Mutual effects of chemical reaction and thermal radiation on MHD peristaltic transport of Jeffrey nanofluids: Tumor tissues treatment

As thermal radiation is one of the fundamental means of heat transfer, therefore, this study analyzes the impacts of thermal radiation and magnetic field on the peristaltic transport of a Jeffrey nanofluid in a nonuniform asymmetric channel. Further, Two models of viscosity are debated: Model (I), in which all parameters dependent on viscosity behave as a constant (as treated before in nanofluid research); Model (II), in which these known parameters are considered to vary with the temperature of the flow. Under the condition of long wavelength and low Reynolds number, the problem is rearranged. The resulting system of partial differential equations (PNE) is solved with aid of Mathematica 11. Furthermore, the streamline graphs are presented by significance of trapping bolus phenomenon. To emphasize the quality of solutions, comparisons between the previous results and recent published results by Reddy et al. have been made and signified. The comparisons are shown in Table 1 and are found to be in good agreement. As the thermal radiation increases, the diameter of nanoparticles rises (thermal radiation is a diminishing function of temperature, and with a decrease in the temperature, the diameter of the nanoparticles increases, that is, the size of nanoparticles increases and they become more active near malignant tumor tissues). Therefore, its work as agents for radiation remedy, produce limited radiation quantities, and selectively target malignant tumor for controlled mutilation (radiotherapy of oncology). Such a model is appropriate for the transportation of physiological flows in the arteries with heat and mass transfer (blood flow models).     

Toward the heat convection enhancement of nanofluids flowing in a 3D microchannel affected by a nonuniform magnetic field

In the present investigation, the behavior of laminar convective flow and heat transfer in a three-dimensional horizontal square duct using different water-based nanofluids (Fe₃O₄/water, and carbon nanotubes/water) is numerically investigated. The channel is subjected to a periodic partial or full magnetic field. The outer surface is subjected to a constant heat flux density. The problem is numerically solved via the finite volume method with a second-order precision. The numerical simulations covered a range of the Reynolds number 50 ≤ Re ≤ 400, Hartmann number 0 ≤ Ha ≤ 50, and concentration of nanoparticles 0 ≤ ϕ ≤ 0.02 for different modes of the magnetic field application and direction. Examination of the hydrodynamic and thermal behavior shows significant heat transfer performances obtained when applying transversal and partial periodic magnetic fields simultaneously. More precisely, it is found that the favorable protocol improved the heat transfer rate by 85% in the duct flowing by the Ferrofluid at Ha = 50. Furthermore, findings illustrate that the overall heat transfer rate presented in terms of the mean Nusselt number and the highest compromise (heat transfer augmentation-pressure losses diminution) are obtained in the case of Fe₃O₄ nanoparticles for all taken values of Reynolds and Hartmann numbers, whatever the manner and direction of the applied magnetic field.     

Thermal radiation and variable electrical conductivity effects on MHD peristaltic motion of Carreau nanofluids: Radiotherapy and thermotherapy of oncology treatment

This study intends to investigate the influences of thermal radiation and variable electrical conductivity on the MHD peristaltic flow of Carreau nanofluids as the radiotherapy and thermotherapy are required for cancer treatment. Formulation of temperature‐dependent electrical conductivity is introduced for the first time in the peristaltic literature. The related equations of momentum, mass, and concentration are reformulated using lubrication approximations (ie, tiny or zero Reynolds number and long wavelength). These simplified equations are solved numerically with the aid of Parameteric‐NDSolve. Results for velocity, temperature, and concentration distributions are obtained in three‐dimensional analytical forms. The streamline graphs are offered in the terminus, which elucidate the trapping bolus phenomenon. A “special case” of our results offered to get the solutions over certain contours for the behaviors of velocity, temperature, and nanoparticle concentration. It is found that the magnetic nanoparticles acquire more energy at high temperature, enabling them to destroy and damage tumors tissues (thermotherapy of oncology). Radiation is the reason for spreading the energy, that is, the energy of all the fluid nanoparticles does not continue with the same value. Therefore, in cancer treatment, doctors use high doses of radiation to cure cancer cells and prevent it from returning (radiotherapy of oncology).     

