Nonlinear Ordinary Boundary Value Problem Research Articles

Computational study of three-dimensional flow and heat transfer of 25 nm Cu–H2O nanoliquid with convective thermal condition and radiative heat flux using modified Buongiorno model

The three-dimensional steady flow of an incompressible 25 nm water-based copper nanoliquid over a bi-directional elongated surface with convective thermal boundary condition is studied. This work may meet various thermal engineering applications for instance thermal energy exchangers, solar energy collectors, geophysical transports, radiators, electronic cooling devices, and nuclear reactors. Corcione's model for effective thermal conductivity and dynamic viscosity is used in conjunction with correlations based on effective medium theory for density, specific heat, and electrical conductivity. The effects of radiative heat and convective thermal energy conditions are also taken into account. Modified Buongiorno inhomogeneous model-based governing equations transmuted to nonlinear ordinary boundary value problem. The subsequent system has been deciphered using computer algebraic system software. The method used is validated against the available data and found an exceptional agreement. Two dimensional charts are designed to analyze the impact of the key parameters involved in the model. Three dimensional surface plots are plotted for the study of the Nusselt number, friction coefficients, and Sherwood number values are tabulated for several key parameters. A regression analysis is also performed for the local Nusselt number.

MHD flow of SWCNT and MWCNT nanoliquids past a rotating stretchable disk with thermal and exponential space dependent heat source

The main purpose of this investigation is to analyze the impacts of a novel exponential space dependent heat source on MHD slip flow of carbon nanoliquids past a stretchable rotating disk. The flow is created due to rotation and stretching of the disk. Aspects of the convective condition and cross-diffusion (Soret and Dufour effects) are also accounted. A comparative study of nanofluids made up of SWCNT’s (single-walled carbon nanotube) and MWCNT’s (multi-walled carbon nanotube) is presented. The governing partial differential equations system is reduced to nonlinear ordinary boundary value problem. The Runge–Kutta–Fehlberg is utilized for numerical simulations. Embedded dimensionless parameters on the flow fields are examined via graphical illustrations. The rate of heat mass transfer can be controlled by cross-diffusion, exponential space-based heat source and thermal-based heat source effects. It is also proved that A novel idea of the exponential space dependent heat source is implemented in the investigation of the slip flow over a rotating deformable disk under the effects of cross-diffusion, temperature based heat source and magnetic field for the first time. A comparison between two different fluids namely SWCNT-H2O nanoliquid and MWCNT-H2O nanoliquid are studied.

Marangoni convective MHD flow of SWCNT and MWCNT nanoliquids due to a disk with solar radiation and irregular heat source

Present study addresses the Marangoni transport of dissipating SWCNT and MWCNT nanofluids under the influence of magnetic force and radiation. A novel exponential space dependent heat source is considered. The flow is generated due to a disk with surface tension created by thermal gradient. The partial differential equations system governing the flow of carbon-water nanoliquids and heat transfer through Marangoni convection is established. Subsequent system is reduced to nonlinear ordinary boundary value problem via generalized Karman transformations. Numerical solutions are developed of the arising nonlinear problem via Runge-Kutta based shooting approach. Impacts of embedded parameters are focused on Nusselt number, velocity and heat transport distributions through graphical illustrations. Our simulations figured out that the heat transfer rate increased via Marangoni convection; however it is decayed by applied magnetic force. The temperature of SWCNT-H2O nanoliquid dominates MWCNT-H2O nanoliquid.

Nonlinear Ordinary Boundary Value Problems under a Combined Effect of Periodic and Attractive Nonlinearities

Nonlinear Ordinary Boundary Value Problems under a Combined Effect of Periodic and Attractive Nonlinearities

Collocation-continuation technique for solving nonlinear ordinary boundary value problems

A new numerical technique is presented for solving the nonlinear ordinary boundary value problems. Theoretical and numerical results are presented. Comparison with Syam's results [1] will be given. These results indicate that our technique works more nicely and efficiently than his technique.