Velocity Slip Boundary Condition Research Articles

Investigation into gas lubrication performance of porous gas bearing considering velocity slip boundary condition

Porous gas bearings (PGBs) have a proactive application in aerospace and turbomachinery. This study investigates the gas lubrication performance of a PGB with the condition of velocity slip boundary (VSB) owing to the high Knudsen number in the gas film. The Darcy-Forchheimer laws and modified Navier-Stokes equations were adopted to describe the gas flow in the porous layer and gas film region, respectively. An improved bearing experimental platform was established to verify the accuracy of the derived theory and the reliability of the numerical analysis. The effects of various parameters on the pressure distribution, flow cycle, load capacity, mass flow rate, and velocity profile are demonstrated and discussed. The results show that the gas can flow in both directions, from the porous layer to the gas film region, or in reverse. The load capacity of the PGB increases with an increase in speed and inlet pressure and decreases with an increase in permeability. The mass flow rate increases as the inlet pressure and permeability increase. Furthermore, the simulation results using VSB are in agreement with the experimental results, with an average error of 3.4%, which indicates that the model using VSB achieves a high accuracy. The simulation results ignoring the VSB overrate the load capacity by 16.42% and undervalue the mass flow rate by 11.29%. This study may aid in understanding the gas lubrication mechanism in PGBs and the development of novel gas lubricants.

Computational methods for pore-scale simulation of rarefied gas flow

Direct simulation at the pore-scale is crucial to unravel rarefaction effect on gas transport in tight porous media. To satisfy the dual demands on modeling accuracy and computation effort, an appropriate method must be chosen. This work, therefore, evaluates four numerical methods for pore-scale rarefied gas flows in a two-dimensional (2D) model porous media over a wide range of rarefaction. These methods are the incompressible Navier-Stokes equation with the first-order velocity-slip boundary condition, and three gas-kinetic solvers i.e. a finite-difference (FD) iterative solver for the linearized Bhatnagar, Gross and Crook (BGK) model kinetic equation, a finite-volume (FV) solver for the non-linear Shakhov model, and an open-source direct simulation Monte Carlos (DSMC) solver. The benchmark cases cover the characteristic Knudsen number ranging from 0.0231 to 4.62 while the characteristic Reynolds numbers are kept to be less than 1.0. All the solvers are developed in OpenFOAM, except the FD solver, allowing us to investigate the effect of local grid refinements using the automatic Cartesian grid generator in OpenFOAM. The flow fields and the apparent permeabilities predicted by all the solvers have been compared in detail. Besides, the computational time of these solvers is measured and analyzed to demonstrate the relative cost of the three kinetic solvers. It is found that the FD solver is the most efficient one and gives accurate results over the whole range of Knudsen number. Finally, this study also evaluates the feasibility of the recently developed discrete unified gas-kinetic scheme (DUGKS), the algorithm in the aforementioned non-linear Shakhov model equation solver, for pore-scale rarefied gas flow. It is found the results predicted by this solver agree well with the other two kinetic solvers.

Keller box study for inclined magnetically driven Casson nanofluid over a stretching sheet: single phase model

The current analysis signifies the Casson nanofluid stream with inclined magnetohydrodynamics, viscous dissipation, joule heating, thermal radiation, particle shape factor effects over a moving flat horizontal surface with entropy analysis. This study presents a novel idea regarding the implementation of Tiwari and Das model on Casson fluid model by considering ethylene glycol as a base fluid. Tiwari and Das model considers nanoparticles volume fraction for heat transfer enhancement instead of the Buongiorno model which heavily relies on thermophoresis and Brownian diffusion effects for heat transfer analysis. The velocity slip and convective slip boundary conditions have been employed at the surface of the sheet. By utilizing the suitable transformations, the modeled PDEs (partial-differential equations) are renewed in ODEs (ordinary-differential equations) and treated these equations numerically with the help of classical Keller box method. Two different classes of nanofluids, Copper-Ethylene Glycol () and Molybdenum Disulfide-Ethylene Glycol () have been taken into considering for our analysis. The behaviour of surface drag coefficient and Nusselt number for the varied values of various sundry parameters is designed via tables. Our findings show that an increase in the Reynolds and Brinkman numbers increased the overall entropy of the system.

