The artificial neural network (ANN) in conjunction with the incompressible smoothed particle hydrodynamics (ISPH) approach, deals with exothermic reaction effects on Cattaneo-Christov (Ca-Ch) heat and mass transport of nano-enhanced phase change material (NEPCM) in a curvilinear cavity. The ANN model, trained on data obtained from ISPH simulations, accurately predicted the mean $ \overline{Nu} $ and $ \overline{Sh} $ values. Two cases of boundary conditions included $ \left({T}_{h}\&{C}_{h}\right) $ on top/bottom walls and $ \left({T}_{c}\&{C}_{c}\right) $ on vertical walls and inner ellipse for C1. The boundary walls of a curvilinear cavity were kept at $ \left({T}_{h}\&{C}_{h}\right) $ and the inner ellipse was maintained at $ \left({T}_{c}\&{C}_{c}\right) $ for C2. The pertinent parameters were scaled as Frank-Kamenetskii number $ Fk\left(0-1, \right) $ Ca–Ch heat, mass transfer parameters $ \left({\delta }_{\theta }\&{\delta }_{\mathrm{\Phi }}\right)(0-0.2), $ Hartmann number $ Ha(0-60), $ buoyancy ratio parameter $ N(-2-4) $, power law index parameter $ n(1.1-1.4) $, Rayleigh number $ Ra({10}^{3}-{10}^{5}) $, Soret/Dufour numbers $ \left(Sr\&Du\right)(0-0.5) $, and fusion temperature $ {\theta }_{f}(0.1-0.9) $. The simulation results demonstrated the effectiveness of Ca-Ch heat and mass transport parameters in lowering temperature and concentration within a curvilinear cavity at C1 and C2. Increasing $ {\delta }_{\theta }\&{\delta }_{\mathrm{\Phi }} $ from 0 to 0.2 resulted in a $ 44.1\% $ and $ 48.9\% $ drop in velocity field at C1 and C2, respectively. Boundary conditions (C1 and C2) significantly affected mass, heat transfer, heat capacity ratio, and velocity field within a curvilinear cavity. An increase in Power law index $ n $ from 1.1 to 1.4, reduced a velocity field by $ 64.68\% $ and $ 64.66\% $ at C1 and C2, respectively. Increasing $ Sr $ and $ Du $ helped distribute concentration. When $ Sr $ and $ Du $ were raised from 0 to 0.5, the velocity field increased by $ 34.17\% $ and $ 29.73\% $, respectively, at C1 and C2.
Citation: Weaam Alhejaili, Munirah Alotaibi, Abdelraheem M. Aly. Integrated ISPH approach with artificial neural network for magnetic influences on double diffusion of a non-Newtonian NEPCM in a curvilinear cavity[J]. AIMS Mathematics, 2024, 9(12): 35432-35470. doi: 10.3934/math.20241683
The artificial neural network (ANN) in conjunction with the incompressible smoothed particle hydrodynamics (ISPH) approach, deals with exothermic reaction effects on Cattaneo-Christov (Ca-Ch) heat and mass transport of nano-enhanced phase change material (NEPCM) in a curvilinear cavity. The ANN model, trained on data obtained from ISPH simulations, accurately predicted the mean $ \overline{Nu} $ and $ \overline{Sh} $ values. Two cases of boundary conditions included $ \left({T}_{h}\&{C}_{h}\right) $ on top/bottom walls and $ \left({T}_{c}\&{C}_{c}\right) $ on vertical walls and inner ellipse for C1. The boundary walls of a curvilinear cavity were kept at $ \left({T}_{h}\&{C}_{h}\right) $ and the inner ellipse was maintained at $ \left({T}_{c}\&{C}_{c}\right) $ for C2. The pertinent parameters were scaled as Frank-Kamenetskii number $ Fk\left(0-1, \right) $ Ca–Ch heat, mass transfer parameters $ \left({\delta }_{\theta }\&{\delta }_{\mathrm{\Phi }}\right)(0-0.2), $ Hartmann number $ Ha(0-60), $ buoyancy ratio parameter $ N(-2-4) $, power law index parameter $ n(1.1-1.4) $, Rayleigh number $ Ra({10}^{3}-{10}^{5}) $, Soret/Dufour numbers $ \left(Sr\&Du\right)(0-0.5) $, and fusion temperature $ {\theta }_{f}(0.1-0.9) $. The simulation results demonstrated the effectiveness of Ca-Ch heat and mass transport parameters in lowering temperature and concentration within a curvilinear cavity at C1 and C2. Increasing $ {\delta }_{\theta }\&{\delta }_{\mathrm{\Phi }} $ from 0 to 0.2 resulted in a $ 44.1\% $ and $ 48.9\% $ drop in velocity field at C1 and C2, respectively. Boundary conditions (C1 and C2) significantly affected mass, heat transfer, heat capacity ratio, and velocity field within a curvilinear cavity. An increase in Power law index $ n $ from 1.1 to 1.4, reduced a velocity field by $ 64.68\% $ and $ 64.66\% $ at C1 and C2, respectively. Increasing $ Sr $ and $ Du $ helped distribute concentration. When $ Sr $ and $ Du $ were raised from 0 to 0.5, the velocity field increased by $ 34.17\% $ and $ 29.73\% $, respectively, at C1 and C2.
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