NONISOTHERMAL CHARACTERIZATION OF THIN FILM OSCILLATING BEARINGS

Flow and heat transfer inside a nonisothermal, incompressible, thin-film squeezing bearing are analyzed. The governing equations have been nondimensionalized and reduced to simpler forms based on an order of magnitude analysis. Various analytical solutions for the temperature distribution and Nusselt number under different physical constraints are obtained. The influence of the thermal squeezing parameter as well as the motion characteristics of an oscillating bearing are determined on a Nusselt number analytically and numerically, and, similarly, the Nusselt number history is shown for an oscillating thin-film bearing.     

The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating

A numerical study of heat transfer from boundary layer flow driven by a continuous moving porous plate is proposed. The flow with electrically fluid due to the plate in the presence of a transverse magnetic field and Ohmic heating was molded as a steady, viscous, and incompressible. Both viscosity and thermal conductivity were variable and considered only a function of temperature. Similar analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for momentum and energy and determine the skin-friction coefficient and heat transfer rate. As the magnetic parameter and variable viscosity parameter increase, the fluid temperature and skin-friction coefficient increase and the fluid velocity and heat transfer rate decrease. The fluid temperature increases and heat transfer rate decreases with an increasing Eckert number and thermal conductivity parameter. The skin-friction coefficient and heat transfer rate increase, whereas the fluid velocity and temperature decrease as the wall suction velocity increase.     

Analysis of flow and heat transfer inside oscillatory squeezed thin films subject to a varying clearance

The flow and heat transfer inside a non-isothermal and incompressible thin film having its upper plate slightly inclined from the horizontal and undergoing an oscillatory squeezing motion is investigated in this work. Two models are analyzed: low and large Reynolds number flow models. The corresponding governing equations for each model are properly non-dimensionalized and solved numerically. The main controlling parameters for the dynamic and thermal behavior of the inclined thin film are found to be the amplitude of the upper plate motion, squeezing Reynolds number, squeezing number, thermal squeezing parameter and the dimensionless slope of the upper plate. It is found that fluctuations in the axial and normal velocities are greater for convergent thin films than for divergent thin films. Furthermore, Nusselt numbers and their amplitudes are found to decrease with an increase in the dimensionless slope of the upper plate. Finally correlations are obtained for Nusselt numbers and their corresponding amplitudes for two different thermal conditions: constant wall temperature and uniform wall heat flux.     

Effect of thermophoresis and Brownian motion on the melting heat transfer of a Jeffrey fluid near a stagnation point towards a stretching surface: Buongiorno's model

This analysis intends to address the coupled effect of phase change heat transfer, thermal radiation, and viscous heating on the MHD flow of an incompressible chemically reactive nanofluid in the vicinity of the stagnation point toward the stretching surface, taking a Jeffrey fluid as the base fluid. Convergent analytical solutions for the nonlinear boundary layer equations are obtained by the successive application of scaling variables and the highly efficacious homotopy analysis method. Error analysis is implemented to endorse the convergence of the solutions. Through parametric examination, influence of various physical parameters occurring in analysis of the profiles of velocity, temperature, and nanoparticle concentration, coefficient of surface drag, rates of mass and heat transfer is explored pictorially. The Deborah number and the melting parameter are found to enhance velocity, and the associated momentum boundary layers are thicker, whereas the magnetic field depreciates the flow rate. Temperature is observed to enhance with the thermophoresis parameter, Prandtl number and Eckert number, whereas a reduction is seen with the thermal radiation parameter and Brownian motion parameter. Nanoparticle concentration is depleted by the chemical reaction parameter, the thermophoresis parameter, and the Lewis number.     

Thermal radiation and magnetic field effects on squeezing motion analysis for Cu–kerosene and Cu–water nanofluids

This article examines the squeezing motion of Cu–kerosene and Cu–water nanofluids with thermal radiation and magnetic field between two parallel sheets. By appropriate transformation, the governing nonlinear partial differential equations are converted into ordinary differential equations and then solved numerically by the Runge–Kutta technique. The motion characteristics have been examined with graphs by relevant parameters. It is observed that fluid temperature reduces if squeezing parameter, thermal radiation, and Hartmann number increases, but fluid temperature improves if nanoparticle volume fraction, Eckert number, and Prandtl number increases and it is observed that liquid momentum improves if the squeezing parameter increases, but fluid velocity reduces if nanoparticle volume fraction and Hartmann number increases.     

