Nanofluid flow and MHD mixed convection inside a vertical annulus with moving walls and transpiration considering the effect of Brownian motion and shape factor

In the present study, the exact solution of a nanofluid flow and mixed convection within a vertical cylindrical annulus with suction/injection, which is adjacent to the radial magnetic field, is presented with regard to the motion of cylinders’ walls. The impact of Brownian motion and shape factor on the thermal state of CuO–water nanofluid is also considered. The influence of such parameters as Hartmann number, mixed convection parameter, suction/injection, volume fraction of nanoparticles and motion of cylinders’ walls on flow and heat transfer is probed. The results show that the shape of the nanoparticles could change the thermal behavior of the nanofluid and when the nanoparticles are used in the shape of a platelet, the highest Nusselt number is obtained (about 2.5% increasement of Nusselt number on internal cylinders’ wall comparison to spherical shape). The results shed light on the fact that if, for example, the external cylinder is stationary and the internal cylinder moves in the direction of z axis, the maximum and minimum heat transfer take place on the walls of internal and external cylinders, respectively (for η?=?300, about 15% increasement of Nusselt number on internal cylinders’ wall). Furthermore, the enhancement of radius ratio between two cylinders increases the rate of heat transfer and decreases the shear stress on the internal cylinder’s wall.

     

Unsteady double-diffusive natural convection in a two-sided lid-driven inclined porous enclosure with sinusoidal boundary conditions with Soret and Dufour effects

Unsteady double-diffusive natural convection in an inclined porous enclosure with sinusoidal boundary conditions and Soret and Dufour parameters is studied. The unique aspects of the set-up are that the left vertical and bottom walls are heated and concentrated non-uniformly and uniformly, respectively, while the right vertical wall is well insulated and the top wall is maintained at a constant concentration and cold temperature. A staggered grid finite-difference method is used to solve the system of partial differential equations that model heat and mass transfer inside the enclosure. We demonstrate the effects of the Soret and Dufour parameters and the inclination angle on the unsteady double-diffusive natural convection in the inclined porous enclosure. With all the numerical studies, the least square curve fitting (exponential non-linear curve fitting) of average Nusselt number and average Sherwood number with respect to different Soret and Dufour numbers at the left vertical wall which is non-uniformly heated and concentrated is examined here. Comparison with previously published results shows an excellent agreement.     

Numerical treatment of Casson nanofluid Bioconvectional flow with heat transfer due to stretching cylinder/plate: Variable physical properties

PurposeThe purpose of the current framework is to scrutinize the two-dimensional flow and heat transfer of Casson nanofluid over cylinder/plate along with impacts of thermophoresis and Brownian motion effects. Also, the effects of exponential thermal sink/source, bioconvection, and motile microorganisms are taken.Methodology/ApproachThe resulting non-linear equations (PDEs) are reformed into nonlinear ODEs by using appropriate similarity variables. The resultant non-linear (ODEs) were numerically evaluated by the use of the Bvp4c package in the mathematical solver MATLAB.FindingsThe numerical and graphical illustration regarding outcomes represents the performance of flow-involved physical parameters on velocity, temperature, concentration, and microorganism profiles. Additionally, the skin friction coefficient, local Nusselt number, local Sherwood number, and local microorganism density number are computed numerically for the current presented system. We noted that the velocity profile diminishes for the rising estimations of magnetic and mixed convection parameters. The Prandtl number corresponds with the declining performance of the temperature profile observed. The enhancement in the values of the Solutal Biot number and Brownian motion parameter increased in the concentration profile.OriginalityIn specific, this framework focuses on the rising heat transfer of Casson nanofluid with bioconvection by using a shooting mathematical model. The novel approach of the presented study is the use of motile microorganisms with exponential thermal sink/source in a Casson nano-fluid through a cylinder/plate. A presented study performed first time in the author’s opinion. Understanding the flow characteristics and behaviors of these nanofluids is crucial for the scientific community in the developing subject of nanofluids.     

