Semi-Analytical and Numerical Solutions of Thermo-Chemically Radiative Tangent Hyperbolic Nanofluid Flow Over a Moving Wedge With Inclined Magnetic Field: An Error Analysis Vishwanath B. Awati, Sarika Hiremath, Akash Goravar ZAMM Zeitschrift Fur Angewandte Mathematik Und Mechanik, 2026 The magnetized thermo‐chemically radiative tangent hyperbolic nanofluid flow (THNF) has significant advanced thermal management and biomedical applications, including nuclear reactors, aerospace engineering, heat exchangers, tumor treatment, and drug targeting. The paper captures the thermo‐physical characteristics of the time‐dependent THNF model over a moving wedge for flux boundary circumstances with an obliquely applied magnetic field. The primary flow constitutive equations are transfigured into ordinary differential equations of nonlinear nature via a suitable scaled‐similarity technique. The optimal solutions of these equations are attained through novel shifted Chebyshev collocation and classical Keller box schemes, respectively, and are validated against each other. The flow behavior for stretching, static, and shrinking scenarios of wedge movement is presented in graphical and tabular form for several non‐dimensional flow governing factors. The findings reveal that thicker momentum and thermal boundary layers occur with amplified Weissenberg number and mass buoyancy factor. The uplifting effects of Schmidt number, Brownian diffusion, and chemical reaction factors maximize the concentration distribution near the surface, resulting in low mass diffusivity. The skin friction coefficient, Nusselt, and Sherwood numbers were reduced with the elevation of the heat generation/absorption, power law index, and mass buoyancy factors, but enhanced with Darcy number, magnetic, and thermal buoyancy parameters. Notably, skin friction coefficient is highest for stretching wedge and lowest for shrinking wedge conditions, while Nusselt and Sherwood numbers exhibit a contrary trend under similar circumstances. An error analysis confirms the convergence of the spectral scheme, whereas Domb–Sykes plots assist in identifying the nearest singularity of the series.
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.
Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial Vishwanath B. Awati, Akash Goravar, Abeer H. Alzahrani, N.M. Bujurke, Ilyas Khan International Journal of Thermofluids, 2023 In this article, the investigation is made to shed a light on the influence of convective boundary conditions on the boundary layer flow over a linearly stretching flat surface. The equations (partial differential equations) describing the model are transformed into system of nonlinear ordinary differential equations using similarity transformations. Equations contain various non-dimensional flow characterizing numbers viz. Prandtl number Pr, Lewis number Le, Biot number Bi, Brownian motion parameter Nb and thermophoresis parameter Nt. The influence of these parameters on thermal boundary layer, concentration distribution and temperature are analyzed in detail, by solving the equations using novel Shifted Chebyshev collocation method. The computed results, reduced Nusselt number, reduced Sherwood number, surface temperature and concentration profiles as functions of dimensionless numbers are validated by comparing the predicted results with available earlier findings (using other methods). To assert the convergence and stability of the scheme used (for much larger, but moderate, parameters values), predicted results are presented in various tabular forms. For presenting finer details of the computed values some results are also given graphically. The innovative semi-numerical scheme is robust and efficient compared with other conventional methods, used in previous studies and enables the analysis of the complex problem adequately.
