Values Of Grashof Number Research Articles

Analysis of thermal transport and wall stresses for MHD peristaltic motion of Reiner‐Philippoff fluid with viscous dissipation and mixed convection effects

AbstractThe present study examines the thermal characteristics and stresses at the boundary for peristaltic motion of Reiner‐Philippoff fluid through a symmetric channel. The Reiner‐Philippoff (R‐P) fluid model is widely recognized for its ability to provide a comprehensive representation of the unique properties exhibited by non‐Newtonian fluids. One notable aspect that initiates this model is the nonlinear relationship between velocity gradient and shear stress. Moreover, this model captures the implicit connection between deformation rate and stress. Additionally, the R‐P fluid model exhibits distinct characteristics, acting as a dilatant fluid for , exhibiting pseudoplastic behavior for , and behaving as a Newtonian fluid when . Governing equations are mathematically modeled under the consideration of mixed convection, viscous dissipation, magnetic field, and Joule heating effects. Long wavelength and small Reynolds number approximations are used to simplify the system. To compute the numerical solution of the simplified nonlinear system, BVP4c technique is employed via MATLAB. The influences of key parameters on Reiner‐Philippoff fluid flow are physically visualized through graphs. A detailed analysis of heat transfer for dilatant, pseudoplastic, and Newtonian fluids is also provided. Additionally, numerical assessments of heat transfer and stresses at the wall are presented via tables. Outcomes reveal that the temperature profile decreases due to R‐P fluid parameter and Bingham number. The findings for the pseudoplastic case indicate that both the enhanced Grashof and Hartmann numbers lead to an increase in the temperature profile. Tabular results indicate that rate of thermal transfer is improved by developing values of Grashof and Brinkman numbers, while stresses at the wall exhibit the opposite behavior. Additionally, the wall stresses decrease with greater values of R‐P fluid parameter and the Bingham number. Furthermore, dilatant fluid is more effective for improving thermal transfer and reducing stresses at the wall compared to Newtonian and pseudoplastic fluids.

Analysis of unsteady heat and mass transfer in rotating MHD convection flow over a porous vertical plate

The aim of this research paper is to investigate the rotational flow of an unsteady magnetohydrodynamic heat and mass transfer flow due to convection over a vertical porous semi-infinite plate. The plate undergoes continuous circular motion, maintaining a constant velocity. To achieve this, we worked on both numerical methods and analytical techniques, particularly utilizing perturbation methods to solve the governing partial differential equations. Consequently, we derive an expression for the Nusselt and Sherwood numbers. We delve into the analysis of the velocity profile, temperature distribution, and concentration variation, exploring their behaviour under different physical parameters, including the magnetic field parameter, Grashof num-ber, Soret number and Schmidt number, as well as the Prandtl number. Our findings reveal that the velocity increases with rising values of Grashof, modified Grashof and Soret numbers, whereas it decreases with declining values of the magnetic field parameter, Prandtl number and Schmidt number. Additionally, as rotation gradually intensifies, the fluid velocity closely follows the boundary and becomes negligible as it moves away from it. To facilitate a comprehensive examination of the fluid flow and heat and mass transfer characteristics, we employ graphical representations. Furthermore, this paper offers an in-depth discussion of the underlying physical aspects and their implications.

Effect of Suction/Injection on Unsteady MHD Natural Convection Flow of Heat Mass Transfer in Porous Channel in the Presence of Soret Term

This research paper explores the effect of suction/injection on unsteady MHD natural convection flow of heat mass transfer in porous channel in the presence of Soret term. The governing partial differential equations are converted to non- dimensional forms and solved numerically by using unconditionally stable and convergent implicit finite difference method. A parametric study illustrating the influence of various physical parameters is performed. It is reported that the velocity profile increases as Soret term, Grashof number, Solutal Grashof number and Porous parameters values increase, while Magnetic field parameter decreases the velocity profile. The temperature profile rises by the influence in increasing values of Variable Thermal Conductivity and decreases by increasing values of Prandtl number and Radiation parameters. While concentration profile increase by the increasing values of Soret term and Chemical reaction. The dependence of the skin friction coefficient, rate of heat transfer and mass transfer on these parameter has been discussed.

