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1001
A Numerical Study on the MHD Ternary Hybrid Nanofluid (Cu-Al2O3-TiO2/H2O) in presence of Thermal Stratification and Radiation across a Vertically Stretching Cylinder in a Porous...
Published 2024-03-01“…The use of a relevant similarity variable has been utilized to simplify the boundary layer equations which control the flow and transform the coupled nonlinear partial differential equations into a collection of nonlinear ordinary differential equations. …”
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1002
Navier slip effect on the thermal-flow of Walters’ liquid B flow due to porous stretching/shrinking with heat and mass transfer
Published 2021-12-01“…The governing equations which are a set of highly nonlinear partial differential equations are converted into a set of highly nonlinear ordinary differential equations by adopting similarity transformations and solved analytically to get velocity solution exponential form. …”
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1003
Method of approximations for the convection-dominated anomalous diffusion equation in a rectangular plate using high-resolution compact discretization
Published 2022-01-01“…Convergence of high-order method is obtained for the nonlinear partial differential equations employing Hausdorff fractal distance metric. …”
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1004
Effect of thermal radiation and chemical reaction on non-Newtonian fluid through a vertically stretching porous plate with uniform suction
Published 2018-06-01“…By applying suitable transformation, the coupled nonlinear partial differential equations are converted to couple ordinary differential equations. …”
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1005
Dual Solutions and Stability Analysis of Cu-H2O-Casson Nanofluid Convection past a Heated Stretching/Shrinking Slippery Sheet in a Porous Medium
Published 2023-01-01“…Using some realistic assumptions and appropriate similarity transformations, the governing nonlinear partial differential equations were formulated and transformed into a system of nonlinear ordinary differential equations and then numerically solved by using the shooting technique. …”
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1006
Effects of Second-Order Slip and Viscous Dissipation on the Analysis of the Boundary Layer Flow and Heat Transfer Characteristics of a Casson Fluid
Published 2016-11-01“…Using appropriate similarity transformations, the basic nonlinear partial differential equations have been transformed into ordinary differential equations. …”
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1007
Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks
Published 2023-02-01“…The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. …”
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1008
Powell-Eyring nanofluid analysis with finite element method when past stretching sheet with convective heating and passive control of nanoparticle
Published 2023-08-01“…The governing equation is made up of a collection of nonlinear partial differential equations that have been constructed and transformed through similarity transformation into sets of nonlinear ordinary differentials of momentum, energy, and concentration. …”
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1009
The unified impact of thermal radiation and heat source on unsteady flow of tangent hyperbolic nanofluid through a permeable shrinking sheet
Published 2023-08-01“…The flow model is mathematically framed through a coupled nonlinear partial differential equations. To transform the non-linear PDEs to ODEs, we use the similarity transformations and reduced ODEs are solved by RK-IV (Runge-Kutta method of order four) with shooting technique using the computational software MATHEMATICA. …”
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1010
Hierarchical method for mathematical modeling of stochastic thermal processes in complex electronic systems
Published 2019-08-01“…Thermal processes that take into account various physical phenomena in complex electronic systems are described by systems of stochastic, unsteady, and nonlinear partial differential equations and, therefore, their computer simulation encounters considerable computational difficulties even with the use of supercomputers. …”
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1011
Impact of temperature-dependant viscosity and thermal conductivity on MHD boundary layer flow of two-phase dusty fluid through permeable medium
Published 2019-04-01“…The governing nonlinear partial differential equations and their physically realistic boundary conditions are reduced into dimensionless form by using appropriate transformations. …”
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1012
Development of a Single-Phase, Transient, Subchannel Code, within the MOOSE Multi-Physics Computational Framework
Published 2022-05-01“…MOOSE is a parallel computational framework targeted at the solution of systems of coupled, nonlinear partial differential equations, that often arise in the simulation of nuclear processes. …”
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1013
Effects of non-Darcy mixed convection over a horizontal cone with different convective boundary conditions incorporating gyrotactic microorganisms on dispersion
Published 2022-10-01“…By imposing appropriate similarity transformations, the nonlinear partial differential equations governing flow, temperature, concentration, and microbe fields are reduced to a system of ordinary differential equations & then solved using the MATLAB BVP4C function. …”
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1014
Modified Finite Element Study for Heat and Mass Transfer of Electrical MHD Non-Newtonian Boundary Layer Nanofluid Flow
Published 2023-02-01“…Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. …”
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1015
Entropy generation in magneto couple stress bionanofluid flow containing gyrotactic microorganisms towards a stagnation point on a stretching/shrinking sheet
Published 2023-12-01“…To facilitate this investigation, the governing nonlinear partial differential equations undergo a transformation, wherein they are converted into nonlinear ordinary differential equations through a suitable similarity transformation. …”
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1016
A rigorous theoretical and numerical analysis of a nonlinear reaction-diffusion epidemic model pertaining dynamics of COVID-19
Published 2024-04-01“…The model is developed using six nonlinear partial differential equations. The infectious individuals are sub-divided into symptomatic, asymptomatic and super-spreader classes. …”
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1017
Free Convection Flow and Heat Transfer of Nanofluids of Different Shapes of Nano-Sized Particles over a Vertical Plate at Low and High Prandtl Numbers
Published 2019-01-01“…The governing systems of nonlinear partial differential equations of the flow and heat transfer processes are converted to systems of nonlinear ordinary differential equation through similarity transformations. …”
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1018
THE MODEL OF FREE SPREADING A FLOW RAPID BEHIND A RECTANGULAR PIPE
Published 2022-06-01“…A system of nonlinear partial differential equations of motion has been adopted as the mathematical model of the flow in the physical plane. …”
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1019
Investigation of dissipation phenomenon of non-Newtonian nanofluid due to a horizontal stretching rough sheet through a Darcy porous medium
Published 2024-03-01“…The mathematical flow model is described by nonlinear partial differential equations, which are subsequently transformed into non-dimensional ordinary differential equations. …”
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1020
Modelling and Analysis of Viscoelastic and Nanofluid Effects on the Heat Transfer Characteristics in a Double-Pipe Counter-Flow Heat Exchanger
Published 2022-05-01“…The mathematical modelling and formulation of the given problem comprises of a system of coupled nonlinear partial differential Equations (PDEs) governing the flow, heat transfer, and stress characteristics. …”
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