The modeling equations for the temperature distribution and temperature polarization profiles in a laminar concurrent‐flow parallel‐plate direct‐contact membrane distillation (DCMD) module were developed theoretically. The analytical solutions for such conjugated Graetz problems in DCMD systems were obtained using the variable separation method with an orthogonal expansion technique extended in power series. A description of the average Nusselt number variations and temperature distributions of both the hot and cold feed streams is given. The feed velocity effect on the temperature profiles and average Nusselt number was examined and is reported by employing the computed eigenvalues and the relevant constants. The analytical results show that the initial saline temperature effect on the hot feed stream regarding the pure water productivity is more significant than that of the hot and cold feed stream velocity variations.

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