Mathematics, Numerical Analysis, Applied Mathematics, Fluid Flow and Transfer Processes
15
Scopus Publications
Scopus Publications
Heat and mass transfer in MHD-UCM nanofluid flow past a porous nonlinear stretching sheet with chemical reaction and bioconvection: a dual-method approach Vishwanath B. Awati, Sachin S. Muchandi, N. Mahesh Kumar, Gabriella Bognár Nanotechnology Reviews, 2026 The study aims to scrutinize the magneto-hydrodynamic (MHD) heat and mass transfer properties of an upper-convected Maxwell (UCM) nanofluid over a nonlinearly stretched porous sheet with gyrotactic microorganisms via numerical and semi-numerical approaches. The UCM nanofluid model encompasses the effects of thermal stratification, heat absorption, chemotaxis movement of microorganisms, velocity ratio and chemical reaction parameters. The prominent mathematical equations of continuity, momentum, energy, nanoparticle concentration and microorganism density are transformed into a self-similar system of coupled nonlinear ordinary differential equations (ODEs) by appropriate similarity variables. These equations were solved through numerical and semi-numerical techniques viz, Keller-box and Haar wavelet collocation methods. The attained results were successfully compared with the prevailing literature and are exemplified through graphs and tables. The exploration revealed that nanofluid velocity decelerates due to the rise in magnetic field, porosity and Deborah number because stronger magnetic forces, porous medium resistance and greater fluid elasticity together oppose the fluid motion. Thermal stratification noticeably reduces the thermal boundary layer thickness due to the lower temperature difference between surface and the ambient fluid. Additionally, motility increases with an increase in the Prandtl number, thermophoresis, and Peclet number, as reduced thermal diffusion and enhanced particle transport strengthen the microorganism accumulation near the surface. It confirms that the presence of gyro-tactic microorganisms enhances nanofluid stability by preventing nanoparticle agglomeration.
Chemically radiative aspects of mixed convection unsteady MHD stagnation point flow with Williamson nanofluid: Semi-numerical approach Vishwanath B. Awati, Akash Goravar, N. Mahesh Kumar, Gabriella Bognár Alexandria Engineering Journal, 2025 The Williamson nanofluid exhibits a wide range of applications in the oil industry, geothermal reservoirs, and biomedical fields. The present study delves into the significant aspects of the heat and mass transfer phenomenon within the unsteady Williamson Buongiorno model over a stretching surface through a porous medium. The influence of magnetic field, thermal radiation, chemical reaction, Brownian motion, and thermophoresis coefficients on flow field are explored. The leading constitutive equations are converted to nonlinear, self-similar ordinary differential equations via appropriate similarity conversion equations. These resultant equations are solved using collocation strategies such as shifted Chebyshev collocation and Haar wavelet collocation techniques. The velocity profiles exhibit a decline in flow-assisting conditions while increasing in flow-opposing situations for the corresponding parameters except for mixed convection, solutal, and radiation parameters. The temperature profiles augment with mixed convection (flow opposing case) and radiation parameters; the contrasting nature of these profiles is noticed for other governing parameters. Concentration profiles initially intensify but subsequently decrease in the far-field flow region under both flow circumstances. The skin-friction coefficient reduces with growing parameters of radiation, mixed convection, Brownian motion, chemical reaction, Schmidt number, and reverse trend in the skin-friction coefficient is noticed for enhancement in remaining flow factors. • Heat and mass transfer traits in unsteady Williamson nanofluid flow over stretching sheet in a porous medium are presented. • The impact of MHD, mixed convection, Brownian motion, and thermophoresis on chemically radiative fluid flow is explored. • Mass flux conditions for nanoparticles are counted. • The system of self-similar equations is solved via shifted Chebyshev and Haar wavelet collocation techniques. • The Chebyshev polynomials are chosen due to the minimax property and Runge phenomenon.
New insights into transport phenomena within steady MHD two-phase nanofluid flows over a permeable elastic sheet of an uneven thickness Vishwanath B. Awati, Sachin S. Muchandi, N. Mahesh Kumar, Taseer Muhammad, M. Zaydan, A. Wakif, Rachid Sehaqui Modern Physics Letters B, 2025 This paper presents the effects of various properties on nanofluid flows and heat transfer over a permeable stretching sheet of variable thickness in the presence of a transverse magnetic field. Mathematically, the leading coupled partial differential equations are transformed into a self-similar system of ordinary differential equations through similarity variables, which are solved thereafter using Keller-box and Haar’s wavelet methods. Moreover, the impacts of various flow parameters involved in the physical problem are discussed thoroughly via tables and graphs. As findings, the analysis discloses that the nanofluid flow is significantly influenced by the physical parameters. Dynamically, the nanofluid flow is accelerated prominently with the strengthening in the injection process and decelerated in other situations. Furthermore, the obtained results are compared successfully with the earlier published findings.
