International Journal of Modern Physics B

Recently, the scientists have been giving attention to the mutual pattern of heat and mass transportation such that both phenomena endorsed the novelty in engineering and industrial equipment’s approximating polymer progressions, fridge-freezers, plastics extrusion, fissile vessels, irrigation of arithmetical kit and power generation, heat exchangers. The Fourier and Fick laws are exploited to describe exactly how the heat and mass transportation via a space with influence of temperature and concentration will change, respectively. Furthermore, the worth of thermo-solutal transport has increased extremely in numerous industrial and scientific progresses, for instance, nutrition processing, utensils power aerials, crop mutilation, thermal transmission in fleshy tissue and numerous others. The theme of this effort is to explore the theory of thermo-solutal relaxation times (Cattaneo–Christov double diffusion) and thermo-solutal stratifications in Carreau fluid with the properties of magnetic field. Additionally, the thermal phenomenon of variable conductivity and mechanism of solutal diffusivity had been studied. The bvp4c algorithm has been exploited for the solution process. It is remarkable to note that both velocity fields decay for magnetic factors. The higher estimations of variable conductivity and thermal stratification factors have contradicting performance on temperature field. Additionally, mass stratification depreciates the concentration of Carreau fluid. The coefficient of skin frictions is enhanced for magnetic factor. The comparative tables compared with past studies with worthy settlement have also been shown.

In this research paper, we take into account the ($2+1$)-dimensional Kadomtsev–Petviashvili equation which is important in the soliton theory of nonlinear physics. To get the desired soliton solutions, the modified F-expansion method using the Riccati equation which has many solution functions, as well as the modified generalized Kudryashov’s method, had been effectively implemented. One of the reasons for the preference of the methods is that the proposed methods have been widely used before and they have not been applied to this problem. First, the wave transform is applied to the considered nonlinear partial differential equation (NLPDE), the nonlinear ordinary differential equation (NODE) form and the balancing constant are determined. The next step is to use the auxiliary equation depending on the proposed method to find the solution of the NODE form and to obtain the linear algebraic equation system. The solution of this system gives different solution sets for unknown parameter values. Then, soliton solution functions are constructed by using the suitable solution sets. After testing and confirming that the obtained solution functions satisfy the main equation, the three- and two-dimensional illustrations are depicted.

In this study, we apply relatively analytical techniques, the multiple $exp$-function method, $exp$-function method and $\frac{G^{\prime }}{G^2}$-expansion method to get approximate and analytic solutions of some nonlinear partial differential equations (PDEs), i.e., the nonlinear space–time fractional partial differential symmetric regularized long wave equation, an impressive model to characterize ion-acoustic and space change waves, the nonlinear $(4+1)$-dimensional Fokas PDE, a meaningful multi-dimensional extension of the Kadomtsev–Petviashvili (KP) and Davey–Stewartson (DS) equations, $(1+1)$-dimensional Bateman–Burgers equation, a simplification of a more complex and sophisticated model, and the $(1+1)$-dimensional Benjamin–Ono equation, a model for the propagation of unidirectional internal waves in stratified fluids. Finally, we propose the numerical results in tables and discuss advantages and disadvantages of the mentioned methods.

The novel wave profiles for the more general $(2+1)$-dimensional Boussinesq equation are established in this paper. To get such outstanding results, we employ the potent Sardar sub-equation technique. The recognized explanations for several physical difficulties have been studied. These technological advancements have been proven to be helpful for the transmission of long-wave and high-power communications networks. The circumstances that gave rise to the emergence of these solutions are described in detail. The physical characteristics of the governing equation have been depicted in contour plots and three dimensions.

Enhanced heat transport in advanced nanofluids (ternary hybrid nanofluids) is one of the major demands of the time and is potentially contributing in food processing to maintain the temperature of building, cooling of electronic devices, paint industries and biomedical engineering. Therefore, an efficient heat transport model is developed in this study and innovative ternary mixture [(Al₂O₃-CuO-Ag)] along with feasible thermophysical attributes comprising the effects of ternary nanoparticles and similarity equations are exercised to obtain the desired sort of nanoliquid model. This model is related to vertically oriented cylinder with novel upgradation of permeability, upthrust forces and nonlinear solar thermal radiations. In the next stage, mathematical treatment of [(Al₂O₃-CuO-Ag)/H₂O]_thnf is done and successfully achieved the desired convergence and then organized the graphical results. The furnished results disclosed that tri-composites-based nanofluid has low velocity than hybrid and common nanofluids. Moreover, temperature in [(Al₂O₃-CuO-Ag)/H₂O]_thnf is dominant over both hybrid and mono nanofluids. The integrated effects of nonlinear thermal radiations are of much interest in the temperature enhancement and observed that Rd and ${\theta }_w$ are better for thermal improvement.