A computation analysis with heat and mass transfer for micropolar nanofluid in ciliated microchannel: With application in the ductus efferentes

Inherited heat enhancement capabilities and their significance in the field of medical sciences and industry make nanofluids the focus of research nowadays. Furthermore, due to the remarkable advancements in bionanotechnology and its significance in biomedical fields such as drug delivery systems, cancer tumor therapy, bioimaging, and many others, it has emerged as a key research area. Contribution of cilia for the flow in ductus efferentes of human male reproductive tract is elaborated. A novel mathematical scheme is presented for the heat and mass transfer of MHD micropolar nanofluid transport in an asymmetric channel lined with cilia. The pertinent equations of nanofluid transport are exposed to lubrication approximation theory and solution for the physical problem is examined with efficient bvp4c technique in MATLAB. Fluid rheology is explored with the variations of different transport parameters like Hartmann number, Grashof number, Brownian motion, buoyancy, thermophoresis and Darcy number. It is reported that nanofluid transport is affected with rise in the Lorentz force and show reverse behavior with rising permeability. The temperature of the nanofluid in ciliated microchannel is raised with enhanced value of Hartmann number, Grashof number, Prandtl number, and Darcy number while diffusion phenomenon of nanofluid is slowed down with these parameters. Spinning motion of the nanofluid is enhanced with Grashof number and slow down with nanoparticle Grashof number and different behavior is recorded for Darcy and viscosity parameters in different flow regime. Reported investigation presents crucial findings for ciliary transport of micropolar nanofluid and tackled with appropriate selection of micropolar parameter, Brownian motion parameter, thermophoresis and Grashof number. Moreover, this investigation will be handful for cilia-based actuators which work as micro-mixers in controlling the flow in minute bio-sensors and may prove their worth in micro-pumps employed in various drug-delivery systems.

Effect of Thermal Radiation on Fractional MHD Casson Flow with the Help of Fractional Operator

This study examines the effects of Newtonian heating along with heat generation, and thermal radiation on magnetohydrodynamic Casson fluid over a vertical plate. At the boundary, the Newtonian heating phenomena has been employed. The problem is split into two sections for this reason: momentum equation and energy equations. To transform the equations of the given model into dimensionless equations, some particular dimensionless parameters are defined. In this article, generalized Fourier’s law and the recently proposed Caputo Fabrizio fractional operator are applied. The corresponding results of non-dimensional velocity and heat equations can be identified through the application of Laplace transform. Moreover, Tzou’s algorithm as well as Stehfest’s algorithm is implemented to recognize the inverted Laplace transform of heat and momentum equations. Finally, a graphical sketch is created using Mathcad 15 software to demonstrate the results of numerous physical characteristics. It has been reported that the heat and velocity drop with rising Prandtl number values, whereas the fluid’s velocity has been seen to rise with increasing Grashof number values. Additionally, current research has shown that flow velocity and temperature increase with rising values of a fractional parameter.

Effects of cooler shape and position on solidification of phase change material in a cavity