Stability Analysis of Mass Transfer on a Continuous Flat Plate Moving in Parallel or Reversely to a Free Stream in the Presence of Chemical Reaction by Haar Wavelets Vishwanath Awati, N. Mahesh Kumar, Akash Goravar Journal of Applied and Computational Mechanics, 2025 This study investigates two-dimensional viscous incompressible boundary layer flow involving mass transfer above an uninterrupted flat surface in the presence of chemical reaction. Applicable similarity transformations, transform the leading equations into a system of nonlinear ordinary differential equations. These equations are solved via collocation approach using Haar wavelets. The double solutions exist and are presented through graphs. The obtained solutions are confirmed by comparing them with earlier findings. The various physical quantities are enfolded and convinced carefully using numerical and theoretical approaches. Enhancement in Schmidt number increases the mass transfer rate for upper branch solution and reduces for lower branch solution. Mass immersion arises for constructive chemical reaction and mass transfer enhances for destructive chemical reaction. Finally, the stability analysis is performed.
Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach Vishwanath B. Awati, Akash Goravar, Mahesh Kumar N, Gabriella Bognár Case Studies in Thermal Engineering, 2024 The present analysis examines the magnetohydrodynamic (MHD) flow of non-Newtonian Casson fluid on an exponentially shrinking surface under constant and exponentially varying wall temperature with suction. The main objective is to investigate multiple solutions of self-similar coupled nonlinear ordinary differential equations derived semi-numerically via the shifted Chebyshev collocation approach. The occurrence of a dual solution is found and variations in the velocity and temperature profiles are analyzed under different physical flow governing factors. The stability analysis is performed and it confirms that the first solution is stable and the second solution is unstable. The obtained results are confirmed by comparing them with earlier published results and show good agreement. The skin friction coefficient and wall temperature gradient increase for the first solution and decline for the second solution with enhancement in Hartmann number and suction parameter in case of exponentially varying surface temperature. Whereas, for constant surface temperature, increasing the Hartmann number and suction parameter results in the intensification of the wall temperature gradient. The velocity and temperature profiles decrease with improving the Casson parameter. As the Prandtl number strengthens, the heat transfer rate in a constant surface temperature situation is comparatively higher than exponentially varying surface temperature situation.
SCRUTINIZATION OF KRYLOV SUBSPACE METHOD FOR THE SOLUTION OF ELECTRIC DOUBLE LAYER EFFECT ON THERMAL LINE CONTACT ELASTO-HYDRODYNAMIC LUBRICATION PROBLEM Kumar N. Mahesh, B. Awati Vishwanath, M. Obannavar Parashuram Engineering Review, 2024 The paper presents, the numerical investigation of electrical double layer (EDL) effect on thermal elasto-hydrodynamic lubrication (EHL) line contact problem. The precise mathematical model consists of modified Reynolds, film thickness, load balance, and energy equations along with appropriate boundary conditions. The numerical computation of the problem involves apparent viscosity along with viscosity-pressure-temperature and density-pressure-temperature relations. The second order finite difference approximations are used to discretize the governing mathematical equations. The resulting systems of non-linear algebraic equations are solved using Newton-generalized minimum residual (GMRES) method with Daubechies D6 wavelet as pre-conditioner. The temperature grown freely in EHL contact area, the influence of temperature rise on EDL effect is studied in detail. The results illustrates that, film thickness increases with increase in EDL effect. The minimum film thickness for isothermal case is larger as compared to thermal film thickness and temperature escalation in contacting region reduces the film thickness. The EDL effect enhances fluid film thickness, while temperature rise in the contact area reducesminimum film thickness. Comparison between isothermal and the thermal results are presented in the form of figures and tables.
Semi-Numerical Investigation of Boundary Layer Flow and Heat Transfer of Magnetohydrodynamics Nano-Fluid Flow in Presence of Chemical Reaction over a Non-Isothermal Porous Medium Vishwanath B. Awati, Akash Goravar, Mahesh Kumar N. ASME Journal of Heat and Mass Transfer, 2023 The technical brief presents, analysis of boundary layer flow and heat transfer in nanofluids under the influence of magnetic field, thermal radiation and chemical reaction over non-isothermal stretching surface through permeable porous medium. The self-similarity equations obtained from governing equations are solved using shifted Chebyshev and Haar wavelet collocation methods. The prescribed surface temperature, prescribed heat flux cases and impact of various flow governing parameters are discussed in detail. The established results are compared with earlier results and are comparable.