Influence of the induced magnetic field and heat transfer on peristaltic transport of a micropolar fluid in a tapered asymmetric channel

In this paper, we investigate the peristaltic transport of a micropolar fluid in a tapered asymmetric channel with heat transfer and induced magnetic field effect. The flow is analyzed by long wavelength and low Reynolds number approximations. The reduced equations have been solved by using Adomian decomposition method and the expressions for velocity, stream function, microrotation component, magnetic‐force function, pressure gradient, axial induced magnetic field, and current density distribution across the channel have been computed. Expressions for shear stresses are also obtained. The effect of pertinent parameters is illustrated graphically.     

Passive control nanoparticles in double‐diffusive free convection nanofluid flow over an inclined permeable plate

The present study has been conducted to acquire the solutions for the flow problem of an incompressible nanofluid past a permeable inclined plate implanted in a porous medium. In this study, double‐diffusivity, Brownian motion, and thermophoresis as well as passive control nanoparticles have been studied. We employ Lie group transformation on the ruling equations to extract nonlinear ordinary differential equations and solve them numerically using the fourth‐order Runge‐Kutta method and shooting approach. The supremacy of affined parameters on temperature and velocity distributions has been exposed by means of tables and graphs. This investigation suggests that both fluid velocity and nanoparticle concentration are enhanced by the modified Dufour parameter and the thermophoresis parameter. The assistance of the Lewis number intensifies the heat transport for suction.     

Magnetohydrodynamic peristaltic flow of unsteady tangent‐hyperbolic fluid in an asymmetric channel

The aim of the present numerical investigation is to explore the impact of magnetic field on peristaltic flow of an incompressible tangent‐hyperbolic fluid in an asymmetric channel. The present physical model is developed based on the considered flow configuration and with the help of small Reynolds number approximations. The current flow problem is revealed under the influence of applied magnetic field. The asymmetric channel has been considered to narrate the present physical problem. Considered physical situation in the current investigation gives the unsteady coupled highly nonlinear system of partial differential equations. Also, the simplified equations for pressure, pressure gradient, and streamlines have been obtained with the help of suitable transformations. A regular perturbation scheme is employed to produce the semi‐analytical results of the present problem. The influence of various physical parameters on pressure, pressure gradient, and streamlines are illustrated with the help of graphs. From the present analysis, it is observed that the increasing magnetic number decreases the pressure and pressure gradient in the channel. Also, the size of trapping bolus increases with increasing values of Weissenberg number.     

Influence of elasticity in an inclined annulus of nanofluid with peristaltic transport

Peristaltic transport of Newtonian nanofluid in an inclined annulus terms of radii regarding peristalsis and elasticity. It is noticed that with an increase in amplitude ratio, flux is getting enhanced in the absence of nanoparticles when compared with viscous fluid with nanoparticles. Our results reduce to the corresponding ones of Rubinow and Keller as a special case for the viscous flow in an elastic tube. The effect of various emerging parameters bounded by two concentric cylinders is studied under the assumption of long wavelength and dominance of viscous effects over inertial effects. The outer cylinder is elastic in nature and has a sinusoidal wave traveling down in its wall, whereas the inner cylinder is rigid. Analytical solutions have been established for velocity, flux, pressure rise, temperature distribution, and nanoparticle concentration. The flux, pressure rise, and frictional forces have been obtained in on the flow characteristic are presented and discussed. Obtained results may be useful in understanding the behavior of peristaltic transport of blood flow in small blood vessels and blood flow through elastic arteries.     