Nuclear reactor application on Jeffrey fluid flow with Falkner-skan factor,Brownian and thermophoresis,non linear thermal radiation impacts past a wedge

In this paper, an impact of non-linear thermal radiation, Brownian and thermophoresis on an MHD through a wedge with dissipative impacts for Jeffrey fluid is investigated. In addition, heat transport analysis is carried out. This work's originality is attributable to the Jeffrey fluid formulation, nonlinear thermal radiation, Brownian and Thermophoresis. The boundary layer approximations are examined, to transform the governing equations into partial differential equations. Utilizing appropriate similarity transformations, the boundary value issue is expressed in ordinary differential form. BVP4C, a nonlinear numerical method, was utilized to determine the outcomes of velocity, concentration and temperature fields at multiple points of the measured quantities. The skin friction term, Sherwood and Nusselt numbers were analyzed in depth, and the findings are achieved graphically and tabularly. A comparison via the previously published data reveals a good degree of concordance. This research focuses mostly on the modelling of flow in a nuclear reactor. The boundary layer flow caused by a wedge surface play s a crucial role the aspects of geothermal and heat exchangers systems.     

A multi-domain spectral method for non-Darcian mixed convection flow in a power-law fluid with viscous dissipation

The purpose of this study is to investigate non-Darcian mixed convection flow, heat and mass transfer in a non-Newtonian power-law fluid over a flat plate embedded in porous medium with suction and viscous dissipation and also is to demonstrate the application and utility of a recently developed multi-domain bivariate spectral quasi-linearisation method (MD-BSQLM) in finding the solutions of highly nonlinear differential equations. The flow is subject to, among other source terms, internal heat generation, thermal radiation and partial velocity slip. The coupled system of nonlinear partial differential equations are solved using a MD-BSQLM to find the fluid properties, the skin friction, as well as the heat and mass coefficients. We have presented selected results that give the significance of some system parameters on the fluid properties. This MD-BSQLM has not been used before in the literature to find the nature of the solutions of power-law fluids. Indeed, validation of this numerical method for general fluid flows, heat and mass transfer problems has not yet been done. This study presents the first opportunity to evaluate the accuracy and robustness of the MD-BSQLM in finding solutions of non-Newtonian fluids.     

Thermal performance improvement in water nanofluid/GNP–SDBS in novel design of double-layer microchannel heat sink with sinusoidal cavities and rectangular ribs

In this numerical study, laminar flow of water nanofluid/GNP–SDBS (graphene nanoplatelet–sodium dodecylbenzene sulfonate) for 0–0.1% solid nanoparticles mass fraction was investigated for Reynolds numbers of 50–1000 in 3D space via finite volume method. In the newly proposed microchannel design, the cooling fluid is moving in countercurrent in the upper and lower layers of the microchannels, and there are cavities and sinusoidal routes on the solid walls of the microchannel, and the presence of rectangular ribs on the flow centerline along the fluid path enhances mixing for cooling fluid and creates better heat transfer for warm surfaces. The results of this study show that this special design of the microchannel can have a substantial increase in Nusselt number and heat transfer so that in the considered geometry by adding solid nanoparticles mass fraction it is possible to increase average Nusselt number for each Reynolds number by approximately 20%. Also, the mixing of the fluid because of formation of secondary flows has a strong effect on making the temperature distribution uniform in the cooling fluid and solid bed (wall) of the microchannel, especially in the lower layer. The upper layer of the microchannel always has a lower temperature due to indirect contact with heat flux compared with the lower layer. In this study, by increasing Reynolds number and mass fraction of solid nanoparticles the Nusselt number is increased and heat resistance of the lower wall of the microchannel is reduced. Based on the investigation of flow field and heat transfer, the use of the proposed design of the microchannel is recommended for Reynolds number less than 300.

