International Journal of Modern Physics B

Particular thermal properties of internal energy, entropy, specific heat capacity and pressure are indicated using static fluctuation approximation (SFA) for specified temperatures and densities where the interaction between particles is still valid. This ab initio study starts initially from the most reliable krypton interatomic potential and develops with complementary SFA assumptions that depend mainly on substituting the local field mean value instead of its operator, thus developing a numerical solution of a nonlinear close set equation by iteration technique. The results are matched with the ideal gas and show a considerable sense.

Hybrid nanofluids (HNF) are the advanced form of nanofluids used for improved heat transfer purposes. Taking this point in mind, the objective of the presented endeavor is to examine the Yamada–Ota HNF flow model comprising (gold–silver/engine oil) over a stretched cylindrical surface and a sheet (as a limiting case) in a permeable medium. The novelty of this research is the consideration of the surface-catalyzed reaction along with the homogeneous–heterogeneous reactions to accelerate the chemical reactions in the shortest possible time. The heat transport phenomenon is strengthened with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition at the surface of the cylinder. The obtained ordinary differential equations are reduced from the partial differential equations using boundary layer theory and are numerically computed using the Keller box method. It is witnessed that for varied estimates of the magnetic parameter, the thermal profile enhances while the velocity field reduces. It is also noted that the fluid concentration is reduced when the surface-catalyzed parameter is enhanced. The validation of the envisioned model in a limiting case is also added to this investigation.

This research is concerned to some modernistic wave solutions of truncated M-fractional new Hamiltonian amplitude (NHA) equation. The dealing model relates with some disabilities of wave-train. The collected solutions can be executed in exposing of this model in prominent form. The obtained results include the trigonometric, hyperbolic trigonometric and exponential functions. Verification of the results is also done by using Mathematica tool. Two techniques named modified simplest equation (MSE) and Sardar sub-equation (SSE) techniques are employed to protect the results. The achieved results are also illustrated by 3D plots for different values of truncated M-fractional parameters. The achieved results are newer than the present results of the model in the literature. The gained results can also be fruitful for the development of model in future.

This paper pays attention to secure the different forms of optical soliton solutions to the spinor Bose–Einstein condensate. Three-component Gross–Pitaevskii (tc-GP) system which describes the F = 1 spinor Bose–Einstein condensate (BEC), with F denoting the atom’s spin, is used as a governing model to secure the solutions in BEC. Superfluidity and superconductivity are two properties of the low-temperature phenomenon that are associated with the BEC, which is formed by a diluted atomic gas. There has been an increasing interest in studying multi-component equations because they can be utilized to explain a wide range of complicated physical phenomena and have more dynamical structures of localized wave solutions. New extended direct algebraic method (NEDAM), a recently developed integration tool, is used to secure the solution. Different kinds of solitons, such as dark, singular, kink, bright–dark, complex and combined, are extracted. In addition, hyperbolic, exponential type and periodic solutions are guaranteed. Nonlinear partial differential equations (NLPDEs) are well-explained by the technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. In addition to discussing the physical representation of some solutions, we also plot 3D, 2D and contour graphs using the appropriate parameter values. The findings of this paper can improve the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the methodology used. We believe that a large number of engineering model specialists will benefit from this research. Findings suggest that the algorithm employed is efficient, prompt, succinct and applicable to complex systems.

The thermal conductivity attributes a major role to the thermal transportation and engineering processes where the fluid is used as an energy source. It has been commonly noted that much attention of research towards the heat and fluid flow is intended by keeping the fluctuation of thermal conductivity as a constant. However, experimental results shows that most of the times, thermal conductivity changes in variation of temperature, pressure or different configurations. The prime attention of current research is to explore the role of variable thermal conductivity for thermal transport of Burgers nanofluid due to inclined surface. The Buongiorno nanofluid model is used to illustrate the Brownian motion and thermophoresis properties. The heat transfer phenomenon is analyzed by incorporating the modified Cattaneo–Christov (CC) theories. Moreover, to maintain the improved heat transfer rate, the novel nonuniform heat source applications are also utilized. After altering the governing problem into dimensionless system, homotopy analysis scheme is used with excellent accuracy. The physical pattern of velocity, heat transfer rate and concentration phenomenon are observed in view of involved parameters. It is noted that the presence of variable thermal conductivity enhanced the thermal process more effectively as compared to constant thermal conductivity assumptions. Both heat and mass transfer phenomenon enhances for Deborah number. The declining concentration change is observed with variation of concentration relaxation number.