Fluoropolymer coatings deposited on rotating cylindrical surfaces by HW CVD: experiment and simulation

The hot wire chemical vapor deposition method has been adapted to deposit fluoropolymer coatings on small-radius rotating surfaces. The influence of the rotational frequency of a cylindrical sample during the deposition process on the formation of a layer of fluoropolymer coating was studied. It was found that the rotational frequency of the cylindrical sample significantly changed the morphology of the resulting coating. It was shown that with an increase in the sample’s rotational frequency from 1 to 100 rpm, the deposition rate decreased and the coating structure degraded. To establish the reasons for this effect, a numerical study of the flow around a rotating cylindrical sample was carried out for a range of low gas velocities and densities in the reactor. The simulations are based on solving the Navier–Stokes equation with no slip and velocity slip boundary conditions for a rotating surface. It was found that the main reason for the decrease in the deposition rate was associated with the effect of the formation of a closed circulation flow region above the sample’s surface during rotation. The dependence of the characteristic size of this region on the rotational frequency of the cylinder sample was close to linear. The effects of surface boundary conditions were also analyzed.

Suppression of electroconvective and morphological instabilities by an imposed cross flow of the electrolyte

Electroconvection and its coupling with a morphological instability are important in many applications, including electrodialysis, batteries and fuel cells. In this work, we study the effects of a two-dimensional channel flow on the electroconvective and morphological instabilities using two approaches. In the bulk analysis, we consider the instability of the electroneutral bulk region driven by a second kind electroosmosis slip velocity boundary condition and derive the asymptotic solutions for small and large wavenumbers. In the full analysis, we consider the entire region of the liquid electrolyte and use the ultraspherical spectral method to numerically solve the eigenvalue problems. Both studies show that the imposed flow significantly affects the electroconvective instability. The imposed flow generates a shielding effect by deforming the perturbed ion concentration field and hinders the ion transfer from low- to high- concentration regions which causes the instability. It fully suppresses the electroconvective instability at small wavenumbers and reduces the growth rate of the perturbations at large wavenumbers. The direct effect of the flow on the morphological instability is minor, while the suppression of the electroconvective instability may change the wavenumber of the most unstable mode of the coupled instabilities. For the electroconvective instability, the bulk analysis is qualitatively different from the full analysis at high wavenumbers. For the morphological instability, good agreement is found between the two studies at both small and large wavenumbers.

RETRACTED: Laminar single‐phase and two‐phase modeling of water/MgO nanofluid flow inside a rectangular microchannel with rhombic vortex generators

AbstractIn the present numerical simulation, laminar single‐phase and two‐phase nanofluid flows are investigated inside a rectangular microchannel with the vortex generators. Rhombic vortex generators with different attack angles are used for a better mixture of fluid. Water/MgO nanofluid is used as the working fluid in the volume fractions of nanoparticles φ = 0‐4% in Reynolds numbers of Re = 1‐300 at the two‐dimensional space. The presence of vortex generators with attack angles of λ = 0‐45°, and simultaneous investigation of heat transfer and flow hydrodynamic parameters distinguish this research from other similar studies. Obtained results revealed that using nanofluid with higher volume fractions, slip boundary condition on the hot wall, and using vortex generator with higher λ lead to significant enhancement of heat transfer. Also, the value of pressure drop augmentation is caused by the increase of φ and λ is significant at higher Reynolds numbers. Unlike the increase of φ, by increasing Reynolds number, the effect of slip boundary condition becomes considerable on the reduction of entropy generation. The behavior of entropy generation graphs with slip velocity boundary condition on the wall is different from the no‐slip boundary condition at Re = 300. The behavior of average entropy generation is different in the various φ, Reynolds numbers, and λ in the no‐slip boundary condition for single‐phase and two‐phase models. Also, the two‐phase model estimates flow behavior with less irreversibility.

Direct Numerical Simulation of Turbulent Heat Transfer with Slip and Temperature Jump

The fully developed turbulent flow and heat transfer in a plane channel at a nominal shear Reynolds number of 180 is studied via the direct numerical simulation technique. A linear velocity-slip boundary condition is assumed on one of the channel walls, whereas the classical no-slip condition is imposed on the other wall. The heat transfer at the slip wall is assumed to occur with and without temperature jump, whereas a classical first-kind temperature boundary condition is assumed on the no-slip wall. Various statistical quantities are shown and discussed. It is observed that the velocity fluctuations are attenuated in the proximity of the slip wall but they are amplified in the vicinity of the no-slip wall. The behavior is somewhat different for the temperature fluctuations. For the case without temperature jump, the temperature fluctuations are amplified near the slip wall, whereas they are attenuated close to the no-slip wall. For the case with temperature jump, the modifications of turbulent heat fluxes are more dramatic and they decrease by increasing the amount of wall slip. In general, the velocity slip condition will result in an enhanced heat transfer if no temperature jump is taken into account. This behavior is reversed when the temperature jump at the slip wall is taken into account. The budget of temperature variance is shown and discussed for the case with temperature jump.