     

Numerical investigation on the effect of magnetic field on natural convection heat transfer from a pair of embedded cylinders within a porous enclosure

The present work examines the influence of magnetohydrodynamic field on natural convection phenomena inside a porous square enclosure with a pair of embedded hot circular cylinders. Numerical investigations are performed to understand the effects of interspacing distance between the embedded cylinders, Hartmann number, Rayleigh number and Darcy number on the thermal transport process and the total irreversibility generation. It is observed that the isotherm distribution is strongly affected by the presence of magnetic field although the distribution of streamlines remains independent of the strength of magnetic field. This underlines the fact that magnetic field strongly influences the heat transfer process and entropy generation characteristics. It reveals that the natural convection is suppressed in the presence of a higher magnetic field as evident from the reduction in Nusselt number. It is observed that an increase in the spacing between the cylinders increases the heat transfer rate, and moreover, the effect of the magnetic field on heat transfer is more pronounced at higher interspacing distance between the embedded cylinders. The heat transfer rate increases significantly with the increase in the permeability of the medium. The entropy generation rate is independent of the strength of applied magnetic field. Further, the contribution of the entropy generation owing to friction is found to be negligible in total irreversibility obtained at lower values of Rayleigh number irrespective of Darcy number. However, the contribution of irreversibility owing to heat transfer is found to be minimal at higher values of Rayleigh number.

     

Numerical analysis of mixed convection heat transfer and laminar flow in a rectangular inclined micro-channel totally filled with Water/Al2O3 Nano fluid

A numerical analysis was carried out of mixed convection heat transfer for a laminar flow in a rectangular inclined microchannel totally filled with a water/Al2O3 nanofluid. The governing conservation equations are translated into a dimensionless form using the thermal single relaxation time and they modify the lattice Boltzmann method with double distribution functions. The viscous dissipation effects are adapted to the energy equation. The effects of nanoparticle volume fractions ? (0?≤???≤?0.04) and inclination angles γ (0°?≤?γ?≤?60°) on the flow of the nanofluid and the heat transfer are investigated. The obtained results are presented in terms of streamlines, isotherms, slip velocity, wall temperature and Nusselt number. The results show that the higher values of the volume fraction of Al2O3 and the large values of inclination angles improve the heat transfer rate.

     

Koo–Kleinstreuer–Li correlation for simulation of nanofluid natural convection in hollow cavity in existence of magnetic field

The lattice Boltzmann method is used to study natural convection of a CuO/water nanofluid in a hollow cavity. The hollow walls are fixed at a uniform temperature, and the effect of an applied magnetic field is examined. The Koo–Kleinstreuer–Li model, which accounts for nanoparticle’s Brownian motion, is used to gain the nanofluid effective thermal conductivity and nanofluid viscosity. The mechanisms how the inclination angle of magnetic field, Hartmann number, Rayleigh number, hollow width and nanoparticle volume fraction affect the streamlines, isotherms and rate of heat transfer are also studied. The results show that the average Nusselt number is increased by incrementing the nanoparticle volume fraction, Ra, magnetic field inclination angle and hollow width, but decreased by the Ha. For L = 0.4, the value of Ra where the dominant mechanism of heat transfer is changed from conduction to convection is larger than 10⁵. But for L = 0.48 or 0.56, the turning point of the dominant heat transfer mechanism is at Ra < 10⁵. Besides, at L = 0.4 or 0.48, the average Nusselt numbers in hot walls are higher than those in cold wall, but the opposite trend is found at L = 0.56.

     

Magnetohydrodynamic (MHD) flow of nanofluid with double stratification and slip conditions

This paper concerns with the analysis of double stratification in magnetohydrodynamic (MHD) flow of nanofluid by a stretching cylinder. Brownian motion and thermophoresis effects are present in the transport equations. The flow is subjected to velocity, thermal and solutal slip conditions. Non-linear ordinary differential equations are obtained from the governing non-linear partial differential equations after using appropriate transformations. The resulting non-linear ordinary differential equations are solved for the convergent series solutions. The velocity, temperature and concentration profiles are illustrated for different emerging parameters. Velocity distribution decays for higher estimation of velocity slip parameter. Furthermore, temperature decreases and concentration enhances for higher values of thermal stratification parameter and thermophoresis parameter, respectively. Numerical results for the skin friction, Nusselt number and Sherwood number are also presented and examined. Comparison between the published limiting solutions and present results is found in an excellent agreement.     

