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An internally cooled parallel-plate membrane contactor has been employed for liquid desiccant air dehumidification. The contactor is comprised of a series of quasi-counter flow parallel-plate membrane channels (QCPMC). The processing air and the liquid desiccant (solution) streams are separated by the membranes. Cooling tubes are installed in the solution channel to take away the absorption heat. The laminar flow and heat transfer in the QCPMC with the cooling tubes in the solution side (QCPMCC) are studied based on a unit cell containing the sandwiched domain outside the cooling tubes between two neighboring membranes. This paper is focused on the effects of the random distributions in the height direction on the transport phenomena in the QCPMCC. The governing equations of the momentum and thermal transports are built up together with a uniform wall temperature boundary condition. The product of the mean friction factor and Reynolds number and the mean Nusselt number are then calculated. Effects of the various random distributions in the height direction on the product of the mean friction factor and Reynolds number and the mean Nusselt number are analyzed. Compared to the regular arrangement, the mean Nusselt number for the random distribution is larger than that for the regular one when the Reynolds number is less than 68.5. However when the Reynolds number is larger than 68.5, the mean Nusselt number for the random distribution is smaller than that for the regular one. [ABSTRACT FROM AUTHOR]