations between Maiti and Sarangi, Joshi and Webb, Manglik, and Bergles. With the data provided, the "j" and "f" factors are computed using our mathematical model, which is a combination of several correlations extracted from the previously listed scholars. The Manglik and Bergles correlations yield values that are comparable to the London and Kays experimental value, with 1.93 and 6.51% variations in the "j" and "f" components, respectively.