Department of Mathematics
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Item Entropy generation and heat transfer in nonlinear Buoyancy–driven Darcy–Forchheimer hybrid nanofluids with activation energy(De Gruyter, 2025-04) Sharma, Bhupendra Kumar; Yadav, SangitaThis 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.Item Computational simulation of heat transfer and nanofluid flow for two-sided lid-driven square cavity under the influence of magnetic field(De Gruyter, 2025-08) Sharma, Bhupendra KumarThe present study investigates the heat transfer for the unsteady, incompressible, two-dimensional mixed convective copper–water nanofluid flow in a lid-driven square cavity in the presence of the magnetic field. The lid-driven square cavity’s top and bottom walls are assumed to be adiabatic. The nanofluid model is developed in ANSYS-FLUENT using Boussinesq approximation. A pressure-based solver with a Semi-Implicit Method for Pressure-Linked Equations algorithm is used to simulate the governing equations of the model. The results obtained from the developed fluid model are examined for the different influential physical parameters to enhance heat transfer from the cavity to the flowing fluid. Qualitative and quantitative results for nanofluid concentration, magnetic field parameter, and Reynolds number are analyzed. A noteworthy observation is that the velocity of the nanofluid reduces with improvement in the magnetic field strength. The findings of the attempt provide the capability of nanofluids in heat transfer, which aids in creating innovative geometries with improved and regulated heat transfer due to applied magnetic fields. This attempt holds potential applications in solar collectors, electrical devices, and the medical field manageable due to the slower fluid flow (nanofluid).Item Computational analysis of radiative heat transfer due to rotating tube in parabolic trough solar collectors with Darcy Forchheimer porous medium(Elsevier, 2023-11) Sharma, Bhupendra KumarThis attempt numerically investigates the heat transfer in parabolic trough solar collectors due to the rotating tube for the hybrid nanofluid flow over the Riga surface with Darcy Forchheimer’s porous medium under the effect of solar radiation. The influences of viscous dissipation and Joule heating are also considered. Equations governing the fluid flow are non-dimensionalized by implementing appropriate similarity variables. The resulting non-dimensionalized ordinary differential equations are solved using the shooting technique with Adam Bashforth and Adam Moulten’s fourth-order numerical approach. The numerical outcomes for various influential physical parameters regarding the fluid velocity, temperature, Nusselt number, and entropy generation are presented in graphical form. It is observed that the thermal profile escalates with the higher values of Reynold’s number, modified magnetic field parameter, and Prandtl number. Also, the Nusselt number diminishes with augmenting values of the Eckert number, modified magnetic field parameter, Forchheimer number, and Darcy number. The optimization of heat transfer in parabolic trough collectors is essential to improve the performance of solar collectors. The concentrated solar power technology is adequate for storing radiation energy in higher amounts.Item Influence of magnetohydrodynamics and chemical reactions on oscillatory free convective flow through a vertical channel in a rotating system with variable permeability(World Scientific, 2024) Sharma, Bhupendra KumarThis study investigates the impact of variable permeability as well as chemical reactions on the oscillatory free convective flow that passes parallel porous flat plates with fluctuating temperature and concentration in the presence of a magnetic field. A vertical channel is assumed to be rotating at an angular velocity Ω. Periodic free stream velocity causes oscillations in one plate, while periodic suction velocity causes oscillations in the other plate. Complex variable notations are used to solve the governing equations. The perturbation technique is used to derive analytical expressions for the temperature, concentration, and velocity fields. In this study, various parameters were investigated in relation to mean velocity, mean temperature, mean concentration, amplitude, and phase difference. The study also examines the impact on secondary velocity, primary velocity, temperature, concentration, and heat transfer rate during transients. The outcomes are presented graphically for the physical parameters of the problem. The findings contribute to optimizing systems and improving efficiency in heat transfer, fluid dynamics, and environmental remediation.Item Investigating the impact of fin configuration on phase change material melting in square cells: A numerical study(Elsevier, 2025-01) Sharma, Bhupendra KumarThis investigation thoroughly explores the effects of different fin arrangements on the melting behavior of phase change materials (PCMs), specifically paraffin wax (RT42), within a 50 × 50 mm2 square cell. Three distinct cases are considered: Case 1 involves no fins, Case 2 incorporates straight rectangular fins, and Case 3 employs undulated fins. To simulate real-world thermal energy storage conditions, the PCM container is thermally insulated, preventing external heat leakage. The primary objective is to identify the optimal fin arrangement to enhance latent heat storage system efficiency by improving both melting and