Nonlinear thermal radiation on MHD tangential hyperbolic hybrid nanofluid over a stretching wedge with convective boundary condition

In this study, two distinct nanoparticles: aluminum oxide (Al₂O₃) and copper (Cu) are chosen as nanomaterials to examine the effects of nonlinear electrically conducting magnetohydrodynamic radiation on the flow of tangential hyperbolic hybrid nanofluid across a nonlinearly stretched sheet with convective boundary conditions. The equations that regulate fluid flow are represented as partial differential equations. These equations are reduced to their equivalent ordinary differential equations, which are solved using the homotopy analysis approach with the help of similarity variables. The effect of essential physical factors on fluid velocity, temperature, skin friction coefficient, and local Nusselt number is investigated and discussed. Results ascertain that the heat transfer rate of Cu/H₂O nanofluid becomes high when equated to Cu–Al₂O₃/H₂O nanofluid. Furthermore, the temperature distribution enhances with the rise in solid volume fraction while it diminishes with improved magnetic field for both nanofluid and hybrid nanofluid.     

Time-dependent double phase dusty fluid flow over an oscillatory rotating disk

The dispersion of solid particles in a viscous fluid leads to a two-phase flow nature. The present study incorporates the time-dependent three-dimensional dusty fluid flow generated by a periodically oscillatory rotating disk. The disk is stretchable along the radial axis with time-based sinusoidal fluctuations. The governing incompressible flow equations for two-phase equilibrium are normalized in the form of similarity systems consisting of the fluid stage and dust phase. The whole normalized system reduces to the familiar Von Kármán similarity system for the flow configuration of rotating disk by removing the dust phase and periodic oscillations of the disk. The two-phase flow model is then numerically solved by a built-in method namely “pdsolve” in Maple built program. The graphical aspects of the obtained physical parameters on velocity and thermal fields of the dust particle stage are investigated to show how the oscillatory disk contributes to the dusty flow features. The wall shears and thermal rates of the fluid and dust particles are also calculated in limiting case of disk rotation. It is observed that in time-based flow, the oscillatory profiles preserve a phase shifting phenomenon. For centrifugal forces, the particle cloud moves away from the surface along a tangential direction. The thermal field is reduced by the dust particle stages.     

Upshot of radiative rotating Prandtl fluid flow over a slippery surface embedded with variable species diffusivity and multiple convective boundary conditions

Here, modeling and computations are performed to explore the impact of variable molecular diffusivity, nonlinear thermal radiation, convective boundary conditions, momentum slip, and variable molecular diffusivity on Prandtl fluid past a stretching sheet. By using the compatible transformation, the partial differential equations regarding momentum, energy, and concentration are reformed into ordinary differential equations and furthermore, these equations are handled numerically via the shooting method. The behavior of intricate parameters that emerge during numerical simulation is displayed in the form of tables and graphs. These outcomes are supplemented with the information for the heat transfer rate and surface drag coefficients. It is perceived that an uplift in the temperature profile occurs by virtue of augmentation in the temperature convection parameter, and furthermore, mass fraction field escalates owing to an amplification in the chemical reaction coefficient.     

Effect of nonlinear partial slip and thermal radiation on Oldroyd 8‐constant fluid in a channel with convective boundary condition

This investigation deals with the effects of nonlinear slip, nonlinear thermal radiation, and non‐Newtonian flow parameters on heat transfer of an incompressible magnetohydrodynamic steady flow of an Oldroyd 8‐constant fluid through two parallel infinite plates with convective cooling. The Rosseland approximation is adopted to simulate the radiation effects. Heat exchange with the surrounding at the surfaces is assumed to obey Newton's law of cooling. The system of coupled and highly nonlinear ordinary differential equations governing the model is solved numerically using the method of weighted residual. The combined effects of non‐Newtonian flow parameters, velocity slip parameter, magnetic field parameter, Biot numbers, thermal radiation on the fluid velocity, temperature distributions, skin friction, and the Nusselt number are presented graphically and discussed. It is found that the velocity slip has an increasing effect on the fluid velocity and temperature profiles. For larger values of the thermal radiation parameter, the temperature profile and the Nusselt number are noticed to be increased.     

MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation,slip condition,and viscous dissipation

This study presents the problem of MHD stagnation point flow of Casson fluid over a convective stretching sheet considering thermal radiation, slip condition, and viscous dissipation. The partial differential equations with the corresponding boundary conditions that govern the fluid flow are reduced to a system of highly nonlinear ordinary differential equations using scaling group transformations. The fourth-order method along shooting technique is applied to solve this system of boundary value problems numerically. The effects of flow parameters on the velocity, temperature, and concentration profiles are presented via graphs. The impact of the physical parameters on the skin friction coefficient reduced Nusselt numbers and reduced Sherwood numbers are investigated through tables. Comparison of the present findings with the previously published results in the literature shows an excellent agreement. It is also noted that a rise in the Eckert number results in a drop in the temperature of the fluid in the thermal boundary layer region of the fluid flow.     

Entropy generation on MHD flow of a Casson fluid over a curved stretching surface with exponential space-dependent heat source and nonlinear thermal radiation

The present model concentrates on entropy generation on a steady incompressible flow of a Casson liquid past a permeable stretching curve surface through chemical reaction and magnetic field effects. The exponential space-dependent heat source cum heat and mass convective boundary conditions are accounted for. The resulting nonlinear boundary layer model is simplified by the transformation of similarity. Chebyshev spectral technique is involved for obtaining numerical results of the converted system of the mathematical models. Behavior of the determining thermo-physical parameters on the profiles of velocity, temperature, concentration, skin friction, heat, mass transfer rate, rate of entropy generation, and finally the Bejan number are presented. The major point of the present investigation show that the curvature term weakens the mass transfer profile as the fluid temperature reduces all over the diffusion regime. A decrease in heat generation strengthens the species molecular bond, which prevents free Casson particle diffusion. Furthermore, the mass transfer field diminishes in suction and injection flow medium.     

Binary chemical reaction with activation energy in radiative rotating disk flow of Bingham plastic fluid

This article presents flow, heat and mass transfer phenomena in Bingham plastic fluid. The flow channel is considered to be a rotating disk with a slip which is different in span and streamwise directions, and heat transfer is investigated using dissipation term of the fluid. Arrhenius activation energy and binary chemical reaction are the imperative features of the study of mass transfer. Bingham plastic fluid and anisotropic slip are the key factors of the study due to their numerous applications in manufacturing industries. On the other hand, the radiative heat transfer phenomenon is considered which is widely used in nuclear and power generating systems. The partial differential equations that govern the flow, and heat and mass transfer are converted into ordinary differential equations by utilizing von Kármán's similarity transformation for rotating disk flows. The velocity, temperature, and concentration profiles and some important physical quantities are examined against important flow parameters. It is observed that the thermal radiation showed an increasing effect on temperature profile and the activation energy enhanced the mass transfer rate. The radial slip increased the volumetric flow rate and reduced the boundary layer thickness. The tangential slip reduced the volumetric flow rate and increased the boundary layer thickness.     

Boundary layer flow of an Oldroyd‐B fluid with convective boundary conditions

This study is presented for the flow of an Oldroyd‐B fluid subject to convective boundary conditions. The two‐dimensional equations are simplified by using boundary layer approximations. The analytic solutions in the whole spatial domain (0 ≤ η < ∞) are derived by a homotopy analysis method (HAM). Interpretation of various emerging parameters is assigned through graphs for velocity and temperature distributions and tables for surface heat transfer. The present results are compared with the previous studies in limiting cases and results are found in very good agreement. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20381     

Heat Transfer and Fluid Flow over a Single Disk in a Fluid Rotating as a Rigid Body

Laminar heat transfer problem is analyzed for a disk rotating with the angular speed ωin a co-rotating fluid (with the angular speed Ω). The fluid is swirled in accordance with a forced-vortex law, it rotates as a solid body at β= Ω/ω= const. Radial variation of the disk's surface temperature follows a power law. An exact numerical solution of the problem is obtained basing on the self-similar profiles of the local temperature of fluid, its static pressure and velocity components. Numerical computations were done at the Prandtl numbers Pr = 1(?)0.71. It is shown that with increasing βboth radial and tangential components of shear stresses decrease, and to zero value at β= 1. Nusselt number is practically constant at β= 0(?) 0.3 (and even has a point of a maximum in this region); Nu decrease noticeably for larger βvalues.     