Computational analysis of the thermal performance of rarefied air flow in V‐shaped microchannels

AbstractIn this study, a computational fluid analysis of a slip flow developing thermally and hydrodynamically in a triangular microchannel has been considered. The wall of the channel is preserved at a fixed temperature. Temperature jump and velocity slip boundary conditions are imposed on the surfaces. The microchannel is constructed from seven triangular‐shaped channels and the angle of the microchannel (θ) is varied from 0° to 40°. Simulations are carried out for , and the air is used as a working fluid with variable physical properties. The simulation results show that the triangular microchannel can improve heat transfer as compared with plain microchannels. An optimal θ of 20° is found to provide the best heat transfer at moderate frictional losses. Finally, correlations for the average Nusselt number and the average friction coefficient among all parameters are proposed as follows: , .

Stochastic Effects of 2D Random Arrays of Cylinders on Rarefied Gas Permeability Using the Lattice Boltzmann Method

A large set of 2D random arrays of circular cylinders is generated to perform a statistical study on rarefied gas flow through micro-porous media. The flow regimes in this work lie for Knudsen numbers (Kn) ranging from the continuum to the transition regimes. Arrays are built by randomly placing cylinders with constant diameter with a uniform distribution without overlapping, and are generated for three target porosities. Fluid flow is assumed to be incompressible and isothermal. A modified lattice Boltzmann model is adopted to account for discrete effects, with slip-velocity boundary conditions and a Kn-dependent multi-relaxation time collision operator. The apparent permeability is modeled with Darcy’s law with a Klinkenberg-type relationship and compared with existing correlations. Velocity fields highlight the increasing contribution of fluid flow through small pores with increasing Kn. Numerical results show that porous media randomness leads to an uncertainty on rarefied gas permeability calculation despite the same structural characteristics and may not strictly follow a specific correlation. The influence of a local collision operator based on a local Kn instead of a global one in the numerical model is also studied. Results show that the permeability in rarefied regimes undergoes significant deviation when applying the local collision operator compared to the global one. These differences could result from a more accurate capture of the pore-scale behavior with a local Kn. Thus, it emphasizes the sensitivity of the model and the apparent permeability calculation to the appropriate definition of Kn.

A numerical study on the natural transition locations in the flat-plate boundary layers on superhydrophobic surfaces

In this paper, the natural transition locations in the flat-plate boundary layers on the superhydrophobic surfaces are studied by numerical methods. The laminar flow field in the whole stream-wise computational domain is obtained by solving the Blasius equation with the slip-velocity boundary condition on the wall. The boundary layer on the superhydrophobic surface becomes thinner than that on the ordinary surface. The linear instability analysis is performed on the laminar boundary layer, and the eN method is employed to predict the transition location. The two-dimensional (2D) Tollmien–Schlichting (T–S) waves are still more unstable than the three-dimensional (3D) ones on the superhydrophobic surfaces, so only the 2D waves are taken into consideration to predict transition. As the slip length becomes longer, the critical location of flow instability moves further downstream, and the unstable zone becomes smaller. Therefore, the superhydrophobic surfaces have the effect of delaying the natural transition and that the delay effect becomes stronger as the slip length becomes longer. The higher oncoming flow velocity leads to higher frequencies of the unstable T–S waves and the larger unstable zone. As the oncoming flow velocity rises, the transition location on the superhydrophobic surface moves once upstream and then downstream. Consequently, there is a “dangerous” oncoming flow velocity corresponding to the transition location, which is the closest to the lead edge. Furthermore, the transition delay effect of the superhydrophobic surface becomes stronger with the increase in the oncoming flow velocity.