Restoring the motor function of paralyzed limbs has always been an important aim in the field of biomedical engineering. In view of the discovery of the repeatable experimental phenomenon that positive and negative stimulation pulses applied to specific points, identified as central pattern generator (CPG) sites, could induce switching of the movement patterns of bilateral hindlimbs, an improved Hodgkin–Huxley (HH) neuron model was established by introducing the electric field effect principle. A CPG neural network model comprising 12 neural units in six joints of the bilateral hindlimbs was modeled. The simulation results showed the alternating movement patterns of the bilateral hindlimbs through the action potential release of extensor and flexor neurons. The explosive electromyogram of the gastrocnemius (GM) and quadriceps femoris (QF) when stimulating the CPG sites with intraspinal micro-stimulation (ISMS) was consistent with the action potential diagram of the flexor and extensor neurons obtained via simulation. Our research considers the neural network model of electric field radiation, which can facilitate a deep understanding of the dynamic characteristics of neurons in the electric field environment, and verifies the correlation between the location of CPG sites, stimulus polarity and movement patterns to induce alternating left–right coordinated movements.

This work analyzes the two-dimensional flow of an incompressible magneto-hydrodynamic fluid over linear stretching sheet in the presence of suction or injection and convective boundary conditions. A scaling group transformation method is applied to the flow governing equations. The system remains invariant due to the relation between the transformation parameters. Upon finding three absolute invariants, third-order ordinary differential equations (ODEs) corresponding to momentum equation and second-order ODEs corresponding to energy and diffusion equations are derived. Shooting technique (R-K fourth-order) is applied to work out the flow equations numerically. MATLAB is used for the simulation and the results are exhibited through graphs. The computational results are validated with the published research work and a modest concurrence was found. The main outcome of this study is found to be that raising values of $f_{\mathrm{\text{si}}}$ and ${\mathrm{\Gamma }}_1$ decline the friction, whereas ${\mathrm{\Gamma }}_1$ and ${\mathrm{\Gamma }}_2$ show the opposite (increasing). The rising values of $f_{\mathrm{\text{si}}}$ and $M$ in addition to $M$ and ${\mathrm{\Gamma }}_2$ show a decline in friction factor. The Nusselt number values are improved as raising values of $Pr$ versus $f_{\mathrm{\text{si}}}$ and $Pr$ versus $M$. It is very clear the monotonically increasing $M$ versus $f_{\mathrm{\text{si}}}$ and strictly increasing $f_{\mathrm{\text{si}}}$ versus $M$ cases. It is very clear the mass-transfer rate is smoothly improved $L{e}_1$ versus $L{e}_2$ and strictly increased $L{e}_1$ versus ${\mathrm{\Gamma }}_1$.

The aim of this paper is to highlight the impact of thermophoretic particle deposition (TPD) and heat source/sink on the steady two-dimensional laminar motion of Casson hybrid-type nanoliquid through a nonlinear stretched surface. Ordinary differential equations (ODEs) are created by taking a collection of partial differential equations (PDEs) and simplifying them using an appropriate similarity component. The reduced ODEs are then evaluated using the shooting method and Runge–Kutta–Fehlberg’s fourth and fifth orders. Finally, tables and graphs are used to display the numerical data. It is seen that the fluid velocity step-downs when the porous parametric quantity and solid nanoparticle values increase. Heat distribution is enhanced with an enhancement in the heat source/sink constraint. Concentration goes down with an enhancement in thermophoretic constraint. The use of nanoparticles improves heat dispersion but reduces concentration in the linear case while increasing axial velocity in the nonlinear scenario.

In many fields, there are various applications of non-Newtonian fluids. Various complicated fluids (polymer melts, clay coatings and oil) belong to the category of non-Newtonian fluids. The third-grade fluid is one of the most important non-Newtonian fluid models. This paper has the primary object of heat transfer mechanism and boundary layer third-grade fluid flow under the effects of thermal radiation. The time-dependent two-dimensional flow is considered to flow above a permeable stretchable vertical Riga plate. For numerical solutions, the setup of ordinary differential equations (ODEs) is acquired by converting nonlinear governing equations through relevant similarity transformations. The nonlinear setup of ODEs is numerically solved with the aid of a suitable software such as MATLAB via its bvp4c technology. Graphs are sketched to discuss the various flow parameters’ significance for the expression of velocity and temperature fields. Tabulated values of surface drag force and heat transfer rate corresponding to the numerous pertinent parameters are described. The current analysis of the concerned flow mechanism concludes that the fluid parameters descend the temperature distribution but amplify the profile of the fluid velocity. The radiation parameter escalates the temperature field.

This analysis inspects an unsteady and incompressible Casson-type fluid moving on a poured inclined oscillating plane with a ramped thermal profile. The physical effects of flow parameters cannot be investigated and studied using a memory effect, just like with regular PDEs. In this study, we have confabulated the solution of magnetised Casson-type fluid with the help of the best and most modified fractional definition, known as the Prabhakar-like thermal fractional derivative. An integral transforms scheme, namely Laplace transformation (LT) solves the dimensionless governed equations. The physical impacts of significant and fractional constraints are examined graphically and mathematically. As a result, we have confabulated that both thermal and momentum dynamics of flowing Casson fluid slow down with the increment in fractional constraint. Additionally, because of the thickness of the boundary layer, the Casson fluid parameter emphasises the dual character of flowing fluid dynamics.