Dirichlet series and closed-form exact solutions of MHD casson fluid flow over a permeable stretching/shrinking sheet Palestine Journal of Mathematics, 2021
Analytic continuation of series solution representing flow between plates Indian Journal of Pure and Applied Mathematics, 2004
RECENT SCHOLAR PUBLICATIONS
Semi‐Analytical and Numerical Solutions of Thermo‐Chemically Radiative Tangent Hyperbolic Nanofluid Flow Over a Moving Wedge With Inclined Magnetic Field: An Error Analysis VB Awati, S Hiremath, A Goravar ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte … , 2026 2026
Heat and mass transfer in MHD-UCM nanofluid flow past a porous nonlinear stretching sheet with chemical reaction and bioconvection: a dual-method approach VB Awati, SS Muchandi, NM Kumar, G Bognár Nanotechnology Reviews 15 (1), 20250251 , 2026 2026
Analysis of unsteady boundary layer flow of nanofluids with heat transfer over a permeable stretching/shrinking sheet via a shifted Chebyshev collocation method VB Awati, A Goravar, A Wakif Waves in random and complex media 36 (1), 822-848 , 2026 2026 Citations: 10
Chemically radiative aspects of mixed convection unsteady MHD stagnation point flow with Williamson nanofluid: Semi-numerical approach VB Awati, A Goravar, NM Kumar, G Bognar Alexandria Engineering Journal 125, 647-662 , 2025 2025 Citations: 2
New insights into transport phenomena within steady MHD two-phase nanofluid flows over a permeable elastic sheet of an uneven thickness VB Awati, SS Muchandi, NM Kumar, T Muhammad, M Zaydan, A Wakif, ... Modern Physics Letters B 39 (15), 2450488 , 2025 2025 Citations: 2
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 VB Awati, N Mahesh Kumar, A Goravar Journal of Applied and Computational Mechanics 11 (1), 160-172 , 2025 2025 Citations: 1
Scruitinization of Krylov subspace method for the solution of electric double layer effect on thermal line contact Elasto-hydrodynamic lubrication problem VB Awati, M Kumar, P Obannavar Engineering Review, 49-64 , 2024 2024 Citations: 1
Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach VB Awati, A Goravar, M Kumar, G Bognar Case Studies in Thermal Engineering 60, 104810 , 2024 2024 Citations: 26
Impact of chemical reaction on MHD boundary layer flow of nanofluids over a nonlinear stretching sheet with thermal radiation Haar wavelet collocation method M Kumar, VB Awati, A Goravar Media Mesin: Majalah Teknik Mesin 25 (2), 100-115 , 2024 2024 Citations: 2
Spectral and Haar wavelet collocation method for the solution of heat generation and viscous dissipation in micro-polar nanofluid for MHD stagnation point flow VB Awati, A Goravar, M Kumar Mathematics and Computers in Simulation 215, 158-183 , 2024 2024 Citations: 26
Scrutinisation of Chebyshev collocation method for mass transfer on a continuous flat plate moving in parallel to a free stream in the presence of a chemical reaction VB Awati, A Goravar, M Kumar N, AJ Chamkha International Journal of Ambient Energy 44 (1), 390-398 , 2023 2023 Citations: 5
Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial VB Awati, A Goravar, AH Alzahrani, NM Bujurke, I Khan International Journal of Thermofluids 20, 100471 , 2023 2023 Citations: 11
Multigrid method for the solution of thermal elastohydrodynamic lubrication point contact problem with surface asperities VB Awati, PM Obannavar, MK Nanjaiah Mechanical Engineering Advances 1 (1), 94-94 , 2023 2023 Citations: 1
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 VB Awati, A Goravar, MK N ASME Journal of Heat and Mass Transfer 145 (8), 084503 , 2023 2023 Citations: 5
Newton-GMRES-Method for the Scritinization of electric double layer and surface roughness on EHL line contact problem VB Awati, P Obannavar, M Kumar Journal of Mechanical Engineering and Sciences, 9370-9382 , 2023 2023 Citations: 2
Numerical solution of thermal EHL line contact with bio-based oil as lubricant VB Awati, M Kumar N, NM Bujurke Australian Journal of Mechanical Engineering 20 (1), 231-244 , 2022 2022 Citations: 7
Haar wavelet scrutinization of heat and mass transfer features during the convective boundary layer flow of a nanofluid moving over a nonlinearly stretching sheet VB Awati, M Kumar, A Wakif Partial Differential Equations in Applied Mathematics 4, 100192 , 2021 2021 Citations: 42
Analysis of forced convection boundary layer flow and heat transfer past a semi-infinite static and moving flat plate using nanofluids-by Haar wavelets VB Awati, N Mahesh Kumar Journal of Nanofluids 10 (1), 106-117 , 2021 2021 Citations: 21