Theoretical investigation for convective heat transfer on Cu/water nanofluid and (SiO2-copper)/water hybrid nanofluid with MHD and nanoparticle shape effects comprising relaxation and contraction phenomenon

A methodological approach has been adopted in order to investigate the magnetohydrodynamic (MHD) flow of (Cu-SiO2)/water hybrid nanofluid keeping in view the peristaltic motion.An endeavor is made to obtain accurate results of velocity slip and convective boundary conditions while studying four different types of geometric shapes (sphere, bricks, cylinder and platelets). The formulated equations are theoretically examined. In the manuscript, flow phenomenon of relaxation and contraction in a geometry of finite length of a non-uniform tube with regards to Cu/water and (Cu-SiO2)/water hybrid nanoparticles are deliberated. Equations related to realistic boundary conditions i.e. dimensionless control equations, are also studied in the manuscript. In order to validate theoretical findings of the work, graphical discussion on supplementary nanoparticles form a part of this manuscript. Effects of these nanoparticles on velocity, temperature distribution and transfer of heat is also discussed in the same manuscript. The analysis shows that conductivity of the nanoparticles is directly proportional to the volume of the nanoparticles. The results also show that there is significantly increase in temperature and velocity due to increase of heat absorption which also results in increases in elevation for hybrid nanofluid. The above discussion implies that convective heat transfer parameter has higher impact in case of (Cu- SiO2)/water hybrid nanofluid as compare to Cu-water/nanofluid. Streamlines pattern of Peristaltic transport is also discussed in the paper. This manuscript also draws the comparison between the results of Cu-water and (Cu- SiO2)/water hybrid.

Rotating Al2O3-H2O nanofluid flow and heat transfer with internal heating, velocity slip and different shapes of nanoparticles

PurposeThis research numerically investigates the steady laminar 3D forced convective flow and heat transfer of a rotating Al2O3/water nanofluid past a linearly stretching sheet with the help of a novel two-phase analysis method by considering different nanoparticle shapes as well as velocity slip boundary condition plus internal heating.Design/methodology/approachThe authors’ novel two-phase analysis method implements the Jang and Choi model for the effective thermal conductivity and incorporates it with Tiwari–Das mathematical model. Besides, the shape factors of the nanoparticles have also taken into account using the Timofeeva model for effective dynamic viscosity. The Prandtl number of the base fluid is kept constant at 6.2 and the temperature of the nanoparticles as well as the base fluid molecules is assumed to be 300 K. In short, after using the similarity transformation method, the obtained dimensionless nonlinear ODEs are numerically solved using the bvp4c built-in function from MATLAB. The governing parameters are solid volume concentration, rotation parameter, velocity slip parameter, heat generation or absorption parameter and Prandtl number of the base fluid.FindingsIt is argued that when the cylindrical shape for alumina is chosen, the maximum values for skin friction coefficients and local Nusselt number have been obtained among the other shapes. Further, the velocity slip enhancement in this problem will lead to a drastic reduction in the foregoing quantities of engineering interest.Originality/valueTo the best of the authors’ knowledge, this research is a novel attitude to two-phase nanofluid model.

Comparative study on ethylene glycol based Ag-Al 2 O 3 and Al 2 O 3 nanofluids flow driven by electroosmotic and peristaltic pumping: a nano-coolant for radiators

This paper aims to provide a comparative analysis of hybrid (Ag- Al 2 O 3) nanofluid and Al 2 O 3 mono nanofluid in a convective heat transfer process driven by electroosmotic and peristaltic pumping. Ethylene glycol (EG) due to its strong anti-freezing properties is taken as a base fluid. The features of mixed convection, magnetohydrodynamics, and Joule heating are also comprised in this study. The slip boundary conditions for axial velocity and temperature are employed at the walls of the microchannel in a porous environment and conditions of zero normal mass flux are imposed for the passive control of nanoparticles. This model is composed by using the Buongiorno flow model along with the modified Maxwell-Garnett model for thermal conductivity of hybrid nanofluids and Poisson-Boltzmann distribution for electric potential generated within the fluid medium. The problem is simplified under the approximations of lubrication theory and Debye–Hückel linearization and the numerical computations have been made through Maple 17 code. The graphical results of flow variables for various involved quantities are prepared and presented with a requisite interpretation. Moreover, contour graphs are also plotted for stream function in order to discuss the trapping phenomenon. The addition of a volume fraction of 9% of aluminum dioxide in ethylene glycol tends to raise the thermal conductivity of working fluid up to 28.97% however further addition of a small number of silver nanoparticles increases its thermal conductivity up to 53.57%. Due to this increment in thermal conductance, it is found that the efficiency of Ag- Al 2 O 3 nanofluid in the heat transfer mechanism is better than the Al 2 O 3 nanofluid. It is further reported that EG based hybrid nanofluid (Ag- Al 2 O 3) as nano-coolant is more applicable for radiators and other cooling systems as compared EG based (Al 2 O 3) nanofluid.