A study of heat and mass transfer of Non-Newtonian fluid with surface chemical reaction

Considering the significance of non-Newtonian fluid usage in manufacturing such as molten plastics, polymeric materials, pulps, and so on, significant efforts have been made to investigate the phenomenon of non-Newtonian fluids. In this article the influences of heat and mass transfer on non-Newtonian Walter's B fluid flow over uppermost catalytic surface of a paraboloid is encountered. An elasticity of the fluid layer is considered in the freestream together with heat source/sink and has the tendency to cause heat flow in the fluid saturated domain. The flow problem of two-dimensional Walter's B fluid is represented using Law of conservation of mass, momentum, heat, and concentration along with thermal and solutal chemical reactive boundary conditions. The governing equations are non-linear partial differential equation and are non-dimensionalized by employing stream function and similarity transformation. The final dimensionless equations yielded are coupled non-linear ordinary differential equations. Furthermore, shooting technique along with RK-4th order method is used to get the numerical results. Graphs and tables are modeled by using MATLAB software to check the effects of Walter's B parameter, Chemical reaction parameter and Thickness parameter on temperature, velocity, and concentration profiles. Tabular analysis shows the results of some physical parameters like skin friction coefficient, Nusselt number and Sherwood number due to the variation of Walter's B parameter, thickness parameter and chemical reactive parameter.     

Thermodynamics of magnetohydrodynamic Brinkman fluid in porous medium

This research article investigates that how heat flow changes versus temperature or time on the rheology of magnetohydrodynamic Brinkman fluid embedded in porous medium for the oscillations of heated plate. A fractional approach namely Caputo–Fabrizio fractional operator is applied for developing the governing partial differential equations of Brinkman fluid flow. The fractional governing partial differential equations have been modeled for temperature distribution, mass concentration and velocity field along with imposed initial and boundary conditions. The solutions are obtained by integral transforms and presented in special and elementary functions. In the limiting sense, the analytical solutions are particularized in the presence and absence of heat and mass transfer, magnetic field and porous medium. The parametric graphs have been depicted for the influence of different embedded rheological parameters on fluid flow. The results show few interesting differences and similarities by comparative analysis for fractional and ordinary Brinkman fluid flow, such as physically higher Prandtl (Pr) number that leads to decay thermal diffusivity which results in the reduction in thermal field; this means that better quality of production can be achieved through proper choice of Prandtl (Pr) and Schmidt (Sc) numbers.

     

Diffusion of liquid hydrogen in time-dependent MHD mixed convective flow

An innovative study on liquid hydrogen diffusion in time-dependent mixed convection flow is carried out in the presence of magnetic field effects. In fact, this is the first approach to analyze such flow problems, and also this is the first research paper to study the non-uniform heat sink/source and nonlinear chemical reaction in the presence of liquid hydrogen diffusion. Initially, the governing equations are reduced to dimensionless form by using non-similar transformations and are linearized by applying quasilinearization technique. Then, the finite difference approximation is utilized to discretize the resulting equations. The mixed convection is analyzed along with exponentially stretching surface through various graphs on profiles as well as gradients. The results display that the non-uniform heat source parameter increases the fluid velocity as well as temperature, and the magnetic parameter reduces the friction at the wall. Specifically, the skin friction coefficient decreases about 40% in the presence of magnetic field. The mass transfer rate increases for high-order chemical reaction and for destructive chemical reaction rate. The mass transfer rate is found to be high for the diffusion of liquid nitrogen than that for the diffusion of liquid hydrogen. In fact, the mass transfer rate increases about 22% for the diffusion of liquid nitrogen. This study can assist the design engineers who are working in pertain to the diffusion of liquid gases in mixed convection regimes. Also, the obtained data in the present study can be more useful for future investigations about time-dependent mixed convection nanofluid flow problems.

