Recycle Effect on Double‐Pass Concentric Circular Mass Exchangers under Uniform Wall Fluxes

Abstract

A study on improvement in device performance of a double-pass concentric circular mass exchanger with uniform wall fluxes and external refluxes was conducted under counterflow operations. The linear superposition of an asymptotic solution and a homogeneous solution with the use of an orthogonal expansion technique for solving such a conjugated Graetz problem is formulated theoretically and the analytical predictions are applied to investigate a substantial masstransfer improvement. A mathematical expression for the average Sherwood numbers and the outlet dimensionless concentration is given. Comparisons of analytical results are made with the single-pass operations of the same working dimensions (without permeable barriers inserted and without recycle). Considerable device improvement in mass transfer rate is obtained by introducing the recycle-effect concept in designing such double-pass devices. The effect of permeable barriers on the mass-transfer efficiency improvement as well as on the power consumption increment has also been delineated. IntroductionThe Graetz problem, where axial conduction or diffusion is ignored, is usually considered to be laminar heat and mass transfer either in circular tubes or between parallel planes [1][2][3]. Among the latter problems are extended Graetz problems [4][5][6] with axial conduction or diffusion, particularly for low Prandtl number fluids such as liquid metals, and conjugated Graetz problems with multistream heat and mass transfer coupled mutual conditions at the boundaries. Papoutsakis and Ramkrishna [7,8] have developed and presented a general mathematical formulation. Yin and Bau [9] used eigenfunction expansion techniques to solve the simultaneous energy equations in the fluid and the solid regions. Symmetric Graetz problems study laminar forced convection heat and mass transfer in a viscous fluid flowing in a conduit of various cross-sectional geometries with uniform wall temperature [10] and heat fluxes [11], and uniform wall concentration [12], respectively, as compared to the asymmetric type with axiallyvarying temperature and concentration, or heat and mass fluxes [13,14]. This study deals with the Graetz problem with uniform mass fluxes on double-pass concentric circular mass exchangers.The application of the recycle-effect concept to achieve heatand mass-transfer efficiency improvements is widely used in designing separation processes and chemical reactors, such as gas absorbers [15] [19], and the draft-tube bubble column [20]. Applications of such recyclic operation in mass exchangers have enhanced the convective mass-transfer coefficient, resulting in improved performance in separation processes and reactor designs [21][22][23]. Moreover, due to the velocity sign change in a double-pass countercurrent-flow device, the solutions of such conjugated boundary value problems of Graetz and conjugated Graetz problems have been solved analytically with the use of eigenfunction expansion techniques [24][25][26][27][28] in terms of an extended power series. The the...

Heat transfer enhancement in cool-thermal discharge systems from ice melting with time–velocity variations

“…The corresponding thermal penetration distance δ(τ) = δ 0 can be obtained by having ψ(0, τ) = 0 in Eq. (11).…”

“…Previous literatures [10,11] suggested that the advantageous effect of convective transfer coefficient increase suppresses the disadvantageous effect of transfer driving force decreasing in double-pass operations with recycle. In conjunction with our previous work [12], this article analyzes the recycle effect and the time variation of required air flow for given outlet chilled air temperature in a cool-thermal discharge system.…”