Heat transfer modeling of conjugated Graetz problems in double-pass parallel-plate heat exchangers under asymmetric wall temperatures

The heat transfer of a Graetz problem is investigated theoretically. The problem involves an improvement to the design of a parallel-plate heat exchanger using an inserted plate which forms a double-pass device with recycle operation. The parallel plates are at different temperatures. The theoretical mathematical model is solved analytically using the separation of variables, superposition principle, and an orthogonal expansion technique in extended power series. Significant heat transfer improvement can be realized by the design compared to a single-pass device. The improvement is greater for a larger Graetz number system. For a small Graetz number system, the single-pass design is preferred. The optimal location of the inserted plate is when the two subchannels are at the same height.