Three-dimensional radiative Maxwell nanofluid flow with chemically reactive waste discharge process and Robin’s conditions

The main aim and novelty of this numerical analysis is to investigate the thermodynamic features of magnetized Cattaneo–Christov heat and mass flux models on the radiative Casson fluid flow past a stretching cylinder manifested with the thermal and mass flow mechanism within the boundary layer regime qualitatively under the influence of Soret and Dufour effects. Pertaining to this numerical investigation, the primitive forms of produced nonlinear coupled partial differential equations are reduced to ordinary differential equations via similarity transformations and are solved by employing numerically efficient and stable Runge–Kutta fourth-order scheme. The graphical results for velocity, thermal and concentration fields, wall shear stress, Nusselt and Sherwood numbers are presented for the various values of parameters such as, , , , , , , , , and . In addition, the produced numerical solutions indicate that, the higher curvature number suppressed the velocity and thermal fields. Elevating thermal relaxation number diminished the thermal energy distribution over a cylinder. Magnifying Lorentz forces decayed the flow velocity and enhanced the thermal field. Finally, a reasonable agreement between the current analysis and previously published results is tabularized.

Impacts of Stefan blowing and mass convention on flow of Maxwell nanofluid of variable thermal conductivity about a rotating disk

The objective of this study is to analyze the natural convection flow of nanofluid along a circular cone placed in a vertical direction. The generalized heat flux and mass flux models are commonly known as the Cattaneo–Christov heat flux model and mass flux models. In the present study, these models are used for both heat and mass transfers analysis in nanofluid flow. For the governing equations, the Buongiorno transport model is used in which two important slip mechanism, namely thermophoresis and Brownian motion parameters, are discussed. The resulting governing equations in the form of partial differential equations (PDEs) are converted into ordinary differential equations (ODEs) due to similar flow along the surface of a circular cone. To solve these ODEs, a numerical algorithm based on implicit finite difference scheme is utilized. The effects of dimensionless parameters on heat and mass transfer in nanofluid flow are discussed graphically in the form of velocity profile, temperature profile, Sherwood number and Nusselt number. It is noted that in the presence of the Cattaneo–Christov heat flux model and mass flux model, the heat transfer rate decreases by increasing both thermal and concentration relaxation parameters; however, Sherwood number decreases by increasing the thermal relaxation parameter, and increases by increasing the concentration relaxation parameter.

Non-orthogonal stagnation point flow of Maxwell nano-material over a stretching cylinder

Generalized heat and mass transport features of MHD Maxwell nanofluid flows past a linearly Bi-stretching surface in the presence of motile microorganisms and chemical reaction

The classical viscous theory is limited to illustrating the characteristics of several materials like pseudoplastic and dilatant fluids. Sutterby fluid has the features of shear thinning and shear thickening fluids because of its Power law index. Therefore, this study considered an incompressible, time-independent and electrically conducting Sutterby fluid flow across a rotating and stretchable disk. The disk experiences the effect of porous space. The energy equation has variable conductivity, heat source and thermal relaxation time features while mass equation exploits the influence of chemical reaction. The aspects of Buongiorno nanofluid theory are also examined in the Sutterby flow model. The phenomenon of Stefan blowing is analysed through mass transfer rate at the surface of disk. The flow expressions are first transferred into a new system of single independent variable and then treated numerically via Runge–Kutta–Fehlberg (RKF) method combined through shooting process. The behaviour of distinguished physical quantities is discussed graphically on momentum, mass species and thermal fields. The numeric data of drag force, Sherwood number and Nusselt number is calculated against several physical parameters.

This article mainly scrutinizes the heat transfer and flow characteristics of a mixed convection ternary hybrid nanofluid in a porous microchannel considering the catalytic chemical reaction and nonuniform heat absorption/generation. Using appropriate similarity transformations, the modeled equations are converted into reduced ones and then solved via the Runge–Kutta–Fehlberg 4th/5th order method. To strengthen this analysis, the convection mechanism has been deployed. The effect of pertinent physical parameters on the fluid motion and thermal field is displayed, including some important engineering variables like the Nusselt number, Sherwood number, and drag force. The novel outcomes display that the flow reduces with porous permeability and nanoparticle volume fraction. The temperature of the nanofluid improves with nonuniform heat absorption/generation. The concentration decreases in the presence of both homogeneous and heterogeneous reaction intensities. The heat transfer rate enhances for the Eckert number, and a similar influence on the mass transfer rate is noticed for homogeneous reaction parameters. Further, the drag force declines for the Grashof number. The outcomes show that, in all cases, the ternary hybrid nanofluid shows a greater impact than the nanofluid. The attained findings represent applications in the era of cooling and heating systems, thermal engineering, and energy production.