solidification processes. The novelty of this research lies in the detailed analysis of various undulated fin geometries and their placements, which have not been extensively explored in previous studies. Numerical simulations were conducted using the ANSYS FLUENT solver. The progression of PCM melting was evaluated via the ANSYS design modeler based on the finite volume method, incorporating transient heat conduction and free convection. The results demonstrate that optimized undulated fin configurations can significantly enhance the melting process by promoting uniform temperature distribution and improving heat transfer rates, thereby reducing melting time. This study provides valuable insights for designing efficient latent heat energy storage systems, contributing to advancements in energy management and sustainable technologies.Item Analytical Study of the Effect of Variable Viscosity and Heat Transfer on Two-Fluid Flowing through Porous Layered Tubes(Springer, 2022-04) Tiwari, AshishThe proposed study is an attempt to perceive theoretically the heat transfer phenomenon in the flow of temperature-dependent viscous blood through microvessels internally surrounded by a thin layer of endothelial glycocalyx at the wall. While flowing through microvessels, the blood separates into erythrocytes suspended fluid and cell-depleted fluid into core and peripheral regions respectively. Therefore, to best represent the flow of human blood in microvessels, it has been modeled as a two-fluid. Erythrocytes appearing in the core stimulates the non-Newtonian behavior of the fluid is manifested here by Herschel-Bulkley fluid with temperature-dependent viscosity. The plasma surrounded over the blood cells in the peripheral layer is expressed as a Newtonian fluid with constant viscosity. An added advantage of utilizing the Brinkman-Forchheimer equation to govern the flow through the layer of endothelial glycocalyx (EGL) is that it is credible for both small and large Darcy numbers (permeability). Linear approximation of the Reynolds, viscosity model is exercised to obtain the analytical solutions for the governing equations of Herschel-Bulkley fluid flowing through the core region. In the non-porous peripheral region, the analytical solutions have been obtained for Newtonian fluid with constant viscosity directly and in the porous peripheral region, the Brinkman-Forchheimer equation is solved using regular perturbation for large Darcy number and singular perturbation with a matched asymptotic condition for small Darcy number. Analytical expressions for the velocity, flow rate, flow impedance, and temperature field have been obtained for the different regions. Graphical analysis revealing significant results regarding the variable viscosity, thermal conductivity, Grashof number, Forchheimer number, Richardson number, and permeability on the hemodynamical variables are conducted and results are discussed in detail. The study concludes that an EGL adjacent to the vessel wall increase the resistance to blood flow. The notable discovery of the study is that the temperature parameters influence all the quantities and therefore establish that the temperature-dependent viscosity plays a vital role in medical treatments involving temperature variation such as chemotherapy.Item Analytical study of the effect of complex fluid rheology and membrane parameters on heat transfer in fluid flow through a swarm of cylindrical particles(Elsevier, 2024-11) Tiwari, AshishThe present research investigates the flow characteristics of a Carreau-Yasuda fluid, which is non-Newtonian in nature, passing through a membrane composed of biporous layered cylindrical particles, utilizing a variable permeability approach. The process of formulating the governing equations entails utilizing both the empirical particle-in-cell model and a heat transfer approach. The structure of the proposed research is configured so that fluid flow near the solid core of the cylindrical particle is governed by the Brinkman-Forchheimer equation with variable permeability. In the intermediate region enveloping the Brinkman-Forchheimer region, the fluid flow is regulated by the Brinkman equation with variable permeability. Meanwhile, the peripheral region, adjacent to the hypothetical cell surface, is governed by the Stokes equation due to its non-porous nature. The thermal equations in a steady-state condition are simplified under viscous dissipation. The nonlinearity and coupling of equations arise in the study of Carreau-Yasuda fluid flow through a biporous layered cylindrical particle. This is attributed to the inclusion of a nonlinear inertia term in the Brinkman-Forchheimer equation, variable permeability, and a nonlinear correlation between shear stress and strain in the Carreau-Yasuda fluid. In addressing this issue, the empirical regular perturbation method is employed to derive asymptotic solutions for the governing equations under conditions of high permeability and low Weissenberg number. Additionally, a numerical approach utilizing the NDSolve command in Mathematica software is applied to illustrate graphical analyses under conditions of low permeability and Weissenberg number. The flow profiles' expressions are employed for analyzing the membrane permeability, Kozeny constant, and temperature variation. The graphical discussion delves into the influence of various control parameters, such as Carreau-Yasuda fluid parameters, variable permeability parameters, and Forchheimer