FHD flow and heat transfer over a porous rotating disk accounting for Coriolis force along with viscous dissipation and thermal radiation

The prime concern of the current findings includes the effect of viscous dissipation and nonlinear thermal radiation on the study of ferrofluid flow and heat transfer past a porous rotating disk. The time-independent flow of incompressible ferrofluid is modeled for the considered geometry, and via similarity transformations, the given system is converted to a dimensionless system of the nonlinear ordinary differential equations. Here, the findings are explored computationally with help of Maple software. The study exhibits the effect of the involved emerging parameters: the interaction parameter $B$, Prandtl number $Pr$, rotation parameter $R$, radiation parameter $Qr$, Eckert number $Ec$, and these are discussed graphically. Moreover, the numerical values of heat transfer rate and skin frictions are also presented in tabular form. From the perspective of numerical findings, it is perceived that the radial flow is dominant when we increase the rotation of the disk. Furthermore, the magnitude of magnetic-fluid temperature is enhanced with the surge in the magnetic field, viscous dissipation, and thermal radiation mechanism. Finally, the current research can successfully fill a gap in the existing literature.     

Numerical solution for natural convection flow near a vertical porous plate having convective boundary condition with nonlinear thermal radiation

This article presents the theoretical study of the effects of suction/injection and nonlinear thermal radiation on boundary layer flow near a vertical porous plate. The importance of the convective boundary condition as regards the heat transfer rate is taken into account. The coupled nonlinear boundary layer equations are translated into a set of ordinary differential equations via a similarity transformation. The consequences of the active parameters like the suction parameter, injection parameter, convective heat transfer parameter, nonlinear thermal radiation parameters, and Grashof number dictating the flow transport are examined. The numerical result obtained shows that with suction/injection, the heat transfer rate could be increased with nonlinear thermal radiation parameter augment whereas decays with the convective heat transfer parameter and Grashof number. In the presence of suction/injection, the wall shear stress generally increases with nonlinear thermal radiation parameter, convective heat transfer parameter, and Grashof number. The suction has an increasing effect on Nusselt number and shear stress whereas a decreasing effect on Nusselt number and skin friction is seen with injection augment. The nonlinear thermal radiation is an increasing function of the temperature gradient far away from the plate whereas a decreasing function near the porous plate.     

Influence of nonlinear thermal radiation on mixed convective hybrid nanofluid flow about a rotating sphere

The present study investigates the mixed convective hybrid nanofluid flow over a rotating sphere under the impact of nonlinear thermal radiation. A model is built to examine the heat transport performance of ferrimagnetic magnetite and copper nanoparticles over a rotating sphere. Nonsimilar transformations are used to nondimensionalize the coupled nonlinear governing equations and the flow model's boundary conditions. Furthermore, the nondimensional governing equations were solved using implicit finite difference approximation and the quasilinearization technique. The impacts of the flow regime on many controlling parameters are then thoroughly addressed. Temperature patterns improve when nonlinear thermal radiation and hybrid nanofluid values increase. The fluid velocity and skin friction coefficient increase in the streamwise direction while decreasing in the rotating direction. The separation of the boundary layer is delayed as the sphere's rotation weakens. The stationary sphere has a larger boundary layer separation than the revolving sphere. The velocity distribution improves with increasing rotation parameter values while decreasing with increasing combined convection parameter values in the rotating direction. An increase in the temperature ratio parameter makes the fluid get hotter, and the Nusselt number goes down simultaneously. Nusselt number and skin friction coefficient in the rotation direction increase, while skin friction coefficient in streamwise direction reduces for increasing values of hybrid nanofluid. The velocity of the fluid enhances in the stream-wise direction while reducing in the rotational direction with the increasing values of the combined convection parameter.     

Three‐dimensional boundary layer flow over a rotating disk with power‐law stretching in a nanofluid containing gyrotactic microorganisms

The nanofluid model containing microorganisms over a rotating disk with power‐law stretching is constructed in this paper. The combined effects of nanoparticles and microorganisms in nanofluid are investigated by solving the governing equations numerically. The numerical solutions of the skin friction coefficient and local Nusselt number are in agreement with the corresponding previously published results. The quantities of physical interest are graphically presented and discussed in detail. It is found that the power‐law stretching index has produced profound influence on the flow as well as the heat and mass transfer.     

Effect of SWCNTs and MWCNTs Maxwell MHD nanofluid flow between two stretchable rotating disks under convective boundary conditions

The aim of the current analysis is to investigate heat and mass transfer characteristics of single and multi‐walled water‐based carbon nanotubes Maxwell nanofluid flow between continuously rotating stretchable disks under the sway of chemical reaction and radiation. Boundary conditions of the convective type of temperature are employed at both lower and upper rotating disks in the preparation. Similarity variables are employed to transform the governing partial differential equations into the nonlinear ordinary differential equations. The computational finite element method is applied to solve this nonlinear system of equations along with boundary conditions. The sway of different admissible parameters on the profiles of concentration, temperature, and velocity are inspected and revealed through graphs. Furthermore, the numerical solutions for rates of temperature, concentration, and rates of velocity are depicted in tabular form. It is revealed that temperature sketches deteriorate with augmented values of Deborah number at both upper and lower disks of single‐walled carbon nanotubes and multi‐walled carbon nanotubes with water‐based Maxwell nanofluids.     