On the analytic solution of MHD flow and heat transfer for two types of viscoelastic fluid over a stretching sheet with energy dissipation,internal heat source and thermal radiation

In this paper we study the magneto-hydrodynamic flow and heat transfer of an electrically conducting, viscoelastic fluid past a stretching surface, taking into account the effects of Joule and viscous dissipation, internal heat generation/absorption, work done due to deformation and thermal radiation. Closed-form solutions for the boundary layer equations of the flow are presented for two classes of viscoelastic fluid, namely, the second-grade and Walters’ liquid B fluids. Thermal transport is analyzed for two types of non-isothermal boundary conditions, i.e. prescribed surface temperature (PST) and prescribed surface heat flux (PHF) varying as a power of the distance from the origin. Results for some special cases of the present analysis are in excellent agreement with the existing literature. The effects of various physical parameters, such as viscoelasticity, magnetic parameter, thermal radiation parameter, heat source/sink parameter, Prandtl number, Eckert number and suction/injection parameter on the velocity and temperature profiles, skin friction coefficient and Nusselt number are examined and discussed in detail.     

Darcy–Forchheimer flow of Ree–Eyring fluid over an inclined plate with chemical reaction: A statistical approach

In spite of various reports on non-Newtonian fluids, little is known on the impact of chemical reaction on the Darcy–Forchheimer flow of Ree–Eyring fluid when Cattaneo–Christov (C-C) heat flux (HF) is significant. The inclusion of porous medium occurs in various procedures which include heat transfer, geophysics design, and so forth. It also influences oil production recovery, energy storage units, solar receivers, and many others. The Darcy–Forchheimer flow model is important in the fields where a high flow rate effect is a common phenomenon, for instance, in petroleum engineering. In this study, we aim to analyze the dissipative Darcy–Forchheimer flow of Ree–Eyring fluid by an inclined (stretching) plate with chemical reaction. We have included the C-C HF model to investigate the heat transfer characteristics of the fluid. Equations in the mathematical model are metamorphosed as ordinary differential equations and then unriddled with the aid of shooting strategy. The main advantage of the shooting method is that it is easy to apply. The shooting method requires good initial guesses for the first derivative and can be applied to both linear and nonlinear problems. Results are explicated through graphs. We took the help of a statistical tool, that is, correlation coefficient to analyze the impression of crucial parameters on surface friction drag (skin friction coefficient), heat and mass transfer rates. The main inferences of this study are porosity parameter and Forchheimer numbers deprecate the fluid velocity, Eckert number ameliorates fluid temperature and concentration minifies with larger chemical reaction parameter. It is discovered that the Forchheimer and Weissenberg numbers deprecate the surface friction drag. Mass transfer rate has a substantial positive relationship with Schmidt number and chemical reaction. Furthermore, the heat transfer rate has a substantial positive correlation with the thermal relaxation parameter and a substantial negative correlation with the Eckert number.     

Heat transfer on peristaltically induced Walter's B fluid flow

This paper look at the effects of heat transfer on peristaltic flow of Walter's B fluid in an asymmetric channel. The regular perturbation method is used to solve the governing equations by taking the wave number as the small parameter. Expressions for stream function, temperature distribution, and heat transfer coefficient are presented in explicit form. Solutions are analyzed graphically for different values of arising parameters. It has been found that these parameters affect considerably the considered flow characteristics. Results show that with an increase in the Eckert and Prandtl numbers, the temperature and heat transfer coefficient increase. Further, the absolute value of the heat transfer coefficient increases with an increasing viscoelastic parameter. Comparison with published results for viscous fluid is also presented. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21021     

Influence of wall properties on the peristaltic flow of a nanofluid: Analytic and numerical solutions