     

Chemical reaction and Soret effects on MHD convective flow of second grade fluid through an absorbent medium with ramped wall temperature as well as ramped surface concentration

In the present paper, the heat generating and/or absorption as well as thermo-diffusion on the unsteady free convection MHD gyrating flow of radiation and chemical reactive second grade fluid past an unbounded perpendicular plate during absorbent medium have been discussed. Here, it is assumed that, the confining plate has the ramped wall temperature with ramped surface concentration and isothermal temperature with ramped surface concentration. The analytical solutions for the governing equations are found by utilization of Laplace transformation methodology. The velocity, temperature and concentration profiles are analyzed with quite few figures. It is determined that, velocity, temperature and concentration distribution sketches in case of ramped temperature as well as ramped surface concentration are not as much of as those of isothermal temperature as well as ramped surface concentration. In addition to the idioms of skin friction, Nusselt number as well as Sherwood number are achieved and characterized numerically with tabular format.     

Numerical solution of nonlinear and non-isothermal general rate model of reactive liquid chromatography

Abstract

A nonlinear general rate model (GRM) of liquid chromatography is formulated to analyze the influence of temperature variations on the dynamics of multi-component mixtures in a thermally insulated liquid chromatographic reactor. The mathematical model is formed by a system of nonlinear convection–diffusion reaction partial differential equations (PDEs) coupled with nonlinear algebraic equations for reactions and isotherms. The model equations are solved numerically by applying a semi-discrete high-resolution finite volume scheme (HR-FVS). Several numerical case studies are conducted for two different types of reactions to demonstrate the influence of heat transfer on the retention time, separation, and reaction. It was found that the enthalpies of adsorption and reaction significantly influence the reactor performance. The ratio of density time heat capacity of solid and liquid phases significantly influences the magnitude and velocity of concentration and thermal waves. The results obtained could be very helpful for further developments in non-isothermal reactive chromatography and provide a deeper insight into the sensitivity of chromatographic reactor operating under non-isothermal conditions.     

Impact of homogeneous–heterogeneous reactions on heat and mass transfer flow of Au–Eg and Ag–Eg Maxwell nanofluid past a horizontal stretched cylinder

The object of this study is to analyze the impact of heterogeneous and homogeneous reactions on the flow, heat and mass transfer analysis of Maxwell nanofluid of Tiwari–Das kind over a stretched cylinder by considering convective boundary condition and velocity slip. Ethylene glycol (Eg) is used as base fluid; while gold (Au) and silver (Ag) are taken as nanoparticles. The governing equations represent nanofluid momentum, and energy and mass are reduced to system of nonlinear ordinary differential equations by utilizing similarity transformation procedure and are numerically evaluated by using finite element method. The sway of several pertinent parameters on the sketches of velocity, temperature and concentration is plotted through graphs. In addition to that the values of rate of heat transfer and skin-friction coefficient are calculated and presented through tables. The values of skin-friction coefficient are intensified as the values of homogeneous–heterogeneous reaction parameters rises. The velocity and concentration scatterings are both declines as the strength of Maxwell parameter raises.

     

Turbulent heat transfer and fluid flow of alumina nanofluid inside three-lobed twisted tube

Turbulent flow characteristics and heat transfer applications of a twisted heat exchanger with 3-lobed cross section along with Y-tape insert are numerically studied. The working fluids for the simulations are pure water and water–Al₂O₃ nanofluid using two-phase mixture model. The study is carried out for various nanofluid volume fractions of 0.01, 0.02 and 0.03 with Reynolds number in the range of 5000–20,000. The effect of nanoparticles in heat transfer augmentation for smooth and lobed tubes is discussed based on presenting the highest thermal performance, which is a relation between heat transfer rate and pressure loss. Results show that implementing the twisted tube with Y-tape insert enhances the heat transfer more than the twisted tube. Relative Nusselt numbers for twisted tubes decrease with Reynolds number in comparison with the plain tube. Turbulent intensity, swirl number and tangential velocity of twisted tube with insert are higher than empty twisted tube indicating that inserting the Y-tape intensifies the turbulence and disturbs the fluid flow further. On the other hand, although the twisted tube increases the pressure drop more than plain tube, the case with Y-tape drastically increases the friction factor. So, the thermal performance of twisted tube with insert is lower than empty twisted tube. Adding nanoparticles to the base fluid has different influence on the investigated cases. It augments the relative Nusselt number inside plain tube and empty twisted tube with slight increment in friction factor. Increasing the nanoparticles concentration enhances the heat transfer rates for these cases while it does not increase the relative Nusselt number inside twisted tube with Y-tape insert at high Reynolds number and nanoparticle concentration. Moreover, it can be found that twisted tube with or without Y-tape insert is more efficient at low Reynolds number in comparison with the plain tube.

