Journal of Oil, Gas and Petrochemical Technology

Journal of Oil, Gas and Petrochemical Technology

Computation of temperature- and concentration-dependent heat and mass diffusivities of solute-solvent systems

Document Type : Research Paper

Author
Department of Chemical Engineering, Faculty of Oil, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr 7516913798, Iran
Abstract
Abstract

The temperature- and concentration-dependent heat and mass diffusivities of a solute-solvent system are computed using an optimization-based computational technique. The input data of this method is the measured transient temperature and concentration at some selected locations of the system. The element-wise differential quadrature method as an accurate and simple numerical technique in conjunction with the Newton-Raphson method were utilized to solve the corresponding nonlinear coupled differential equations. The objective function of the algorithm is the difference between the measured data and the numerical solutions of the heat and mass transfer governing equations. The optimization algorithm is developed using the conjugate gradient method (CGM). Also, the corresponding nonlinear coupled partial differential equations are solved by employing the element-wise differential quadrature method as a powerful numerical technique. The applicability and reliability of the approach are illustrated by solving the problem under different conditions. The results showed that the heat and mass diffusivities of the system could be satisfactory estimated, which enable us to advise the application of this algorithm for the other transport phenomena.
Keywords

[1] M.S. Shafeeyan, W.M.A.W. Daud, A. Shamiri, A review of mathematical modeling of fixed-bed columns for carbon dioxide adsorption, Chemical Engineering Research and Design, 92(5) (2014) 961-988.
[2] A. Lima, A. Ochoa, J. Da Costa, J. Henríquez, CFD simulation of heat and mass transfer in an absorber that uses the pair ammonia/water as a working fluid, International Journal of Refrigeration, 98 (2019) 514-525.
[3] S.H. Lin, Three-points approach to three-parameters diffusivity of mobile phase in polymer film, Journal of the Taiwan Institute of Chemical Engineers, 41(2) (2010) 162-168.
[4] A.N. Alla, M.b. Feddaoui, H. Meftah, Comparison of two configurations to improve heat and mass transfer in evaporating two-component liquid film flow, International Journal of Thermal Sciences, 126 (2018) 194-204.
[5] S. Shirazian, M. Rezakazemi, A. Marjani, S. Moradi, Hydrodynamics and mass transfer simulation of wastewater treatment in membrane reactors, Desalination, 286 (2012) 290-295.
[6] H. Rahideh, R. Azin, A New Application of the Differential Quadrature Element-Incremental Method in Moving-Boundary Problems, Transport in Porous Media,  (2018) 1-15.
[7] M. Capobianchi, T.F. Irvine Jr, N.K. Tutu, G.A. Greene, A new technique for measuring the Fickian diffusion coefficient in binary liquid solutions, Experimental Thermal and Fluid Science, 18(1) (1998) 33-47.
[8] Y.D. Hsu, Y.P. Chen, Correlation of the mutual diffusion coefficients of binary liquid mixtures, Fluid Phase Equilibria, 152(1) (1998) 149-168.
[9] M. Monde, Y. Mitsutake, A new estimation method of thermal diffusivity using analytical inverse solution for one-dimensional heat conduction, International Journal of Heat and Mass Transfer, 44(16) (2001) 3169-3177.
[10] W.F. Waite, L.A. Stern, S. Kirby, W.J. Winters, D. Mason, Simultaneous determination of thermal conductivity, thermal diffusivity and specific heat in sI methane hydrate, Geophysical Journal International, 169(2) (2007) 767-774.
[11] N. Jeong, D.H. Choi, C.L. Lin, Estimation of thermal and mass diffusivity in a porous medium of complex structure using a lattice Boltzmann method, International Journal of Heat and Mass Transfer, 51(15-16) (2008) 3913-3923.