Free convective MHD micropolar fluid flow with thermal radiation and radiation absorption: A numerical study

An analysis is carried out for the free convective flow of an electrically conducting micropolar fluid through permeable stretching sheet in the presence of porous medium. Inclusion of thermal radiation to the energy equation enhances the thermal properties of polar fluid. In addition to that the radiation absorption parameter occurs due to the interaction of solutal concentration difference also considered in the heat transfer equation. Suitable similar transformation is used to convert the governing partial differential equations to ordinary differential equations. Furthermore, though analytical solutions of these complex nonlinear coupled equations are more complicated therefore, numerical solution such as Runge‐Kutta fourth order method associated with shooting technique is adopted. Behavior of characterizing parameters for the flow phenomena are presented via graphs and computed values of physical quantities of interest are obtained and shown in tabular form. Present result validates with that of earlier results in particular case which confirms the existence of present solution methodology. However, the main findings of contributing parameters are laid down as; angular velocity profile contributes a dual character from the point of contact at the middle of the channel. Fluid temperature is affected by the inclusion of absorption coefficient.     

Double-diffusive natural convective stream due to moving vertical plate with nonlinear thermal radiation and Newton's boundary constraint

This article investigates the heat and mass transmission of the double-diffusive convective stream over a moving vertical plate with nonlinear thermal radiation and newton boundary conditions. The governing partial differential equations of the stream, heat, and concentration profiles were transformed into a system of nonlinear ordinary differential equation by utilizing resemblance transformation. This system was then resolved numerically by applying the fourth order Runge-Kutta method with most efficient shooting technique. The effect of convection, buoyancy ratio, nonlinear thermal radiation, Prandtl number, Rayleigh number and Schmidt number are graphically scrutinized. The numerical results are obtained for velocity, temperature, and concentration profiles. It is found that when the velocity profile increases, heat and mass transfer rate decreases with an increase in the parametric value of buoyancy ratio parameter. It is found that the effect of nonlinear thermal radiation stabilizes the thermal boundary layer growth. The skin friction coefficient decreases with an increase in Prandtl number. However, the Nusselt number increases with an increase in the local convective heat transfer rate. The present results are very much promising, and further, there is a very good agreement of results when compared with earlier published results for some limiting conditions.     

Free convective magnetohydrodynamic flow over an exponentially stretching sheet with radiation

The study explores a steady two‐dimensional magnetohydrodynamic boundary layer flow phenomenon of an incompressible viscous fluid with buoyancy‐driven force over an exponentially stretching sheet. In addition to that, the interaction of thermal radiation in conjunction with dissipative effects, that is, viscous and Joule dissipation is also considered, which is justified due to the presence of magnetic field. The boundary layer equations governed by the flow phenomena are transformed into ordinary differential equations by a suitable choice of similarity transformation. Numerical methods, such as fourth‐order Runge‐Kutta scheme in association with the shooting technique is employed to get an approximate solution of these transformed equations. The numerical computations for the wall shear stress and the heat transfer coefficients are obtained, analyzed, and then discussed. Furthermore, the major findings are pick‐in velocity distribution near the plate is marked with an increase in buoyancy parameter and the rate of heat transfer profile is linear in its boundary layer for low Prandtl number.     

Effects of nonlinear Boussinesq approximation and double dispersion on a micropolar fluid flow under convective thermal condition

This article investigates the effect of double dispersion on the natural convective flow of a micropolar fluid along an inclined plate in the presence of the convective thermal condition. In addition, the nonlinear convection is considered to analyze the heat and mass transfer phenomena of thermal systems, which are performed at moderate‐ and high‐level temperatures. A combination of local nonsimilarity and successive linearization techniques is used to evaluate the associated complicated nondimensional governing equations. This study discusses the impact of relevant factors on the fluid characteristics through graphs. The influence of nonlinear convection parameters on the heat and mass transfer rates seems to be more in Darcy porous media compared with that in non‐Darcy porous media.