BackgroundFor balancing the imbalance between the energy supply and demand, phase-change materials (PCMs) provide an efficient means in terms of thermal energy storage and release. The performance of the energy storage is primarily dependent on the melting as well as the solidification process of the storage medium. Faster charging or discharging of the thermal energy is a primary concern for any thermal energy storage unit. On this background, the present study explores the novel approach for enhancing the solidification process of PCM considering the effects of cooler shape (namely semi-circular, triangular, and rectangular) and their position (namely top, side, and bottom) in a molten PCM-filled enclosure. The middle portion of the cooler wall is curved; whereas the remaining cooler wall is straight maintaining the same cooler wall length. MethodsTo analyze the solidification process, the involved transport equations are solved numerically following a finite volume-based computational approach using Ansys Fluent solver in conjunction with the appropriate boundary conditions. The computational model is generated for all the geometry comprising different shapes, as well as positions of the cooler wall. The third-order upwind scheme (QUICK) technique is utilized to discretize the momentum and energy equations. This scheme is well capable to accurately capture the gradients in the temperature and flow domains. Furthermore, the semi-implicit pressure-linked equation (SIMPLE) technique is utilised to address the pressure-velocity coupling. The resolved data are then saved as selective variables (U, V, and θ), which undergo post-processing to produce a local thermo-fluid flow field and extract average data. Significant findingsThe shape, as well as the position of a cooler, dictates the solidification process in an energy storage system. Thermal energy storage with a triangular-shaped cold wall positioned at the top could be opted as an appropriate design approach of an efficient energy storage system compared to a semi-circular or rectangular-shaped cooler model. The shortest solidification time of PCM occurs when the cooler wall is positioned at the top. The top position of the cooler having a triangular shape with higher Grashof number (Gr) values leads to a faster solidification process. Some ideas for possible future research areas in this field are provided after a comprehensive examination.

Flow and Heat Transfer Characteristics in the Entry and Stabilized Flow Regions of a Circular Channel Rotating About a Parallel Axis

Abstract Cooling of heavy-duty electrical machines such as generators and motors is crucial for the smooth operations without thermal runaway. A commonly employed technique for the cooling of rotors in these machines is to place channels at different radial locations for the continuous passage of coolant. These channels are therefore rotating about a parallel axis, and the rotation-induced forces alter the flow and thermal behavior of the coolant compared to stationary channels. The present study reports a detailed numerical investigation on a long circular channel rotating about a parallel axis. The objective is to analyze the flow, heat transfer, and rotation-induced forces (Coriolis and centrifugal forces) in the entry region as well as in the region where flow is stable (the term ‘stable’ is used rather than ‘developed’ due to the presence of secondary flows in this region). The rotating channel was subjected to constant wall heat flux and constant wall temperature conditions at different Rotation numbers of 0, 0.15, 0.4, and 0.6. The Coriolis force is observed to be strong enough in the entry region to influence the flow. In the “stable flow” region, the centrifugal force becomes more dominant and forms counter-rotating secondary vortex pair, which causes circumferential variation in the Nusselt number. The flow and heat transfer characteristics for constant wall heat flux and wall temperature boundaries are the same for rotation conditions with similar values of rotational Grashof number. A correlation is presented for the circumferential variation of the Nusselt number in the stable flow region.

Energy Budget Characterisation of the Optimal Disturbance in Stratified Shear Flow

Stratified Taylor–Couette flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy flux (BP), and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of the amplification factor resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Grashof number.

Modeling of Opposing Mixed Convection of Air in Partially Cooled Vertical Channels

in this paper opposing laminar mixed convection in partially cooled vertical channel is investigated numerically. Temperature profiles, Nusselt number and velocity profiles at various axial locations in the cooled part of opposing buoyancy flow are presented. Streamlines and isotherms have been also plotted for different values of Grashof number, Gr. Conservation equations of continuity, momentum and energy were solved simultaneously using Finite volume method. The effect of the cooled section on the flow pattern and heat transfer performance is investigated for given Grashof numbers. The influence of axial diffusion and it's relevant to flow reversal at the entrance region of the channel was taken into account in the governing equations and particular attention is given to the ratio │Gr / Re2│. The effect of opposing bouncy forces on the hydrodynamic and thermal fields was examined for air with Re = 500, 105 ≤ │Gr ≤ │ 3*105. Reversal flow was observed near the channel wall for this opposing buoyancy flow. It was noticed that the friction factor, f•ReL ,for the ratio │Gr / Re2 │≥ 1.2 was unstable over the cooled length, becomes negative and then increases to an asymptotic value of 16 over the insulated section. The presented numerical results revealed some interesting features which may be summarized as: (i) Globally Nusselt number decreases and reaches asymptotic value at the end of the cooling section. However for Gr = -3*105 Nusselt decreases and reach a minimum value approximately equal to 3.12. (ii) For Gr up to │3ₓ105│ the Boussinesq approximation still predicts reasonably the heat transfer rate.