Entropy generation on MHD peristaltic flow of Cu‐water nanofluid with slip conditions

The current research explores entropy generation and effect of magnetic field on peristaltic flow of copper‐water nanofluid in an asymmetric configuration saturated with porous medium. Slip conditions are invoked for velocity and temperature. Governing flow problem is constructed under the long wave length assumption. Analytical result for the problem is computed by exploiting homotopy analysis methodology. The influences of involved physical parameters are investigated through plots.     

Influence of relative motion of magnetic field on time‐dependent MHD natural convection flow

The effects of relative motion of magnetic field on unsteady magnetohydrodynamic free convection flow with ramped motion and temperature‐dependent heat source/sink have been analyzed. The motion of the inner cylinder is ramped while the motion of the outer cylinder is fixed. The momentum and energy equations are solved using the well‐known Laplace transform. The time‐domain solution is obtained using the Riemann‐sum approximation method. The influence of the governing parameters on fluid velocity, fluid temperature, volume flow rate, and rate of heat transfer are discussed with the help of line graphs. It is found that Hartmann number has a retarding effect on fluid velocity, skin friction at the outer surface of the inner cylinder, and mass flow rate when the magnetic field is fixed with the fluid and when the velocity of the magnetic field is less than the velocity of the moving cylinder. Whereas, the reverse effect is noticed when the magnetic field is fixed with the moving cylinder.     

An application of paired quasilinearization on double‐diffusive convection flow over a cone embedded in a porous medium in the presence of nanoparticles

Mixed convection flow of a nanofluid near a vertical cone embedded in a a porous medium with Soret and Dufour effects is exercised. The bearing of a porous medium is recounted by the Darcy model. The partial differential equations, modeling the concerned problem, is nondimensionalised by implementing compatible transformations, which results in a similar form. A new paired spectral quasilinearization method is adopted to get the accurate numerical solution. Convergence and accuracy of the solution is elaborated by analyzing the norm of residual and solution errors. Alteration of velocity, temperature, nanoparticle and solute concentration profiles due to flow controlling parameters, namely, Brownian motion, thermophoresis, Soret, Dufour, Lewis number, and buoyancy ratio is outlined by reproducing the obtained numerical solution in graphs and tables. Analysis reveals that the flow profiles are greatly influenced by the physical parameters under investigation.     

Thermophoresis and Brownian motion effects on Williamson nanofluid flow past a stretching surface with thermal radiation and chemical reaction

The heat transfer mechanism of nanofluids has numerous industrial applications owing to the non-Newtonian behavior and has been exercised as a thermophysical phenomena in presence of thermal radiation. The present paper deals with the thermal transfer characteristics of time-independent magnetohydrodynamics Williamson fluid past a stretching surface in presence of the reaction of chemical equilibrium is dealt. The flow constitutive nonlinear partial differential coupled equations are transmitted into ordinary differential equalities by employing relevant similarity transmutations. These deduced equations are determined by using the Runge–Kutta numerical technique with a shooting approach with the aid of MATLAB software. Influences of distinct pertinent flow parameters like an inclined uniform magnetic field, Soret number, heat generation/absorption, and Schmidt number constrained to convective boundary condition is displayed through graphs with relevant physical interpretations. Computed numerical values for the friction factor coefficient, local Nusselt parameter, and Sherwood number are tabulated.      

Newtonian and non-Newtonian nanofluids with entropy generation in conjugate natural convection of hybrid nanofluid-porous enclosures: A review

The current study summarizes previous studies carried out on heat convection, fluid flow, and entropy generation of porous enclosures filled with hybrid/nanofluid. Newtonian and non-Newtonian base fluids and the magnetohydrodynamics effects are considered. Natural convective heat transmission is one of the most common types of heat transfer due to its wide engineering applications like solar collectors, electronic equipment, cooling systems, nuclear reactors, and geothermal engineering. By offering a large surface area per unit volume and the disorderly movement of fluids passing through the relevant pores, in several applications, a porous media can increase convective heat transmission. Moreover, the problem related to the low thermal conductivity of conventional fluids can be addressed by introducing nanoparticles known as nanofluids. To increase the performance of thermal equipment, combining nanofluids with porous materials can be very advantageous. The impact of different governing parameters and the numerical methods used to solve the differential equations are also summarized.     