In this paper, hybrid nanofluid flow with mediated compressions and dilations subject to the temperature-dependent viscosity/ thermal conductivity and inclined magnetic field is considered. In medical science, the flow mediated dilation of the artery exists when the blood flow is enhanced in the artery. The compressed/ dilated type flow can be utilized in food processing, hot plate welding, rheological testing, cardiovascular drugs, measurement of brachial artery dilation, blood vessel damage caused by cigarette smoke. The volume of the dilated flow is maintained by injecting the same fluid into the flow field through the exponentially permeable and stretchable walls of the channel. This phenomenon is modeled mathematically and solved by Chebyshev pseudo-spectral method utilizing quasi-linearization approach. It is interestingly analyzed that squeezing/ dilating forces generate two points of inflection in the flow field where the magnitude of permeable fluid velocity is enhanced by 17.21% in the mid portion of the channel by the increase of dilating forces, however it is reduced by 20.35% due to the strengthening of the compressing forces of the channel. The reported flow mediated dilation/ contraction of the study can be used in targeted drug delivery (especially cardiovascular drugs), assessment of endothelial function, measurement of brachial artery dilation and blood vessel damage. The angled magnetic field can be utilized to successfully control the environmental skin-friction and heat transfer.

The purpose behind this research is to utilize the knack of Bayesian solver to determine numerical solution of functional differential equations arising in the quantum calculus models. Functional differential equations having discrete versions are very difficult to solve due to the presence of delay term, here with the implementation of Bayesian solver with means of neural networks, an efficient technique has been developed to overcome the complication in the model. First, the functional differential systems are converted into recurrence relations, then datasets are generated for converted recurrence relations to construct continuous mapping for neural networks. Second, the approximate solutions are determined through employing training and testing steps on generated datasets to learn the neural networks. Furthermore, comprehensive statistical analysis are presented by applying various statistical operators such as, mean squared error (MSE), regression analysis to confirm both accuracy as well as stability of the proposed technique. Moreover, its rapid convergence and reliability is also endorsed by the histogram, training state and correlation plots. Expected level for accuracy of suggested technique is further endorsed with the comparison of attained results with the reference solution. Additionally, accuracy and reliability is also confirmed by absolute error analysis.

Gyrotactic microorganisms may be mobile ones that exist in surroundings, for instance oceans, pools, and reservoirs. The convective heat transfer due to the movement of these microorganisms in the base fluids is known as bio-convection. In this paper, the analysis of MHD bio-convection of nanofluid in the $\mathrm{\Gamma }$-shaped enclosure with gyrotactic microorganisms inside is conducted. The effect of thermal Rayleigh number Ra_t (10⁴–10⁵), bio-convection Rayleigh number (10–100), Lewis number (0.1–0.9), and Peclet number (10${}^{-3}$–10${}^{-1}$) on the natural convection (NC) and concentration of the micro-organisms (C) is investigated. The Navier–Stokes equations are used as the governing equations and are solved by Finite Element Method. The results reveal that Le may have a reverse impact on Nu_avg (upto 42%); however, Pe has a positive impact on both Nu_avg (upto 10%) and Sh_avg (upto 12%) and enhances heat transfer performance.

For the ($2+1$)-dimensional time conformable Maccari system with beta-derivative, exact solutions are obtained in this paper using the improved sub-equation method. This technique has been used to find rational solutions, generalized hyperbolic function solutions and generalized trigonometric function solutions. The new structures of the solutions are shown after the proper parameter values have been given. It is easier to understand the intricate physical processes of these dynamical models by viewing the physical surfaces of some obtained solutions in various forms. The outcomes demonstrate the efficiency of the applied strategy, which may be used to solve a number of nonlinear physical problems. ($2+1$)-dimensional time conformable Maccari system is considered and the graphs of solutions are sketched using MAPLE software after its exact solutions which are acquired using the improved sub-equation method.

This paper depicts the fully developed natural convective flow on a conducting viscous fluid towards a nonlinearly stretching sheet. Furthermore, the porous dissipation, thermal radiation and heating parameter effects are implemented on both the vertical walls of the stretchy channel. To model the stretchy flow equations, the Cartesian coordinates’ system is utilized. Through the utilization of similarity variables, the nonlinear partial differential equations that describe the flow (mass, momentum and energy conservation) are converted into nonlinear ordinary differential equations. With the help of the MAPLE, a well-known fourth-order Runge–Kutta procedure is used to do a numerical evaluation of the stated nonlinear and non-dimensional set of equations. For each of the several nonlinear radiative parameters regulating the flow regime, the velocity and temperature distribution functions are determined, viz the nonlinear heating parameter ${\theta }_R$, Eckert number $Ec$, Prandtl number $Pr$, porosity variable $Pm$ and thermal radiation parameter $N_R$. Graphic representations are provided for every outcome. Furthermore, skin friction and Nusselt number are also computed to give an approximation of the surface shear stress and cooling rate, respectively. A remarkable compaction is obtained between computed numerical data and published results. It has been demonstrated that an increase in the value of the nonlinear parameter $Pm$ outcomes creates a reduction in the dimensionless translational velocity $g^{\prime }$ of both viscous and Newtonian fluids. Dimensionless temperature mostly upsurges with growth in nonlinear parameters $Ec$, $Pm$, ${\theta }_R$ and decreases with an intensification in convective parameters, $Pr$, $N_R$. There is a detailed discussion on the implications of all embedded stretching sheet variables on the flow. The flow regime is extremely useful in the technology of polymer processing as well as in the field of materials science.