Microbic flow analysis of nano fluid with chemical reaction in microchannel with flexural walls under the effects of thermophoretic diffusion

The current investigation examines the peristaltic flow, in curved conduit, having complaint boundaries for nanofluid. The effects of curvature are taken into account when developing the governing equations for the nano fluid model for curved channels. Nonlinear & coupled differential equations are then simplified by incorporating the long wavelength assumption along with smaller Reynolds number. The homotopy perturbation approach is used to analytically solve the reduced coupled differential equations. The entropy generation can be estimated through examining the contributions of heat and fluid viscosities. The results of velocity, temperature, concentration, entropy number, and stream functions have been plotted graphically in order to discuss the physical attributes of the essential quantities. Increase in fluid velocity within the curved conduit is noticed for higher values of thermophoresis parameter and Brownian motion parameter further entropy generation number is boosted by increasing values of Grashof number.

ACTIVATION ENERGY EFFECT ON MHD CONVECTIVE MAXWELL NANOFLUID FLOW WITH CATTANEO-CHRISTOVE HEAT FLUX OVER A POROUS STRETCHING SHEET

The current article investigates the heat and mass transfer of convective magnetohydrodynamics (MHD) Maxwell nanofluid flow over a porous stretching sheet with Cattaneo-Christove heat flux. The influences of heat sources, radiation, and viscous dissipation are investigated. Also, the activation energy with binary chemical reaction and suction/injection are considered into the account. The dimensional governing equations are transmitted into nondimensional form by similarity transformations. Further, the obtained mathematical model is solved numerically in MATLAB. The effects of physical parameters pertaining in flow regime are investigated through figures and tables. It is noticed that the fluid velocity drops with an increase in the magnetic field, porosity, and suction parameter. The increased Brownian motion, heat generation, and radiation improves the temperature field, while it declines with an upsurge in values of thermal relaxation time. An increasing thermophoresis and activation energy lead to an increase in the concentration, whereas the opposite trend is seen for increasing chemical reaction. The Nussult number enhances due to the larger values of thermal Grashof number, solutal Grashof number, and Biot number, whereas it declines with the escalating values of Brownian motion, thermophoresis, and Eckert number. The comparison of the present results is carried out with the published results and noted a good agreement. These findings are useful for the space technology, metal thinning, power generation, water purification in the soil, polymer extrusion, and the thermal control of heat exchangers in upcoming technologies.

Finite element analysis of MHD naturally convective flow past an exponentially accelerated plate with viscous dissipation

The MHD finite element analysis naturally convective flow across an exponentially accelerating plate with viscous dissipation is investigated numerically. In this process dimensional partial differential equations are changed to dimensional less form. The Galerkin finite element method is emerged to solve non-dimensional partial differential equations. Obtained results are effectively depicted through the utilization of graphs, allowing for a comprehensive understanding of the impact that different physical parameters on primary velocity, transverse velocity, temperature, and concentration profiles. The study effectively differentiated between the present and prior findings, ultimately demonstrating a strong consensus of excellent agreement between the results. The key findings of this study are: The primary velocity increases on growing the values of Thermal Grashof number, Solutal Grashof number, Eckert number, and Dufour number and decreases on climb up the values of Magnetic parameter, Prandtl number, Schmidt number, and Hall parameter. The secondary velocity increases on raising the values of Thermal Grashof number and Solutal Grashof number and diminishes on enhancing the value of Hall parameter. The temperature increases on increasing the values Eckert number and Dufour number and decreases on improving the value of Prandtl number. The concentration decreases on increasing the value of Schmidt number.

