Department of Mathematics

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    Entropy generation and heat transfer in nonlinear Buoyancy–driven Darcy–Forchheimer hybrid nanofluids with activation energy
    (De Gruyter, 2025-04) Sharma, Bhupendra Kumar; Yadav, Sangita
    This study investigates the influence of a magnetic field, activation energy, and heat source on the heat and mass transfer within a cross fluid embedded with mono-, di-, and tri-nanoparticles, considering thermal radiation and Darcy–Forchheimer effects. Utilizing the Cattaneo–Christov theory, non-Fourier heat transfer is modeled for a vertical moving surface. A mathematical model is developed and subsequently converted into a dimensionless form through an appropriate similarity transformation, resulting in a system of first-order ordinary differential equations. The numerical approach to solve the system is BVP4C solver in MATLAB, a tool specifically designed for boundary value problems. Graphical representations have been analyzed for velocity profiles, temperature profiles, and concentration distributions for different values of physical parameters. It is observed that the velocity profiles exhibit an upward trend with an increase in the parameters associated with nonlinear thermal convection and nonlinear concentration convection. Additionally, the analysis of surface shear stress, heat transfer coefficients, and mass transfer coefficients revealed that an increase in the porosity parameter and Forchheimer number results in decreased shear stress. Entropy generation is also investigated to quantify irreversibilities in the system. The analysis showed that increasing the Brinkman number, diffusion parameter, and temperature and concentration difference parameters leads to higher entropy generation, indicating greater irreversibility in the system. A comparative analysis demonstrates that tri-nanoparticles substantially improve flow velocity, thermal conductivity, and solute diffusion compared to di- and mono-nanoparticles, with tri-nanofluids exhibiting the most optimal overall performance.
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    Exponential space and thermal-dependent heat source effects on electro-magneto-hydrodynamic Jeffrey fluid flow over a vertical stretching surface
    (World Scientific, 2022) Sharma, Bhupendra Kumar
    This paper deals with the study of an incompressible electro-magneto-hydrodynamic (EMHD) Jeffrey fluid flow over a vertical nonlinear stretching surface of variable thickness. Heat and mass transfer effects are analyzed by considering different source terms like viscous dissipation, Ohmic heating, thermophoresis, Brownian motion, thermal heat source, exponential heat source and activation energy. Governing equations for the flow system are converted into dimensionless forms using appropriate similarity transformations. The solution for the resulting governing equations is obtained by using the shooting technique with RK-4 method. The effects of various physical parameters such as magnetic field parameter (M), Grashof number (Gr), solutal Grashof number (Gc), Brownian diffusion parameter (Nb), thermophoresis diffusion parameter (Nt), thermal heat source parameter (Qt), exponential heat source parameter (Qe), Prandtl number (Pr) and Lewis number (Le) are presented with the help of graphs. It is observed that the heat transfer effects increase by increasing thermal and exponential heat sources, and mass transfer effects enhance by increasing the activation energy. Entropy generation for this flow system is also analyzed. Entropy decreases with an increase in the electric field parameter. In contrast, the Bejan number initially increases with an increase in the electric field parameter. After some particular value of electric field parameter, it changes its behavior in the boundary layer and decreases with an increase in the electric field parameter. Entropy and Bejan number increase with an increment in the concentration difference parameter. The accuracy of the results is validated by those of published literature and found in reasonable justification. The present results may be helpful in many engineering and industrial applications like manufacturing lubrication, natural gas networks, cooling nuclear reactors and spray processes.
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    Impact of Arrhenius activation energy on MHD nanofluid flow past a stretching sheet with exponential heat source: A modified Buongiorno’s model approach
    (World Scientific, 2023) Sharma, Bhupendra Kumar
    Nanofluids have a wide range of applications in biological research. They are employed in targeted medication administration, hyperthermia (for cancer treatment) and differential diagnostics like magnetic resonance image (MRI). In light of these medical applications, the impact of an external magnetic field and an exponential heat source on the dynamics of TiO2–H2O over a nonlinearly stretched surface has been investigated. A realistic modified Buongiorno model has been used which includes the effects of reaction rate, Biot number and activation energy. The boundary value problem governing the model is solved on MATLAB R2022a using the solver, BVP5C. Further, the consequences of different parameters on rate of heat transfer coefficient (Nusselt number), rate of mass transfer coefficient (Sherwood number), drag coefficient, velocity, temperature and volume fraction profile are observed graphically. It is noted that volume fraction and uniform heat source intensity have a positive effect on the Nusselt number and negative effect on Sherwood number. The effects of thermal radiation and magnetic field on volume fraction profile are, respectively, positive and negative. The current physics of flow across a vertical stretching surface is expected to serve as the foundation for various medical science, engineering and technology applications.
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    Impact of arrhenius activation energy on mhd nanofluid flow past a stretching sheet with exponential heat source: a modified buongiorno’s model approach
    (World Scientific, 2023) Sharma, Bhupendra Kumar
    Nanofluids have a wide range of applications in biological research. They are employed in targeted medication administration, hyperthermia (for cancer treatment) and differential diagnostics like magnetic resonance image (MRI). In light of these medical applications, the impact of an external magnetic field and an exponential heat source on the dynamics of TiO2–H2O over a nonlinearly stretched surface has been investigated. A realistic modified Buongiorno model has been used which includes the effects of reaction rate, Biot number and activation energy. The boundary value problem governing the model is solved on MATLAB R2022a using the solver, BVP5C. Further, the consequences of different parameters on rate of heat transfer coefficient (Nusselt number), rate of mass transfer coefficient (Sherwood number), drag coefficient, velocity, temperature and volume fraction profile are observed graphically. It is noted that volume fraction and uniform heat source intensity have a positive effect on the Nusselt number and negative effect on Sherwood number. The effects of thermal radiation and magnetic field on volume fraction profile are, respectively, positive and negative. The current physics of flow across a vertical stretching surface is expected to serve as the foundation for various medical science, engineering and technology applications.