[12] M. Cui, X. Gao, J. Zhang, A new approach for the estimation of temperature-dependent thermal properties by solving transient inverse heat conduction problems, International Journal of Thermal Sciences, 58 (2012) 113-119.
[13] C. Blesinger, P. Beumers, F. Buttler, C. Pauls, A. Bardow, Temperature-dependent diffusion coefficients from 1D Raman spectroscopy, Journal of Solution Chemistry, 43(1) (2014) 144-157.
[14] K.G. Nayar, M.H. Sharqawy, L.D. Banchik, Thermophysical properties of seawater: a review and new correlations that include pressure dependence, Desalination, 390 (2016) 1-24.
[15] M. Huntul, D. Lesnic, An inverse problem of finding the time-dependent thermal conductivity from boundary data, International Communications in Heat and Mass Transfer, 85 (2017) 147-154.
[16] S. Varma, S.S. Rao, A. Srivastava, Simultaneous measurement of thermal and solutal diffusivities of salt-water solutions from a single-shot dual wavelength interferometric image, Experimental Thermal and Fluid Science, 81 (2017) 123-135.
[17] S. Chanda, K. Muralidhar, Y.M. Nimdeo, Joint estimation of thermal and mass diffusivities of a solute-solvent system using ANN-GA based inverse framework, International Journal of Thermal Sciences, 123 (2018) 27-41.
[18] O.M. Alifanov, Solution of an inverse problem of heat conduction by iteration methods, Journal of Engineering Physics and Thermophysics, 26(4) (1974) 471-476.
[19] H. Rahideh, M. Mofarahi, P. Malekzadeh, An inverse method to estimate adsorption kinetics of light hydrocarbons on activated carbon, Computers & Chemical Engineering, 93 (2016) 197-211.
[20] Y. Heydarpour, M. Mohammadi Aghdam, A New Multistep Technique Based on the Nonuniform Rational Basis Spline Curves for Nonlinear Transient Heat Transfer Analysis of Functionally Graded Truncated Cone, Heat Transfer Engineering, 40(7) (2019) 588-603.
[21] H. Rahideh, M. Mofarahi, P. Malekzadeh, Application of inverse method to predict the breakthrough curve in fixed-bed adsorption, Inverse Problems in Science and Engineering, 26(4) (2018) 581-600.
[22] P. Malekzadeh, A. Setoodeh, M. Shojaee, Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method, Computer Methods in Applied Mechanics and Engineering, 340 (2018) 451-479.
[23] M.A. Makarem, M. Mofarahi, B. Jafarian, C.H. Lee, Simulation and analysis of vacuum pressure swing adsorption using the differential quadrature method, Computers & Chemical Engineering, 121 (2019) 483-496.
[24] B. Liu, S. Lu, J. Ji, A. Ferreira, C. Liu, Y. Xing, Three-dimensional thermo-mechanical solutions of cross-ply laminated plates and shells by a differential quadrature hierarchical finite element method, Composite Structures, 208 (2019) 711-724.
[25] Y. Heydarpour, P. Malekzadeh, F. Gholipour, Thermoelastic analysis of FG-GPLRC spherical shells under thermo-mechanical loadings based on Lord-Shulman theory, Composites Part B: Engineering, 164 (2019) 400-424.
[26] Y. Heydarpour, P. Malekzadeh, R. Dimitri, F. Tornabene, Thermoelastic analysis of rotating multilayer FG-GPLRC truncated conical shells based on a coupled TDQM-NURBS scheme, Composite Structures, 235 (2020) 111707.
[27] M. Shojaee, A. Setoodeh, P. Malekzadeh, Vibration of functionally graded CNTs-reinforced skewed cylindrical panels using a transformed differential quadrature method, Acta Mechanica, 228(7) (2017) 2691-2711.
[28] R. Brittes, F.H. Franca, A hybrid inverse method for the thermal design of radiative heating systems, International Journal of Heat and Mass Transfer, 57(1) (2013) 48-57.
[29] W.L. Chen, H.M. Chou, H.L. Lee, Y.C. Yang, An inverse hyperbolic heat conduction problem in estimating base heat flux of two-dimensional cylindrical pin fins, International Communications in Heat and Mass Transfer, 52 (2014) 90-96.
[30] H. He, C. He, G. Chen, Inverse determination of temperature-dependent thermophysical parameters using multiobjective optimization methods, International Journal of Heat and Mass Transfer, 85 (2015) 694-702.