This study is concerned with the peristaltic transport of nanofluid in a channel with complaint walls. Transport equations involve the combined effects of Brownian motion and thermophoretic diffusion of nanoparticles. Mathematical modeling is carried out by utilizing long wavelength and low Reynolds number assumptions. The coupled nonlinear boundary value problem (BVP) has been solved numerically by using shooting technique through software Mathematica. The analytic solutions are computed by a robust analytical tool namely the homotopy analysis method (HAM). Attention has been focused on the behaviors of Brownian motion parameter (Nb), thermophoresis parameter (Nt), Prandtl number (Pr) and Eckert number (Ec). The results indicate an appreciable increase in the temperature and nanoparticles concentration with the increase in the strength of Brownian motion effects. Further heat transfer coefficient is a decreasing function of Nb and Nt.     

Peristaltic transport in an asymmetric channel with heat transfer — A note

The problem of heat transfer for the motion of a viscous incompressible fluid induced by travelling sinusoidal waves has been analytically investigated for a two-dimensional asymmetrical channel. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with the velocity of the wave. The momentum and energy equations have been linearized under long-wavelength and low-Reynolds number assumptions and closed form expressions for temperature and coefficient of heat transfer have been derived. The effect of Hartmann number, Eckert number, width of the channel and phase angle on temperature and coefficient of heat transfer are discussed numerically and explained graphically.     

Flow and heat transfer inside thin films supported by soft seals in the presence of internal and external pressure pulsations

The effects of both external squeezing and internal pressure pulsations are studied on flow and heat transfer inside non-isothermal and incompressible thin films supported by soft seals. The laminar governing equations are non-dimensionalized and reduced to simpler forms. The upper plate displacement is related to the internal pressure through the elastic behavior of the supporting seals. The following parameters: squeezing number, squeezing frequency, frequency of pulsations, Fixation number (for the seal) and the thermal squeezing parameter are found to be the main controlling parameters. Accordingly, their influences on flow and heat transfer inside disturbed thin films are determined and discussed. It is found that an increase in the Fixation number results in more cooling and a decrease in the average temperature values. Also, it is found that an increase in the squeezing number decreases the turbulence level at the upper plate. Furthermore, fluctuations in the heat transfer and the fluid temperatures can be maximized at relatively lower frequency of internal pressure pulsations.     

Non-Darcy mixed convection from a line source of heat in saturated porous medium

Local non-similarity solutions are reported for mixed convective heat transfer from a line source of heat in a saturated porous medium. Non-Darcy effects which include the flow inertial and thermal dispersion are considered in this study. The governing parameters are the Ergun number Er, the thermal dispersion coefficient C and mixed convection parameter & (=Ra/Pe). While the inertial effect tends to reduce the mixed convective flow, the thermal dispersion is to increase it. Both effects, however, have considerably thickened the thermal boundary layer.     

Thermophoretic hydromagnetic dissipative heat and mass transfer with lateral mass flux,heat source,Ohmic heating and thermal conductivity effects: Network simulation numerical study

A two-dimensional mathematical model is presented for the laminar heat and mass transfer of an electrically-conducting, heat generating/absorbing fluid past a perforated horizontal surface in the presence of viscous and Joule (Ohmic) heating. The Talbot–Cheng–Scheffer–Willis formulation (1980) is used to introduce a thermophoretic coefficient into the concentration boundary layer equation. The governing partial differential equations are non-dimensionalized and transformed into a system of nonlinear ordinary differential similarity equations, in a single independent variable, η. The resulting coupled, nonlinear equations are solved under appropriate transformed boundary conditions using the Network Simulation Method. Computations are performed for a wide range of the governing flow parameters, viz Prandtl number, thermophoretic coefficient (a function of Knudsen number), Eckert number (viscous heating effect), thermal conductivity parameter, heat absorption/generation parameter, wall transpiration parameter, Hartmann number and Schmidt number. The numerical details are discussed with relevant applications. Excellent correlation is achieved with earlier studies due to White (1974) and Chamkha and Issa (2000). The present problem finds applications in optical fiber fabrication, aerosol filter precipitators, particle deposition on hydronautical blades, semiconductor wafer design, thermo-electronics and nuclear hazards.     

