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  • Open Access

    ARTICLE

    Numerical Analysis of Heat and Mass Transfer in Tangent Hyperbolic Fluids Using a Two-Stage Exponential Integrator with Compact Spatial Discretization

    Mairaj Bibi1, Muhammad Shoaib Arif 2, Yasir Nawaz3, Nabil Kerdid4,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.145, No.1, pp. 537-569, 2025, DOI:10.32604/cmes.2025.070362 - 30 October 2025

    Abstract This study develops a high-order computational scheme for analyzing unsteady tangent hyperbolic fluid flow with variable thermal conductivity, thermal radiation, and coupled heat and mass transfer effects. A modified two-stage Exponential Time Integrator is introduced for temporal discretization, providing second-order accuracy in time. A compact finite difference method is employed for spatial discretization, yielding sixth-order accuracy at most grid points. The proposed framework ensures numerical stability and convergence when solving stiff, nonlinear parabolic systems arising in fluid flow and heat transfer problems. The novelty of the work lies in combining exponential integrator schemes with compact… More >

  • Open Access

    ARTICLE

    Bioconvection Mangnetohydrodynamic Tangent Hyperbolic Nanofluid Flow with Quartic Chemical Reaction Past a Paraboloid Surface

    S. M. Atif1, W. A. Khan2,*, Muhammad Abbas3,*, Umair Rashid4

    CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.1, pp. 205-220, 2022, DOI:10.32604/cmes.2022.017304 - 29 November 2021

    Abstract In this numerical study, the effect of quartic autocatalysis type of chemical reaction, buoyancy force and thermal radiation phenomenon and magnetic effect on tangent hyperbolic nanofluid past an upper horizontal surface of a paraboloid has been studied. By considering the Buongiorno model approach, a diffusion of unequal coefficients in the presence of gyrotactic microorganism is discussed. Implementation of microorganism's idea is used to stabilize the nanoparticles through bioconvection. The modeled PDEs of the problems are converted into nonlinear ODEs with the assistant of the similarity transformations. To tackle nonlinear ODEs, MATLAB package bvp4c is used. More >

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