Unsteady bioconvection Darcy-Forchheimer nanofluid flow through a horizontal channel with impact of magnetic field and thermal radiation

Unsteady bioconvection Darcy-Forchhiemer nanofluid flow is considered in the current investigation in the presence of micro-organisms. The flow is exposed to thermal radiation and a uniform magnetic field in a horizontal channel. The impacts of Brownian motion and thermophoresis are also considered for the flow problem. The unsteady governing equations are modeled and transformed into a nondimensional form by employing a suitable group of similar variables. The solution of the modeled equations is determined by the semianalytical method homotopy analysis method. The features of flow characteristics such as temperature, concentration, velocity, and the motile micro-organism distributions in response to the variations of the emerging parameters are simulated and examined in detail. Among the many results of the study, it is found that velocity upsurges with rising values of the unsteadiness parameter while declining with growth in the magnetic, inertial, and porosity parameters. Temperature augments with growing estimations of Brownian, unsteadiness, and radiation parameters and declines with enhancing values of Prandtl number. Amassed estimations of the Brownian factor reduce the concentration of nanoparticles while growing values of thermophoresis, unsteadiness parameters, and Schmidt number increase it. Moreover, the motile micro-organism profile is a reducing function of the bioconvection Lewis numbers, Peclet, and bioconvection concentration difference parameter.     

Influence of Lewis number on double‐diffusive convection in a square cavity filled with binary gas

This paper presents double‐diffusive convection in a square cavity filled with binary gas, due to horizontal opposing temperature and concentration gradients. The effect of Lewis number was considered under the conditions of Prandtl number Pr = 1, buoyancy ratio N = 1, and thermal Rayleigh number Ra_T = 10⁴ and 10⁵. Numerical solutions are obtained by a Chebyshev collocation technique with high resolution. Depending on the Lewis number, three kinds of flow structures are identified: symmetric steady flow, asymmetric oscillatory flow, and symmetric oscillatory flow. Oscillatory flow occurs in the regime of thermal dominant flow and it leads to a periodic change between stable and unstable states in species stratification due to the thermo‐solutal interaction. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(1): 85–97, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10073     

Simultaneous effects of radiation,magnetic field on peristaltic flow of Carreau nanofluid submerged in gyrotactic microorganisms with heat and mass transfer

Our study intends to examine the combined effects of radiation, magnetic field, and chemical reaction on the peristaltic flow of a non-Newtonian fluid containing gyrotactic microorganisms and nanoparticles. The system of our equations is understood numerically by using the Rung-Kutta-Merson method with Newton iteration in a shooting and matching procedure. The effect of physical implanted parameters is represented and discussed through a lot of charts for velocity, temperature, nanoparticle concentration, the density of motile microorganisms. From this discussion, we notice that the motile microorganisms profile is affected by the arising with the Brownian motion parameter and radiation parameter but the thermophoresis parameter, traditional Lewis number, and bioconvection of Peclet number are decremented the motile microorganisms profile.     