Entropy generation analysis of non-miscible couple stress and Newtonian fluid in an inclined porous channel with variable flow properties: HAM Analysis

The aim of this study is to investigate the entropy production characteristics of two non-miscible fluids in an inclined porous channel with temperature-dependent thermal conductivity and viscosity. The porous region of the channel is divided in two regions. In region-1 and region-2, the Couple stress and Newtonian fluid take place due to constant pressure gradient, respectively, under the influence of a uniform magnetic field. Here, the Darcy–Brinkman model is used for the flow of immiscible fluid through the porous media. In this work, we used a semi-analytical method named as homotopy analysis method (HAM) to solve the coupled nonlinear ordinary differential equations. The goal of the considered problem is to examine the consequences of a variety of thermophysical parameters, including Hartmann number, varying viscosity parameter, varying thermal conductivity parameters, and Grashof number on the characteristics of entropy generation, Bejan number distribution, thermal behavior and flow characteristics of non-miscible couple stress and Newtonian fluid passing through a porous channel. The novel aspect of this study is the formation of entropy and Bejan number as a result of non-miscible Newtonian and couple stress fluids with varying thermal conductivity and viscosity in porous media. In terms of rheological investigation, a semi-analytical simulation for changeable thermal and flow properties in an immiscible Newtonian and couple stress fluid via an inclined porous channel is a brand-new concept, and the behaviors of such flows have not been examined yet. From this study, it is concluded that on raising the variable thermal conductivity, Hartmann number and the permeability of the porous medium, the flow velocity, thermal characteristics and entropy generation number decrease. The authors also come to the significant conclusion that non-miscible Newtonian and couple stress fluids have larger entropy production numbers, flow velocities, and temperature profiles for higher values of Grashof number, variable viscosity parameter, and couple stress parameter. The findings of this work have also been graphically validated through the previously established work. The results of the present analysis can be used in petroleum industry, lubrication theory, etc.

Computation of inclined magnetic field, thermophoresis and Brownian motion effects on mixed convective electroconductive nanofluid flow in a rectangular porous enclosure with adiabatic walls and hot slits

This analysis theoretically investigates the transport phenomena of mixed convection flows in an enclosure of rectangular geometry saturated with a permeable medium filled with an electrically conducting nanofluid. An inclined magnetic field is taken into consideration. Buongiorno’s model is utilized to characterize the nanoliquid. The enclosure has adiabatic walls and hot slits. A uniform cold temperature is maintained at the enclosure’s lower and upper walls. The enclosure’s vertical walls are thermally insulated with hot slits at the center of the walls. This kind of analysis on mixed convective, electrically conducting nanofluid flows in enclosures finds applications in smart nanomaterial processing systems and hybrid electromagnetic nanoliquid fuel cells. The Marker-And-Cell (MAC) method is utilized to solve the transformed nondimension system of governing equations subject to the fitted boundary conditions. The effects of key physical parameters on streamlines, isotherms, iso-concentration contour plots and the heat transmission rate are examined. The simulations demonstrate that the Richardson number has a predominant impact on the thermo-solutal features of nanofluid flow in the rectangular enclosure. Variations in magnetic field and buoyancy ratio parameters exert a notable influence on the iso-concentrations and isotherms. An increase in the Darcy number values exhibits a tendency to magnify the local heat transfer rate. Higher Grashof number values reduce the local Nusselt number profiles. The effect of porous parameter is significant in the streamlines, isotherms and iso-concentrations. Thus, the porous medium can significantly control the transport phenomena in the enclosure. The concentration, temperature and velocity contours are strongly modified by the variations in the Grashof number.