number, on hydrodynamic and thermal quantities like fluid velocity, membrane permeability, Kozeny constant, temperature variations, and Nusselt number. The notable finding of the present study is that increasing variable permeability parameters in both the Forchheimer and Brinkmann regions, along with the Forchheimer number, lead to a decrease in fluid velocity and temperature profiles across the flow domain, ultimately resulting in a reduced Nusselt number profile. The present study includes a comparative analysis with existing works, focusing on reduced cases, and reveals that the findings closely match with the previously published studies on membrane filtration processes. The findings of the current study show potential for enhancing our comprehension of crucial physical and biological applications, such as filtration processes in wastewater treatment, characteristics of petroleum reservoir rocks, and the dynamics of blood flow through smooth muscle cells.Item H-theorem and boundary conditions for two-temperature model: Application to wave propagation and heat transfer in polyatomic gases(AIP, 2023-12) Rana, Anirudh SinghPolyatomic gases find numerous applications across various scientific and technological fields, necessitating a quantitative understanding of their behavior in nonequilibrium conditions. In this study, we investigate the behavior of rarefied polyatomic gases, particularly focusing on heat transfer and sound propagation phenomena. By utilizing a two-temperature model, we establish constitutive equations for internal and translational heat fluxes based on the second law of thermodynamics. A novel reduced two-temperature model is proposed, which accurately describes the system's behavior while reducing computational complexity. Additionally, we develop phenomenological boundary conditions adhering to the second law, enabling the simulation of gas-surface interactions. The phenomenological coefficients in the constitutive equations and boundary conditions are determined by comparison with relevant literature. Our computational analysis includes conductive heat transfer between parallel plates, examination of sound wave behavior, and exploration of spontaneous Rayleigh-Brillouin scattering. The results provide valuable insights into the dynamics of polyatomic gases, contributing to various technological applications involving heat transfer and sound propagation.Item Unsteady MHD Hybrid Nanoparticle (Au-Al2 O3 /Blood) Mediated Blood Flow Through a Vertical Irregular Stenosed Artery: Drug Delivery Applications(Springer, 2022-10) Sharma, Bhupendra KumarThe current study investigates the influence of hybrid nanoparticles (Au & Al2O3) on blood flow through a vertical artery with irregular stenosis with two-dimensional pulsatile blood flow, an inclined external magnetic field, viscous dissipation, and Joule heating. The blood flow is assumed to be unsteady, laminar, viscous, and incompressible, and the artery walls are considered permeable. The Reynolds temperature-dependent viscosity model is used to determine the variable viscosity effects. The governing momentum and energy equations are solved using Crank–Nicolson finite difference method by employing an appropriate coordinate transformation to build an accurate mesh using rectangular mesh units. Outcomes of the work are represented graphically for non-dimensional velocity, wall shear stress, flow rate, and non-dimensional temperature, respectively. The recent findings could be useful to biological researchers looking into the therapy of different cardiovascular disorders.Item Mathematical analysis of two-phase blood flow through a stenosed curved artery with hematocrit and temperature dependent viscosity(IOP, 2021) Sharma, Bhupendra KumarAtwo-phase blood flow model is considered to analyze the fluid flow and heat transfer in a curved tube with time-variant stenosis. In both core and plasma regions, the variable viscosity model (Hematocrit and non linear temperature-dependent, respectively) is considered. A toroidal coordinate system is considered to describe the governing equations. The perturbation technique in terms of perturbation parameter ε is used to obtain the temperature profile of blood flow. In order to find the velocity, wall shear stress and impedance profiles, a second-order finite difference method is employed with the accuracy of 10−6 in the each iteration. Under the conditions of fully-developed flow and mild stenosis, the significance of various physical parameters on the blood velocity, temperature, wall shear stress (WSS) and impedance are investigated with the help of graphs. A validation of our results has been presented and comparison has been made with the previously published work and present study, and it revels the good agreement with published work. The present mathematical study suggested that arterial curvature increase the fear of deposition of plaque (atherosclerosis), while, the use of thermal radiation in heat therapies lowers this risk. The positive add in the value of λ1 causes to increase in plasma viscosity; as a result, blood flow velocity in the stenosed artery decreases due to the assumption of temperature-dependent viscosity of the plasma region. Clinical researchers and biologists can adopt the present mathematical study to lower the risk of lipid deposition, predict cardiovascular disease risk and current state of disease by understanding the symptomatic spectrum, and then diagnose patients based on the risk.