Entropy generation analysis for radiative peristaltic motion of silver-water nanomaterial with temperature dependent heat sink/source

The generation of entropy is correlated with irreversibility of any thermodynamic system. It provides an indication of a loss of energy and therefore a system’s efficiency. Therefore, an attempt has been made to investigate entropy generation and thermal analysis for peristalsis of silver-water nanomaterial through an inclined symmetric channel. The flow is influenced by magnetic field, temperature dependent heat generation/absorption, thermal radiation, mixed convection and viscous dissipation effects. Problem is modelled by utilizing long wavelength approximation. Two phase model of nanofluid is employed. Convective and velocity slip boundary conditions are used. Numerical results are evaluated for axial velocity, heat transfer, Bejan number and entropy generation. Results reveal that velocity of nanofluid decreases by enhancing Hartman number. Addition of nanoparticles volume fraction enhances the temperature of nanofluid. Heat transfer rate at boundary decreases by enhancing velocity slip parameter. Entropy generation increases for radiation parameter and Brinkman number. Further, Bejan number shows increasing behavior when nanoparticles volume fraction is enhanced.

LBM modeling and analysis on microchannel slip flow and heat transfer under different heating conditions

This article aims to explore the effects of buoyancy force and thermal boundary condition on the mixed convection heat transfer performance of air in a horizontal microchannel. Three different heat flux models, including bottom wall heated, top wall heated (single wall heating – a novel heating approach compared to recent studies) and both walls heated, are analyzed at four different values of the Grashof number (Gr = 0, 100, 300, 600) using a lattice Boltzmann method (LBM). The slip velocity boundary condition is also applied to the bottom and top walls. It can be found that the buoyancy force changes the velocity distribution structure near the bottom wall and top wall, particularly at the inlet regions in all models, and a negative slip velocity is generated due to the backflow formed at a relatively large Grashof number and it strictly determines the local wall friction coefficient. Either the bottom wall or the top wall is heated. A vortex is found close to the top wall because the mixing position of the hot and cold fluids is in the vicinity of the top wall. This feature facilitates the heat transfer near the top wall and core flow zone. The thermal performance is most positive for the case when the top wall is heated due to the generation of an induced vortex and no influence of the vortex near the bottom wall.

Magnetized Darcy-Forchheimer Stagnation Point Flow of Micropolar Ferrosoferric Oxide Fluid with Velocity Slip and Convective Boundary Condition

The present communication develops the governing expressions that describe a steady incompressible two-dimensional flow of micropolar Ferrosoferric Oxide fluid towards a stretched surface under the impact of Lorentz force (magnetic field). Ferrofluids are made out of nanoscale ferromagnetic materials suspended in a base fluid (oil, kerosene, water). The distinction between the magnetorheological fluids (MRF) and ferrofluids (FF) is the size of the materials. The materials in a ferrofluid fundamentally comprise of nanomaterials, which are suspended by Brownian diffusion and generally under normal conditions will not settle. Here, Ferrosoferric Oxide (Fe₃O₄) is considered as nanoparticle and water as a base fluid. The governing equations are modeled by using Tiwari-Das nanofluid model with the help of appropriate similarity transformations. Furthermore, radiative heat flux and convective boundary condition is accounted. The numerical results of the governing equations are obtained through implementation of Built-in-Shooting technique. The impact of radiation parameter, stretching ratio parameter, magnetic parameter, thermal Biot number, micro-rotation parameter, velocity slip parameter and Darcy-Forchheimer number on the flow velocity and temperature are revealed graphically and discussed. The engineering curiosity like skin friction and Nusselt number are computationally computed and tabulated.

Activation energy impact on radiated magneto-Sisko nanofluid flow over a stretching and slipping cylinder: entropy analysis

