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Abstract The study of thermo-physical characteristics is essential to observe the impact of several influential parameters on temperature and velocity fields. The transportation of heat in fluid flows and thermal instability/stability is a charming area of research due to their wider applications and physical significance because of their utilization in different engineering systems. This report is prepared to study thermal transportation in Maxwell hybrid nanofluid past over an infinite stretchable vertical porous sheet. An inclusion of hybrid nanofluid is performed to monitor the aspects of thermal transportation. Keeping in mind the advantages of thermal failure, non-Fourier theory for heat flux model is utilized. Aspects of external heat source are also considered. The mathematical formulation for the considered model with certain important physical aspects results in the form of coupled nonlinear PDEs system. The obtained system is reduced by engaging boundary layer approximation. Afterwards, transformations have been utilized to convert the modeled PDEs system into ODEs system. The converted nonlinear ODEs system is then handled via finite element method coded in symbolic computational package MAPLE 18.0. Grid independent survey is presented for the validation of used approach and the comparative analysis has been done to confirm the reliability of obtained solution. The obtained solution is discussed and physical aspects have been explored and recorded against numerous involved influential variables. Motion into hybrid nanoparticles and nanoparticles becomes slow down versus higher values of Forchheimer and Darcy’s porous numbers. Thermal growth is enhanced for the case of hybrid nano-structures rather than for case of nanofluid. Thickness regarding momentum layer is dominated for hybrid nanoparticles rather than case of nanoparticles.

The present research investigates the Susceptible-Infected-Recovered (SIR) epidemic model of childhood diseases and its complications with the Atangana-Baleanu fractional derivative operator in the Caputo sense (ABC). With the aid of the Elzaki Adomian decomposition method (EADM), the approximate solutions of the aforesaid model are discussed by exerting the Adomian decomposition method. By employing the fixed point postulates and the Picard–Lindelöf approach, the stability, existence, and uniqueness consequences of the model are demonstrated. Furthermore, we illustrate the essential hypothesis for disease control in order to find the role of unaware infectives in the spread of childhood diseases. Besides that, simulation results and graphical illustrations are presented for various fractional-orders. A comparison analysis is shown with the previous findings. It is hoped that ABC fractional derivative and the projected algorithm will provide new venues in futuristic studies to manipulate and analyze several epidemiological models.

Partial differential equations are among the most important mathematical tools for scientists in describing many physical and engineering problems related to real life. Accordingly, in this work, an efficient technique is proposed for getting different collections of solutions to a third-order version of nonlinear Schrödinger’s equation. Some numerical simulations related to the acquiblack solutions are also provided in this research. All results presented in this article can be consideblack as new achievements for the model. Further, it is emphasized that the used technique enables us to study other forms of nonlinear models. It is obtained that the technique is a reliable tool in handling many nonlinear partial differential equations arising in engineering, fluid mechanics, nonlinear optics, oceans, seas, and many mathematical physics. Moreover, the present results help the plasma physics researchers for investigating many nonlinear modulated structures that can generate and propagate in laboratory and space plasmas.

In this paper, the flow of a power law fluid has been investigated for Newtonian and non-Newtonian fluids with the temperature distribution in a rectangular channel containing a heated circular cylinder near the inlet with different blockage ratios. The generalized non-Newtonian power law model coupled with the energy equation is solved numerically, considering power law index in the range of 0.8≤n≤1.2 and Reynolds number in the range from 1000 to 10000. A heated circular cylinder is fixed near the inlet of the channel with blockage ratios (from radius to the height of the channel) of 1:10, 2:10, and 3:10 The governing partial differential equations coupled with energy equation are discretized to investigate the simulation of the current problem with finite element-based software of COMSOL Multiphysics 5.4. The results are shown with the help of surface plots, tables, and graphs. The computational results for maximum and minimum pressure around the cylinder, temperature along the center line of the cylinder, and local Nusselt number are specially discussed in detail.

The present research paper illustrates how noninteger derivative order analysis affects the reflection of partial thermal expansion waves under the generalized theory of plane harmonic wave reflection from a semivacuum elastic solid material with both gravity and magnetic field in the three-phase lag model (3PHL). The main goal for this study is investigating the fractional order impact and the applications related to the orders, especially in biology, medicine, and bioinformatics, besides the integer order considering an external effect, such as electromagnetic, gravity, and phase lags in a microstretch medium. The problem fractional form was formulated, and the boundary conditions were applied. The results were displayed graphically, considering the 3PHL model with magnetic field, gravity, and relaxation time. These findings were an explicit comparison of the effect of the plane wave reflection amplitude with integer derivative order analysis and noninteger derivative order analysis. The fractional order was compared to the correspondence integer order that indicated to the difference between them and agreement with the applications in biology, medicine, and other related topics. This phenomenon has more applications in relation to the biology and biomathematics problems.

This article investigates the semi-analytical method coupled with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). In addition, we apply this method to the time-fractional Swift–Hohenberg equation (SHe) with various initial conditions (IC) under gH-differentiability. Some aspects of the fuzzy Caputo fractional derivative (CFD) with the Elzaki transform are presented. Moreover, we established the general formulation and approximate findings by testing examples in series form of the models under investigation with success. With the aid of the projected method, we establish the approximate analytical results of SHe with graphical representations of initial value problems by inserting the uncertainty parameter 0≤℘≤1 with different fractional orders. It is expected that fuzzy EADM will be powerful and accurate in configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

Details on the hydrothermal characteristics of turbulent flows in a solar channel heat exchanger (CHE) are highlighted. The device has transverse T-shaped vortex generators (VGs). Two staggered VGs (baffles) are inserted on the lower and upper walls of the CHE. The working fluid is Newtonian and incompressible, with constant physical properties. The ANSYS Fluent 17.0 is utilized in this survey. The second-order upwind and QUICK schemes were utilized to perform the discretization of pressure and convective terms, respectively. The SIMPLE algorithm was employed to achieve the speed-pressure coupling. The residual target 10−9 was selected as a convergence criterion. The effects of the T-VGs’ geometrical shape and Reynolds numbers were inspected. At the baffle level, the wall effect was augmented due to the reduction of the passage area of flows, which is estimated here to be 55%, resulting thus in a considerable resistance to the movement of fluid particles. The thermal distribution is highly dependent on the flow structures within the CHE. Since the fluid agitation yields an enhanced mixing, it allows thus an excellent heat transfer. The most considerable rates of thermal transfer were obtained with high Re, which resulted from the intensified mixing of fluid particles through the formation of recirculation cells and the interaction with the walls of the T-VGs and the CHE. The T-baffles with intense flow rates yielded negative turbulent speeds and intensify the fluid agitation, which improves the thermal exchange rates.