Influence of Viscous Dissipation on Mixed Convection in a Non‐Darcy Porous Medium Saturated with a Nanofluid

In this study, the effects of viscous dissipation on mixed convection heat and mass transfer along a vertical plate embedded in a nanofluid‐saturated non‐Darcy porous medium have been investigated. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis. The new far‐field thermal boundary condition that has been recently developed is employed to properly account for the effect of viscous dissipation in mixed convective transport in a porous medium. The nonlinear governing equations and the associated boundary conditions are transformed to a set of nonsimilar ordinary differential equations and the resulting system of equations is then solved numerically by an improved implicit finite‐difference method. The effect of the physical parameters on the flow, heat transfer, and nanoparticle concentration characteristics of the model are presented through graphs and the salient features are discussed. As expected, a significant improvement in the heat transfer coefficient is noticed because of the consideration of the nanofluid in the porous medium. With the increase in the value of the viscous dissipation parameter, a reduction in the non‐dimensional heat transfer coefficient is noted while an increase in the nanoparticle mass transfer coefficient is seen. Further, an increase in the mixed convection parameter lowered both the heat and nanoparticle mass transfer rates. Moreover, the increase in the Brownian motion parameter enhanced the nanoparticle mass transfer rate but it reduced the heat transfer rate in the boundary layer. A similar trend is also found with the thermophoresis parameter. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 397–411, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21083     

Non-similar analytic solution for MHD flow and heat transfer in a third-order fluid over a stretching sheet

This paper investigates the magnetohydrodynamic (MHD) flow and heat transfer characteristics in the presence of a uniform applied magnetic field. The boundary layer flow of a third-order fluid is induced due to linear stretching of a non-conducting sheet. The heat transfer analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing non-linear differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence of these solutions is discussed. Velocity and temperature distributions are shown graphically. The numerical values for the skin friction coefficient and the Nusselt number are entered in tabular form. Emphasis has been given to the variations of the emerging parameters such as third-order parameter, magnetic parameter, Prandtl number and the Eckert number. It is noted that the skin friction coefficient decreases as the magnetic parameter or the third grade parameter increases.     

Double dispersed bioconvective Casson nanofluid fluid flow over a nonlinear convective stretching sheet in suspension of gyrotactic microorganism

Microorganisms play a vital role in understanding the ecological system. The motions of micororganisms are self‐propelled while the impact of thermophoresis and Brownian motion property of nanoparticle shows more challenges in biotechnological and medical applications. The present problem is based on the understanding of double‐dispensed bioconvection for a Casson nanofluid flow over a stretching sheet. Suction phenomenon is introduced at the surface of the stretching sheet along with the convective boundary condition. The convection and movement of the microorganisms are assisted by an applied magnetic field, nonlinear thermal radiation, and first‐order chemical reaction. The governing equations are highly coupled and thus we used the spectral quasilinearization method to solve the governing equations. The study of the residual errors on the systemic parameters had given a confidence with the present results. The final outcomes are displayed through graphs and tables. The thermal dispersion coefficient shows a positive response in the temperature while a similar response is observed for the concentration with solutal dispersion coefficient. The response is reversible for the heat transfer rate at the surface with thermal dispersion coefficient. The density of the motile microorganism at the surface decreases with increase in the Casson number, thermal dispersion coefficient, and solute dispersion coefficient, while an opposite phenomenon was observed with increase in the density ratio of the motile microorganism.     

Numerical analysis of MHD nanofluid flow over a wedge,including effects of viscous dissipation and heat generation/absorption,using Buongiorno model

The key purpose of this article is to examine magnetohydrodynamics flow, generative/absorptive heat, and mass transfer of nanofluid flow past a wedge in the presence of viscous dissipation through a porous medium. The investigation is completely theoretical, and the present model expresses the influence of Brownian motion and thermophoresis using the nanofluid Buongiorno model. The fundamental model of partial differential equations is reframed into the structure of ordinary differential equations implementing the nondimensional similarity transformation, which are tackled through the fourth–fifth-order Runge–Kutta–Fehlberg algorithm together with the shooting scheme. The analysis of sundry nondimensional controlling parameters, such as magnetic parameter, Eckert number, heat generation/absorption parameter, porosity parameter, Brownian motion parameter, and thermophoresis parameter on velocity, temperature, and concentration profiles are discussed graphically. The effects of the physical factors on the rate of momentum and heat and mass transfer are also determined with appropriate analysis in terms of skin friction, Nusselt number, and Sherwood number. The outcomes illustrate that the local Nusselt number and local Sherwood number are reduced for higher values of the thermophoresis parameter. Besides, it is found that higher estimations of heat generation/absorption and viscous dissipation parameters increase temperature. Moreover, it is found that the temperature profile increases with the involvement of the Brownian motion parameter, while an opposite trend is observed in the concentration profile. A comparison is also provided for limiting cases to authenticate our obtained results.     