Dirichlet series and closed-form exact solutions of MHD Casson fluid flow over a permeable stretching/shrinking sheet OD Makinde, VB Awati, NM Bujurke Palestine Journal of Mathematics 10 (1), 109-119 , 2021 2021 Citations: 10
An Isothermal Elastohydrodynamic lubrication of elliptical contact with Multigrid method VB Awati, S Naik Australian Journal of Mechanical Engineering 18 (3), 375-384 , 2020 2020 Citations: 3
MOST CITED SCHOLAR PUBLICATIONS
Haar wavelet scrutinization of heat and mass transfer features during the convective boundary layer flow of a nanofluid moving over a nonlinearly stretching sheet VB Awati, M Kumar, A Wakif Partial Differential Equations in Applied Mathematics 4, 100192 , 2021 2021 Citations: 42
Effect of surface roughness on squeeze film poroelastic bearings with special reference to synovial joints NM Bujurke, RB Kudenatti, VB Awati Mathematical Biosciences 209 (1), 76-89 , 2007 2007 Citations: 40
Boundary Value Problems for Third‐Order Nonlinear Ordinary Differential Equations PL Sachdev, NM Bujurke, VB Awati Studies in Applied Mathematics 115 (3), 303-318 , 2005 2005 Citations: 32
Approximate analytical solutions of a class of boundary layer equations over nonlinear stretching surface RB Kudenatti, VB Awati, NM Bujurke Applied Mathematics and Computation 218 (6), 2952-2959 , 2011 2011 Citations: 30
Stability analysis of magnetohydrodynamic Casson fluid flow and heat transfer past an exponentially shrinking surface by spectral approach VB Awati, A Goravar, M Kumar, G Bognar Case Studies in Thermal Engineering 60, 104810 , 2024 2024 Citations: 26
Spectral and Haar wavelet collocation method for the solution of heat generation and viscous dissipation in micro-polar nanofluid for MHD stagnation point flow VB Awati, A Goravar, M Kumar Mathematics and Computers in Simulation 215, 158-183 , 2024 2024 Citations: 26
Analysis of forced convection boundary layer flow and heat transfer past a semi-infinite static and moving flat plate using nanofluids-by Haar wavelets VB Awati, N Mahesh Kumar Journal of Nanofluids 10 (1), 106-117 , 2021 2021 Citations: 21
Homotopy analysis method for the solution of lubrication of a long porous slider V Awati Applied Mathematics and Nonlinear Sciences , 2016 2016 Citations: 19
Dirichlet series and analytical solutions of MHD viscous flow with suction/blowing. VB Awati Applied Mathematics & Nonlinear Sciences 2 (2) , 2017 2017 Citations: 16
On graphs with equal dominating and c-dominating energy SM Hosamani, VB Awati, RM Honmore arXiv preprint arXiv:1811.06269 , 2018 2018 Citations: 15
Series analysis for the flow between two stretchable disks VB Awati, M Jyoti, KV Prasad Engineering science and technology, an international journal 20 (3), 1211-1219 , 2017 2017 Citations: 15
Multigrid method for the solution of EHL line contact with bio-based oils as lubricants VB Awati, S Naik, M Kumar Applied Mathematics and Nonlinear Sciences 1 (2), 359-368 , 2016 2016 Citations: 15
Computer extended series and homotopy analysis method for the solution of MHD flow of viscous fluid between two parallel porous plates VB Awati, M Jyoti, NN Katagi Gulf journal of Mathematics 4 (3) , 2016 2016 Citations: 14
Analysis of Laminar flow in a channel with one porous bounding wall N Bujurke, NN Katagi, VB Awati International Journal of Fluid Mechanics Research 37 (3) , 2010 2010 Citations: 13
Convective heating and mass transfer in Buongiorno model of nanofluid using spectral collocation method of shifted Chebyshev polynomial VB Awati, A Goravar, AH Alzahrani, NM Bujurke, I Khan International Journal of Thermofluids 20, 100471 , 2023 2023 Citations: 11
Series solution of boundary layer flow of a nanofluid over a moving semi-infinite plate VB Awati Journal of Nanofluids 6 (2), 311-317 , 2017 2017 Citations: 11
Approximate analytical solutions of MHD flow of a viscous fluid on a nonlinear porous shrinking sheet VB Awati, NM Bujurke Bulletin of the International Mathematical Virtual Institute 4, 145-155 , 2014 2014 Citations: 11
Analysis of unsteady boundary layer flow of nanofluids with heat transfer over a permeable stretching/shrinking sheet via a shifted Chebyshev collocation method VB Awati, A Goravar, A Wakif Waves in random and complex media 36 (1), 822-848 , 2026 2026 Citations: 10
Dirichlet series and closed-form exact solutions of MHD Casson fluid flow over a permeable stretching/shrinking sheet OD Makinde, VB Awati, NM Bujurke Palestine Journal of Mathematics 10 (1), 109-119 , 2021 2021 Citations: 10
Solution of pressure gradient stretching plate with suction RB Kudenatti, VB Awati Applied mathematics and computation 210 (1), 151-157 , 2009 2009 Citations: 10