     

Thermal onset chemically reactive Oldroyd-B nanofluid with immersion of microorganism in three-dimensional accelerating frame

The current research effort focuses on the employment of nanoparticles for 3-D chemically reactive flow of an Oldroyd-B nanofluid caused by a bidirectional accelerating surface. The implication of thermal radiation is also taken into account. The main characteristics of nanofluids, such as Brownian motion and thermophoresis are investigated using classic Buongiorno nanofluid design. The suitable transformation has been used to decrease the relevant equation for the defined theoretical model, for which the exact method is determined using the method of homotopic. Following that, a comprehensive graphic assessment of dimensionless velocities, concentration, and temperature distribution, as well as their physical significance, is considered. Furthermore, interesting physical quantities such as local Nusselt and Sherwood numbers are calculated and determined mathematically. The study stresses that increasing relaxation time reduces variation in both components of velocities, but the effect of continuous retardation time is exactly the reverse. For a while, larger combined convection and floating proportion parameters, the velocity distribution is said to have a rising movement in the horizontal plane. Furthermore, increasing the thermophoresis parameter improves temperature and centration distributions.     

Lattice Boltzmann study of multi-walled carbon nanotube (MWCNT)-Fe3O4/water hybrid nanofluids natural convection heat transfer in a Π-shaped cavity equipped by hot obstacle

In the present paper, the effect of nanofluid and the hot obstacle in a Π-shaped cavity is investigated. Lattice Boltzmann method is used to simulate the fluid flow and heat transfer. The effects of the parameters such as the nanoparticle solid volume fraction, the Rayleigh number, aspect ratio of cavity and hot obstacle position on the flow pattern and heat transfer parameters are studied. The numerical results are compared with previous results for validation, and a good agreement obtained. It is found that the average Nusselt number is increased by increasing the nanoparticle solid volume fraction, the Rayleigh number and the aspect ratio of cavity. Moreover, the effect of Rayleigh number on the average Nusselt number at high Rayleigh numbers (10⁵–10⁶) is more pronounced than that at low Rayleigh numbers (10³–10⁴) due to the different heat transfer mechanisms. The position of the hot obstacle affects the heat transfer significantly. When the hot obstacle is located on the center, the heat transfer is more effective.

     

First and second laws of thermodynamics analysis of nanofluid flow inside a heat exchanger duct with wavy walls and a porous insert

This paper investigates the combined effects of using nanofluid, a porous insert and corrugated walls on heat transfer, pressure drop and entropy generation inside a heat exchanger duct. A series of numerical simulations are conducted for a number of pertinent parameters. It is shown that the waviness of the wall destructively affects the heat transfer process at low wave amplitudes and that it can improve heat convection only after exceeding a certain amplitude. Further, the pressure drop in the duct is found to be strongly influenced by the wave amplitude in a highly non-uniform way. The results, also, show that the second law and heat transfer performances of the system improve considerably by thickening the porous insert and decreasing its permeability. Yet, this is associated with higher pressure drops. It is argued that the hydraulic, thermal and entropic behaviours of the system are closely related to the interactions between a vortex formation near the wavy walls and nanofluid flow through the porous insert. Viscous irreversibilities are shown to be dominant in the core region of duct where the porous insert is placed. However, in the regions closer to the wavy walls, thermal entropy generation is the main source of irreversibility. A number of design recommendations are made on the basis of the findings of this study.