The current investigation is focused on the effects of heterogeneous and homogeneous reactions on the flow of nanofluid over a rotating disk. The current investigation reflects the magnetic field's effectiveness and melting impact. In this study, the Maxwell-Bruggeman and Krieger-Dougherty models of nanoparticle aggregation are applied. The thermal conductivity and viscosity are correctly represented by these models. Furthermore, the flow phenomena of non-Newtonian materials are an issue of great interest to both researchers and academics. Similarity variables are used to reduced the controlling partial differential equation (PDE) into an ordinary differential equation (ODE). Later, the obtained system is numerically solved using the shooting technique and Runge–Kutta–Fehlberg's fourth–fifth order approach (RKF-45). The resulting numerical findings are then graphically shown and analyzed in depth. The findings show that the liquid flow without nanoparticle aggregation has improved heat transport when the melting parameter is increased. Furthermore, increase in strength of heterogeneous and homogeneous reaction parameters shows larger mass transfer for fluid flow with aggregation condition.

Activation energy impact in nonlinear radiative stagnation point flow of Cross nanofluid

Stretching flow problems have several real-world applications in engineering, biological, and industrial fields. The real-world applications of the stretching sheet flow problems are continuous cooling of fiber, manufacturing of rubber and plastics sheets, metal-working processes, crystal growth processes, drawing of the filaments through a quiescent fluid, and consideration of the liquid's films and many others. The present problem focuses on the study of heat and mass transmission phenomena of the magnetohydrodynamics flow of three-dimensional micropolar liquid over a bidirectional stretching surface. In the current analysis, the heat and mass transport mechanism are demonstrated by incorporating the Cattaneo–Christov heat and mass flux model. The micro-organisms are only used to stabilize suspended nanoparticles via bioconvection, which is caused by the combination of magnetic field and a buoyancy force. The current model is demonstrated in the system of higher order partial differential equations (PDEs), which are changed into nonlinear ordinary differential equations (ODEs) by the exploitation of appropriate similarity variables. For the analytical solution, the resulting nonlinear ODEs are simulated by employing the homotopy analysis scheme. The physical significance of velocities, microrotation, temperature, concentration, and micro-organism profiles of the fluid via various embedded parameters are calculated and discussed in a graphical form. The Nusselt number, Sherwood number and micro-organism density number are calculated via tables. Some major findings of the current problem are that the Nusselt number is weakened for the boosted estimation of radiation and thermal relaxation time parameter. The bioconvection Lewis number raised the micro-organism density number. The nanofluid microrotation profile is boosted with the augmentation of the microrotation parameter. The temperature of nanoliquid is lower for thermal relaxation time parameter and nanofluid concentration is lower the for solutal relaxation time parameter.

The characteristics of Cattaneo-Christov heat and mass fluxes in an unsteady two-dimensional squeezing flow of a magneto-hydrodynamic (MHD) Casson fluid between two parallel plates with thermal radiation and Joule dissipation effects under the influence of time-dependent homogenous first-order chemical reaction is examined numerically. Present physical model is analyzed under the influence of Lorentz forces to investigate the effect of a magnetic field on the flow behaviour. Further, the heat generation or absorption concept with chemical reaction is introduced to visualize the heat and mass transfer behaviour under the influence of Cattaneo-Christov heat and mass flux models. The non-Newtonian behaviour of the Casson fluid flow model results in highly nonlinear, coupled, time-dependent partial differential equations and that are reduced to a system of nonlinear ordinary differential equations by using the similarity transformation approach. The numerical methods such as, the Runge-Kutta fourth-order integration scheme with shooting method (RK-SM) and bvp4c techniques are being used to generate the similarity solutions of the governing equations. The convergence between RK-SM and bvp4c techniques is established. The graphical trends of various control parameters concerning to velocity, temperature and concentration fields with skin-friction coefficient, Nusselt and Sherwood numbers are analysed and discussed. The outcomes of the present numerical simulations indicate that the temperature and concentration distributions are fewer in case of the Cattaneo-Christov heat and mass flux models as compared to the classical Fourier's and Fick's laws of heat and mass diffusions. Also it is observed that the magnitude of local heat transfer rate increases with increasing values of heat source/sink parameter. To check the correctness of the current numerical methods, the comparison has been made with the existing results in the literature and excellent agreement was found.