Entropy generation on MHD pulsatile flow of third grade hybrid nanofluid in a vertical porous channel with nonuniform heat source/sink, variable viscosity, thermal conductivity, and Joule heating: A numerical study

This investigation inspects the entropy generation of magnetohydrodynamic pulsating third grade hybrid nanofluid flow between two vertical porous walls under the influence of nonuniform heat generation/absorption. Variable viscosity, variable thermal conductivity, Joule heating, thermal radiation, and slip effects are considered. Blood is taken as base fluid (third grade), iron oxide or magnetite and titanium dioxide are as nanoparticles. The nondimensional quantities are utilized to attain the dimensionless flow governing nonlinear partial differential equations (PDEs) and then the perturbation technique is employed to obtain the set of nonlinear ordinary differential equations (ODEs) from PDEs. The Runge-Kutta 4th order technique along with shooting procedure is utilized to get solutions for the set of ODEs. The variations in different physical quantities on velocity, temperature, heat transfer rate, entropy generation, and Bejan number are depicted via graphs. The velocity enhances for the higher values of Grashof number. Accelerating space and temperature-dependent heat source/sink coefficient accelerates the temperature. The presence of variable viscosity and thermal conductivity intensifies the temperature when compared to their absence. A rise in radiation parameter accelerates the entropy and Bejan number. An increment in Eckert number and radiation parameter increases the heat transfer rate. Intensifying Hartmann number reduces the skin friction.

Joint Effects of Heat Source and Magnetic Field on Unsteady Chemically Reacting Fluid Flow Towards A Vertically Inclined Plate in Addition of Cu-Nanoparticles

The primary goal of this evaluation task is to research the mathematical analysis for unstable, free convective incompressible viscous heat also mass transfer fluid movement across an inclined a plate that is vertically positioned in the occurrence of copper nanoparticles, Magnetism, thermal generator & chemical reaction in porous media. For this investigation, we assumed the effects of Cu-nanoparticles and Angle of inclination effects in the governing equations. Additionally, the effects of fluctuating temperature & concentration are studied. We established a set of basic equations for this fluid flow and translated nonlinear partial difference equations into linear incomplete comparisons, which were then answered using the implicit limited alteration technique. The impacts of several engineering fluid variables on flow variables such as velocity, temperature, & concentration profiles were explored in this research study via the use of graphs to show the findings. Along with the other findings, the mathematical standards of skin friction, heat transmission rate, & mass transmission constants are calculated and reported in tabular form. Finally, and perhaps most importantly, the mathematical consequences of the code validation programme are related to previously publish analytical results. In the instance of pure and nanofluids, the velocity profiles are shown to increase with rising values of the Heat transfer using the Grashof number, the mass movement Grashof number, the parameter for permeability, and the passage of time Increases in magnetic field component, the Schmidt number and the Prandtl number, the parameter for the heat source, the component of the chemical reaction, and the degree of inclination all result in a drop in the velocity profiles. With respect to temperature profiles, they have been on the rise with passing time, in contrast to the Prandtl number and the heat source parameter, for which the opposite trend has been seen. We discovered that the temperature and velocity profiles are both steeper for nanofluids than for pure fluids when the parameters are increased. The concentration profiles rise with increasing times, but the opposite is true for the Schmidt number. Moreover, increasing Chemical reaction parameter values result in decreasing profiles of concentrations.

Mechanism of double diffusive convection due to magnetized Williamson nanofluid flow in tapered asymmetric channel under the influence of peristaltic propulsion and radiative heat transfer

PurposeThe purpose of this study, thermal radiation and viscous dissipation impacts on double diffusive convection on peristaltic transport of Williamson nanofluid due to induced magnetic field in a tapered channel is examined. The study of propulsion system is on the rise in aerospace research. In spacecraft technology, the propulsion system uses high-temperature heat transmission governed through thermal radiation process. This study will help in assessment of chyme movement in the gastrointestinal tract and also in regulating the intensity of magnetic field of the blood flow during surgery.Design/methodology/approachThe brief mathematical modelling, along with induced magnetic field, of Williamson nanofluid is given. The governing equations are reduced to dimensionless form by using appropriate transformations. Numerical technique is manipulated to solve the highly nonlinear differential equations. The roll of different variables is graphically analyzed in terms of concentration, temperature, volume fraction of nanoparticles, axial-induced magnetic field, magnetic force function, stream functions, pressure rise and pressure gradient.FindingsThe key finding from the analysis above can be summed up as follows: the temperature profile decreases and concentration profile increases due to the rising impact of thermal radiation. Brownian motion parameter has a reducing influence on nanoparticle concentration due to massive transfer of nanoparticles from a hot zone to a cool region, which causes a decrease in concentration profile· The pressure rise enhances due to rising values of thermophoresis and thermal Grashof number in retrograde pumping, free pumping and copumping region.Originality/valueTo the best of the authors’ knowledge, a study that integrates double-diffusion convection with thermal radiation, viscous dissipation and induced magnetic field on peristaltic flow of Williamson nanofluid with a channel that is asymmetric has not been carried out so far.