Actions of viscous dissipation and Ohmic heating on bidirectional flow of a magneto-Prandtl nanofluid with prescribed heat and mass fluxes

The present contribution determines the impacts of viscous dissipation and Ohmic heating with magnetic coating on Prandtl nanofluid flow driven by an unsteady bidirectionally moveable surface. Random motion of nanoparticles and thermophoretic diffusion are elaborated through a two-phase nanofluid model. The novelty of the investigation is fortified by prescribed heat flux and prescribed mass flux mechanisms. The appropriate combination of variables leads to a system of strong nonlinear ordinary differential equations. The formulated nonlinear system is then tackled by an efficient numerical scheme, namely, the Keller–Box method. Nanoliquid-temperature and mass-concentration distributions are conferred through various plots with the impacts of miscellaneous-arising parameters. The rates of heat and mass transferences are also discussed through tables. The thermal states of the nanomaterial and mass concentration are reduced for incremental amounts of the unsteady factor, ratio parameter, elastic parameter, and Prandtl fluid parameter. Moreover, escalating amounts of the Brownian parameter, Eckert number, magnetic factor, and thermophoresis parameter enhances the temperature of the nanoliquid. An error analysis is also presented to predict the efficiency of the method used for the computational work.     

HEAT TRANSFER AND HYDROMAGNETIC CONTROL OF FLOW EXIT CONDITIONS INSIDE OSCILLATORY SQUEEZED THIN FILMS

The influence of fluids inertia and the effects of the presence of a magnetic field normal to the direction of the flow of an electrically conducting fluid are studied on flow and heat transfer inside a nonisothermal and incompressible thin film undergoing oscillatory squeezing. The governing equations have been nondimensionalized and solved numerically. Further, the influence of the squeezing Reynolds number, thermal squeezing number, Hartmann number, and the squeezing frequency are determined. It is shown that flow instabilities appear at large squeezing Reynolds numbers and that the Nusselt number is affected by inertia effects as a result of increased squeezing Reynolds number. Further, it is found that flow instabilities are reduced when the magnetic field is introduced.     

Computational analysis of coupled radiation-convection dissipative non-gray gas flow in a non-Darcy porous medium using the Keller-box implicit difference scheme

The effects of thermal radiation parameter (F), transpiration (γ), Eckert number (Ec), Prandtl number (Pr), buoyancy (Grashof number Gr), a Darcy parameter (Re/Gr Da) and a Forcheimmer inertial parameter (Fs Re/Gr Da) on two-dimensional free convective flow of an optically thin, near-equilibrium, non-gray gas past a vertical surface in a non-Darcy porous medium, are studied using the robust Keller finite-difference technique incorporating Newtonian quasilinearization and block-tridiagonal elimination. The Darcy–Brinkman–Forcheimmer inertial-viscous flow model is used for the momentum equation and the Cogley–Vincenti–Giles formulation is adopted to simulate the radiation component of heat transfer. The one-dimensional thermal radiation model works successfully for gases in the optically thin limit. Pseudo-similarity transformations are employed to simplify the highly non-linear partial differential equations for momentum and heat transfer into numerically manageable pseudosimilar ordinary differential equations which are solved with Keller's box method. Effectively, the radiation contribution is seen to take the form of a linear temperature term Fθ coupled with the streamwise pseudo-similar variable ξ. Local wall shear stress and local heat transfer rates are systematically computed for a wide selection of radiation parameter F values. The results are presented graphically for different gases. © 1998 John Wiley & Sons, Ltd.