Unsteady MHD Mixed Convective Boundary‐Layer Slip Flow and Heat Transfer with Thermal Radiation and Viscous Dissipation

A numerical analysis has been carried out to investigate the problem of MHD boundary‐layer flow and heat transfer of a viscous incompressible fluid over a moving vertical permeable stretching sheet with velocity and temperature slip boundary condition. A problem formulation is developed in the presence of radiation, viscous dissipation, and buoyancy force. A similarity transformation is used to reduce the governing boundary‐layer equations to coupled higher‐order nonlinear ordinary differential equations. These equations are solved numerically using the fourth‐order Runge–Kutta method along with shooting technique. The effects of the governing parameters such as Prandtl number, buoyancy parameter, slip parameter, magnetic parameter, Eckert Number, suction, and radiation parameter on the velocity and temperature profiles are discussed and shown by plotting graphs. It is found that the temperature is a decreasing function of the slip parameter S_T. The results also indicate that the cooling rate of the sheet can be improved by increasing the buoyancy parameter. In addition the numerical results for the local skin friction coefficient and local Nusselt number are computed and presented in tabular form. The numerical results are compared and found to be in good agreement with previously published results on special cases of the problem. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res, 43(5): 412–426, 2014; Published online 3 October 2013 in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21086     

Thermal slip and radiative heat transfer effects on electro‐osmotic magnetonanoliquid peristaltic propulsion through a microchannel

A mathematical study is described to examine the concurrent influence of thermal radiation and thermal wall slip on the dissipative magnetohydrodynamic electro‐osmotic peristaltic propulsion of a viscous nanoliquid in an asymmetric microchannel under the action of an axial electric field and transverse magnetic field. Convective boundary conditions are incorporated in the model and the case of forced convection is studied, that is, thermal and species (nanoparticle volume fraction) buoyancy forces neglected. The heat source and sink effects are also included and the diffusion flux approximation is employed for radiative heat transfer. The transport model comprises the continuity, momentum, energy, nanoparticle volume fraction, and electric potential equations with appropriate boundary conditions. These are simplified by negating the inertial forces and invoking the Debye–Hückel linearization. The resulting governing equations are reduced into a system of nondimensional simultaneous ordinary differential equations, which are solved analytically. Numerical evaluation is conducted with symbolic software (MATLAB). The impact of different control parameters (Hartmann number, electro‐osmosis parameter, slip parameter, Helmholtz–Smoluchowski velocity, Biot numbers, Brinkman number, thermal radiation, and Prandtl number) on the heat, mass, and momentum characteristics (velocity, temperature, Nusselt number, etc) are presented graphically. Increasing Brinkman number is found to elevate temperature magnitudes. For positive Helmholtz–Smoluchowski velocity (reverse axial electrical field) temperature is strongly reduced, whereas for negative Helmholtz–Smoluchowski velocity (aligned axial electrical field), it is significantly elevated. With increasing thermal slip, nanoparticle volume fraction is also increased. Heat source elevates temperatures, whereas heat sink depresses them, across the microchannel span. Conversely, heat sink elevates nanoparticle volume fraction, whereas heat source decreases it. Increasing Hartmann (magnetic) parameter and Prandtl number enhance the nanoparticle volume fraction. Furthermore, with increasing radiation parameter, the Nusselt number is reduced at the extremities of the microchannel, whereas it is elevated at intermediate distances. The results reported provide a good insight into biomimetic energy systems exploiting electromagnetics and nanotechnology, and, furthermore, they furnish a useful benchmark for experimental and more advanced computational multiphysics simulations.     

Hydromagnetic non‐Newtonian nanofluid transport phenomena from an isothermal vertical cone with partial slip: Aerospace nanomaterial enrobing simulation

In this article, the combined magneto‐hydrodynamic heat, momentum, and mass (species) transfer in external boundary layer flow of Casson nanofluid from a vertical cone surface with convective conditions under an applied magnetic field is studied theoretically. The effects of Brownian motion and thermophoresis are incorporated in the model in the presence of both heat and nanoparticle mass transfer convective conditions. The governing partial differential equations (PDEs) are transformed into highly nonlinear, coupled, multidegree, nonsimilar PDEs consisting of the momentum, energy, and concentration equations via appropriate nonsimilarity transformations. These transformed conservation equations are solved subject to appropriate boundary conditions with a second‐order, accurate finite difference method of the implicit type. The influences of the emerging parameters, that is, magnetic parameter (M), Casson fluid parameter (β), Brownian motion parameter (Nb), thermophoresis parameter (Nt), Lewis number (Le), Prandtl number (Pr), velocity slip (S_f) and thermal slip (S_T) on velocity, temperature, and nanoparticle concentration distributions is illustrated graphically and interpreted at length. Validation of solutions with a Nakamura tridiagonal method has been included. The study is relevant to enrobing processes for electrically conductive nanomaterials, of potential use in aerospace and other industries.     