Computational analysis and biomechanical study of Oldroyd-B fluid with homogeneous and heterogeneous reactions through a vertical non-uniform channel

Abstract Homogeneous and heterogeneous reactions play a decisive role in biological procedures such as burning, polymer creation, ceramic construction, distillation, and catalysis. The magnetic properties of hemoglobin molecules are organic. Magnetic resonance imaging (MRI) and electronic components with an electromagnetic field are now readily available, allowing for the explanation of fundamental biological processes. These ideas form the foundation of an ongoing study that attempts to look into the impact of both homogeneous and heterogeneous reactivity on the peristaltic transport of magnetohydrodynamics Oldroyd-B fluid. When convective and partial sliding conditions are present, the configuration changes to a non-uniform vertical channel. The fundamental partial differential equations are resolved utilizing the Homotopy Analysis Method. Entropy optimization has been carried out. The primary limits entering the problem are investigated, and then a graph is used to show the influences of temperature, velocity, skin fraction, Nusselt number, and pressure increase against mean circulation, trapping phenomena, homogeneous reactions, and heterogeneous way to respond. When magnetic parameter rises, the velocity of Oldroyd-B fluid and Bejan number decrease, while temperature, entropy generation, and pressure gradient increase. The tables show that the skin friction coefficient rises for accumulative values of the Grashof number and magnetic parameter, while the skin friction coefficient drops for rising values of the velocity slip parameter and Reynolds number. The Nusselt number increases for large values of Eckert, Grashof numbers, and magnetic parameters.

Numerical Study in Effect of Thermal Slip on Two Fluid Flow in a Vertical Channel

The present study investigates the effect of thermal slip on an immiscible flow of micropolar and viscous fluids in a vertical channel. The left boundary is subjected to thermal slip with appropriate boundary and interface conditions, resulting in a linked system of nonlinear partial differential equations. The ND Solve technique in Mathematica software is used to implement the Runge-Kutta method of the sixth order. The velocity, temperature, and concentration equations are then calculated. The mass, heat, and velocity transmission rates at the boundaries were recorded for all the variations in the governing parameters. In addition, the impact of relevant parameters on various physical properties of micropolar and viscous fluids is analyzed through graphical means. The results are then discussed in detail. Thermal slip, Grashof number, molecular number, magnetic parameter, and Reynolds number are crucial factors that significantly affect heat and mass transfer in fluid flow. The effect of the increased thermal slip is noted to result in a decrease in both the velocity profile and temperature. It was also observed that higher values of Grashof and molecular Grashof numbers led to increased velocity and angular velocity.

Analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical surface

This work considers the analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical sheet. The principal objective of this study is to make an effort to improve the heat transfer ratio, which is the core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using the similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Homotopy Asymptotic Method, and graphical interpretations are given to highlight the influence of different contributing parameters such as unsteady parameter, nanoparticle volume fraction, mixed convection parameter, Grashof number and Prandtl number on the velocity profile and temperature distribution. It is noted that increasing the values of nanoparticle volume fraction and stretching parameter slow down the velocity profile. Also, increasing the values of mixed convection parameter and Grashof number (Gr) enhance the velocity profile, and increasing values of Prandtl number and Graship number reduce the temperature distribution. The Nusselt number and the skin friction are examined through graphical representation. It is noted that increasing the value of mixed convection parameter decreases the skin friction of the fluids, and the Nusselt number decreases with the growing value of Prandtl number.