A comparative study of radiative Casson and Jeffrey fluids flows generated by the chemically reactive bidirectional stretched sheet is presented. Energy and mass species analysis is performed under radiative heat generation impacts. The Robin’s heat and mass conditions are imposed for the analysis of considered model. The boundary-driven equations are simplified into one independent variable equation by the implication of similarity constraints. The resulted model is tackled by the help of homotopic scheme. The results of various parameters are sketched and interpreted for both Casson and Jeffrey nanofluids. The convergence is expressed through numeric benchmarks and graphical form. The numeric evaluation of Sherwood and Nusselt number is presented against the versatile parametric values. The results showed that the higher velocity curves appeared in Casson nanofluid case as comparative to case of Jeffrey nanofluid. The temperature heat generation constraints boosted the temperature of both Casson and Jeffrey nanofluids. The incrementing trend of chemical reactive and Lewis number resulted weaker concentration profiles for Jeffrey and Casson fluids. The conducted research model has magnificent appliances in solar energy devices, chemical reactors, solar reservoirs, nuclear power plants, heat reservoirs, microwave oven, thermal radiant, thermal imaging and many others.

ABSTRACTThis study examines the transient magnetohydrodynamic (MHD) flow of Walter's‐B viscoelastic fluid over a vertical porous plate within a porous medium, considering the effects of radiation and chemical processes. The nonlinear flow control equations are solved using a closed‐loop method, producing detailed numerical solutions for velocity, temperature, and concentration profiles. Velocity decreases with increasing permeability (K), Schmidt number (Sc), radiation (R), and magnetic field strength (M). In contrast, it increases with higher Prandtl number (Pr), permeability (K), and time (t). Temperature decreases with higher radiation but rises with Prandtl number and time. Concentration decreases with higher permeability and Schmidt number but increases with time. Notably, an increase in the Brownian motion parameter enhances heat and momentum transfer, thickening the velocity and thermal boundary layers. This research has practical applications in fields, such as blood oxygenators, chemical reactors, and polymer processing industries. The novelty of the study lies in its integration of radiation, chemical processes, and MHD flows in the analysis of viscoelastic fluids, a topic that has not been widely explored in previous studies. Future research could focus on optimizing MHD Walter's‐B viscoelastic flow systems, with particular attention to the effects of magnetic field strength and viscoelastic parameters on flow behavior.

Cattaneo-Christov heat and mass flux effect on upper-convected Maxwell nanofluid with gyrotactic motile microorganisms over a porous sheet

The present study invokes the application of Cattaneo-Christov theory for the thermal analysis in the buoyancy driven three dimensional flow of Maxwell nanofluid. The flow is induced above the vertical bidirectional stretching sheet. The phenomena of thermophoresis and Brownian diffusion of nanoparticles in the flow Maxwell liquid are deliberated with the help of Buongiorno model for nanofluid. The physical problem is formulated in the form of boundary layer partial differential equations (PDEs). Moreover, suitable ansatz for flow mechanism are employed to reduce the governing PDEs into the non-linear ordinary differential equations (ODEs). The flow mechanism of Maxwell fluid along with energy transport is analyzed in the form of homotopic solutions of the governing ODEs. The outcomes are presented graphically and discussed with physical explanation. The analysis revealed that both buoyancy and mixed convection parameters enhanced the [Formula: see text]-component of velocity field but declined the [Formula: see text]-component. Moreover, in assisting mode these two parameters also increased the thermal and solutal energy transport in nanofluid. It is noted that the thermophorectic force boosts up the thermal energy transport in the flow in the presence of thermal relaxation phenomenon. The validation of the present results are confirmed through tabular data with some previous studies.