PurposeThe purpose of this article is to analyze the heat and mass transfer with entropy generation during magnetohydrodynamics (MHD) flow of non-Newtonian Sisko nanofluid over a linearly stretching cylinder under the influence of velocity slip, chemical reaction and thermal radiation. The Brownian motion, thermophoresis and activation energy are assimilated in this nanofluid model. Convective boundary conditions on heat and mass transfer are considered. The physical model may have diverse applications in several areas of technology underlying thermohydrodynamics including supercritical fluid extraction, refrigeration, ink-jet printing and so on.Design/methodology/approachThe dimensional governing equations are nondimensionalized by using appropriate similarity variables. The resulting boundary value problem is converted into initial value problem using the method of superposition and numerically computed by employing well-known fourth-order Runge–Kutta–Fehlberg approach along with shooting technique (RKF4SM). The quantitative impacts of emerging physical parameters on the velocity, temperature, concentration, skin friction coefficient, Nusselt number, Sherwood number, entropy generation rate and Bejan number are presented graphically and in tabular form, and the salient features are comprehensively discussed.FindingsFrom graphical outcomes, it is concluded that the slip parameters greatly influence the flow characteristics. Fluid temperature is elevated with rising radiation parameter and thermal Biot number. Nanoparticle concentration is reported in decreasing form with activation energy parameter. Entropy is found to be an increasing function of magnetic field, Brownian motion and material parameters. The entropy is less generated for shear-thinning fluid compared to shear-thickening as well as Newtonian fluids in the system.Originality/valueTill now no study has been documented to explore the impact of binary chemical reaction with Arrhenius activation energy on entropy generation in an MHD boundary layer flow of non-Newtonian Sisko nanofluid over a linear stretching cylinder with velocity slip and convective boundary conditions.

A lattice Boltzmann study of rarefied gaseous flow with convective heat transfer in backward facing micro-step

Rarefied pressure-driven gaseous flow with heat transfer in a microchannel with a backward facing micro-step is investigated in this paper using the lattice Boltzmann method (LBM) in slip and transition flow regimes. In a novel approach, a two-relaxation-time LB equation is used to solve the flow velocity and the single-relaxation-time to handle the heat transfer. The asymmetric relaxation time is determined by equating the analytical second-order slip velocity boundary condition and the slip velocity obtained from applying the implemented bounce back specular boundary condition in the LBM. A second-order implicit temperature jump boundary condition is also implemented to capture the rarefaction effect on the fluid temperature at walls. Velocity slip, temperature jump, centerline temperature, and Nusselt number variations are evaluated for channels with and without the micro-step for a wide range of the Knudsen number. Effects of the micro-step on the rarefied gaseous flow and convective heat transfer are evaluated and discussed. The numerical model is verified by comparing with direct simulation Mont Carlo results.

Resistance of velocity slip flow in pipe/channel with a sudden contraction

A novel approach based on the local entropy generation rate, also known as the second law analysis (SLA), is proposed to compute and visualize the flow resistance in mass transfer through a pipe/channel with a sudden contraction component (SCC) at low Reynolds number (Re) featuring velocity slip. The linear Navier velocity slip boundary condition is implemented using the explicit scheme. At small Reynolds number, i.e., Re ≤ 10.0, the flow resistance coefficient of the SCC, KSCC, is found to be a function of the dimensionless velocity slip length Lslip* and Re−1, and gradually increase to a constant value at contraction ratio Rarea ≥ 8, reaching a formula KSCC=(0.4454Lslip* 3−1.894Lslip* 2+2.917Lslip*+8.909)/Re. Over this range of Re, the equivalent length of the flow resistance is almost independent of Re, while out of this range, the equivalent length increases monotonically with Re. Moreover, the dimensionless drag force work around the SCC is negative and reaches a minimum at a critical Lslip*. The SLA reveals that the regions affected by the SCC mainly concentrate around the end section of the upstream pipe/channel rather than the initial partition of the downstream section reported in large Re turbulent flow, and this non-dimensional affected upstream length increases with Lslip*. The fluid physics are further examined using SLA to evaluate the energy loss over the entire domain, decomposed as the viscous dissipation inside the domain and the drag work on the wall boundary.

Heat Transfer Analysis on Peristaltic Transport of a Jeffery Fluid in an Inclined Elastic Tube with Porous Walls

This article analyses the effects of heat transfer and thermal conductivity on the peristaltic transport of Jeffery fluid through an inclined elastic tube with porous walls. The velocity slip and convective boundary conditions are taken into account. The modeled governing equations are solved analytically by considering the long wavelength and small Reynolds number approximations. The closed-form solutions are obtained for velocity, flow rate, and the theoretical determination of flow rate is calculated with the help of equilibrium condition given by Rubinow and Keller. A parametric analysis has been presented to study the effects of Jeffery parameter, thermal conductivity, Darcy number, the angle of inclination, velocity slip, Biot number, amplitude ratio, Prandtl number, and Eckert number on velocity, flow rate, and temperature are scrutinized. The streamlines show that the bolus moves with the same speed as that of the wave and further the study reveals that an increase in the Biot number reduces the magnitude of the temperature.