Mixed convective heat and mass transfer on a peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel

In the present analysis we discuss the effects of mixed convective heat and mass transfer on the peristaltic flow of a non‐Newtonian fluid in a vertical asymmetric channel. The flow is investigated in a wave frame of reference moving with the velocity c away from the fixed frame. The governing equations for the present flow problem are first modeled and then discussed. The analytical solution of the present flow problem is discussed using regular perturbation technique. The graphical results are discussed to see the effects of various physical parameters of interest. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21020     

Mutual influences of a chemical reaction and thermal radiation on a peristaltic pump of synovial nanofluids in a 3D tapered asymmetric channel

This investigation discusses the influences of a chemical reaction and concentration‐dependent viscosity on a magnetohydrodynamics peristaltic pump of synovial nanofluid in a tapered channel. Chemical reaction and Hall current effects are considered in the proposed investigation. The current study is solved for two suggestion models. In Model‐(I), the concentration is considered as a function in viscosity. In Model‐(II), concentration is considered as a function of the shear‐thinning index. The related study is rearranged under the models of low Reynolds number and long wavelength. The system study of highly nonlinear partial differential equations is explained mathematically with the aid of ParametricNDSolve by using Mathematica 11. Both models have been compared numerically and a huge difference is found between them. Results for velocity profile, temperature, and nanoparticle concentration distributions are obtained graphically for similar values of various physical parameters in three‐dimensional forms. Furthermore, a trapping bolus sketch is proposed in the terminus. The results confirm that the AJ patients can be cured by using the magnetic field in the presence of an electrically inducing influence, as a result of the effort of the ions inside the cell, which accelerates the metabolism of fluids. In addition, maximum values of velocity can control the friction between the joints and thus reduce arthritis.     

Effect of thermal radiation on magnetohydrodynamic three‐dimensional motion of a nanofluid past a shrinking surface under the influence of a heat source

An analytical technique known as the homotopy analysis method is used to acquire solutions for magnetohydrodynamic 3‐D motion of a viscous nanofluid over a saturated porous medium with a heat source and thermal radiation. The governing nonlinear partial differential equations are changed to ordinary differential equations employing appropriate transformations. Validation of the present result is done with the help of error analysis for flow and temperature. The influences of pertinent parameters on momentum, energy, and Nusselt number are studied and discussed. The major findings are: the velocity of the nanofluid is affected by the nanoparticle volume fraction and the thickness of the thermal boundary layer becomes thinner and thinner subject to sink, whereas the effect is revered in case of the source.     

Influence of Lewis number on double‐diffusive convection in a square cavity filled with a binary gas

This paper considers double‐diffusive convection in a square cavity filled with a binary gas, due to horizontal opposing temperature and concentration gradients. The effect of Lewis number was considered under the conditions of Prandtl number Pr = 1, buoyancy ratio N = 1, and thermal Rayleigh numbers R_aT = 10⁴ and 10⁵. Numerical solutions are obtained by a Chebyshev collocation technique with high resolution. Depending on the Lewis number, three kinds of flow structures are identified: symmetric steady flow, asymmetric oscillatory flow, and symmetric oscillatory flow. Oscillatory flow occurs in the regime of thermal dominant flow, and leads to a periodic change between stable and unstable states in species stratification due to the thermo‐solutal interaction. © 2000 Scripta Technica, Heat Trans Asian Res, 30(1): 63–75, 2001     

Mixed convective peristaltic flow of Eyring‐Prandtl fluid with chemical reaction and variable electrical conductivity in a tapered asymmetric channel

The influence of inconstant electrical conductivity and chemical reaction on the peristaltic motion of non‐Newtonian Eyring‐Prandtl fluid inside a tapered asymmetric channel is investigated. The system is concerned by a uniform external magnetic field. The heat and mass transfer are considered. The problem is controlled mathematically by a system of nonlinear partial differential equations which describe the velocity, temperature, and nanoparticle concentration of the fluid. By means of long wavelength and low Reynolds numbers, our system is simplified. It is explained by using the multi‐step differential transform method as a semi‐analytical technique. The distributions of velocity, temperature, nanoparticle concentration, as well as pressure gradient and pressure rise are obtained as a function of the physical parameters of the problem. The effects of these parameters on these distributions are deliberated numerically and illustrated graphically through a set of figures. The results indicate that the parameters play a significant role in controlling the velocity, temperature, nanoparticle concentration, pressure gradient, and pressure rise.