Gaseous slip flow affected by inclined low magnetic field using second‐order boundary conditions

In this study, asymptotic solutions of a near continuum gaseous slip flow in two‐dimensional rectangular microchannels under the effect of electromagnetic force are presented. An inclined magnetic field was assumed in this study. Nondimensional equations were obtained that relate the pressure ratio, Mach number, magnetic Reynolds number, magnetic force number, and Reynolds number. The asymptotic solutions for the compressible, laminar, and steady flow were obtained by applying second‐order slip velocity and temperature jump wall boundary conditions. It was found that the electric and magnetic field with inclined angle had significant effects on the flow properties. The solutions obtained here using the second‐order boundary conditions result in tangible improvement over those obtained using first‐order boundary conditions. We compared our solutions against the numerical solutions that were provided in the literature and showed that our solutions were in good agreement with the numerical solution.     

Behavior of slip boundary conditions for the flow of nanofluid in the presence of an inclined magnetic field

The inflated heat transport rate of nanofluids is of great interest to researchers. Conviction of nanosuspension with an enhanced model under the consideration of inclined magnetic field is also vital for the enhancement of heat transport rate. Therefore, in this article, an inclined magnetic field has been considered during a boundary layer flow over an extending sheet, with the sheet being permeable. The sequels of heat radiation, thermophoresis, and Brownian parameters are also taken into consideration in this study. The importance of the study is the slip boundary conditions used for velocity, temperature, and concentration. A set of nonlinear partial differential equations is transformed into ordinary differential equations with a suitable choice of similarity variables. The set of first-order differential equations is quite difficult to solve analytically. Therefore, the numerical Runge-Kutta-Fehlberg method, accompanied with shooting technique, is used. The results of the physical components characterizing the flow phenomena, such as magnetic parameter, thermal radiation, thermophoresis, Brownian parameter, and slip parameters, are elaborated through graphs. The numerical results of physical quantities of attention are presented in tables. The existing outcome conforms to that of the previous published result in a particular case.     

Unsteady squeezed Casson nanofluid flow by considering the slip condition and time-dependent magnetic field

The present flow problem investigates the incompressible and squeezed flow between two parallel plates. The mathematical formulation includes the constitutive equations of Casson nanofluid, which is treated as a lubricant. Brownian movement, slip condition, and thermophoretic mechanisms are also considered. The formulated model is tackled by Runge-Kutta-Fehlberg fourth- and fifth-order numerical scheme joint with shooting criteria. Momentum, thermal, and mass species behavior is executed by plots of distinct physical constraints values. It is found that the velocity component is boosted for the larger squeezed parameter whereas the temperature component shows the same behavior for Brownian motion and thermophoresis parameter. Near the lower half of the plate, velocity increases for the slip parameter whereas it decreases for magnetic and Casson parameters.     

Hall current and ion‐slip effects on free convection flow in a vertical microchannel with an induced magnetic field

The steady fully developed hydromagnetic flow of a viscous incompressible and electrically conducting fluid in a vertical microchannel has been studied taking into account the influence of Hall current, ion‐slip effects and an induced magnetic field. Exact solutions for the governing equations responsible for the flow formation are obtained by the method of the undetermined coefficient and presented graphically. It is found that in the presence of the ion‐slip effect, both primary and secondary components of fluid velocity increase with the Hall parameter for symmetric as well as asymmetric heating of the microchannel surfaces. Also, the magnetic field supports flow along the secondary flow direction while the reverse impact is observed along the primary flow direction.     

Heat transfer enhancement by crossflow‐induced vibration

A new method of heat transfer enhancement by water crossflow‐induced vibration is presented. A heat transfer element which involves elastic tube bundles has been designed. This system has excellent response characteristics of vibration to the crossflow. A triangular pole device for producing pulsating flow was adopted. This device can induce vibration in a fixed range of frequencies and has a profound influence on heat transfer augmentation. For the constant heat flux boundary condition, experiments are carried out on the heat transfer characteristics of elastic tube bundles augmented by flow‐induced vibration in a water crossflow. Compared with static tube bundles, the out‐tube average convective heat transfer coefficients of the elastic tube bundles are increased by 100–150% under the condition of crossflow‐induced vibration. Dimensionless equations describing the outside heat transfer coefficient for the elastic tube bundles were acquired. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(4): 211–218, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20012     

横管降膜过程中液膜内流动和传热特性分析

横管降膜流动过程中,液膜速度和温度及其分布是影响传热传质的关键因素,由于实验研究方法的局限性,实验研究结果一般只是液膜内各参数的平均值,而液膜内部的速度和温度具体分布特性却很难得到。借助FLUENT软件,利用VOF模型研究了橫管外液膜速度和温度及其分布特性。通过建立三维数理模型,模拟研究了常温常压下,橫管外液膜无相变条件下横管液膜的传热过程,并从边界层的角度解释了液膜波动对传热过程的影响。     

混合对流条件下浮升力对环形通道中流动及传热的影响

讨论了混合对流条件下环形通道中浮升力对流动及传热的影响。实验时用LDA测量了水向下流过竖直环形通道时的平均流速和湍流强度。对于逆浮升力方向的流动情况，湍流速度脉动和湍流剪切应力都因浮升力的影响而增加，从而传热得到了增强。当浮升力的影响特别大时。靠近环形内壁的流动出现反向流，在这种情况下即使流动在无浮升力影响时是层流。湍流也会由于浮升力的存在而产生，传热维持较好的效果。     

Cattaneo–Christov heat flux model for heat transfer of Marangoni boundary layer flow in a copper–water nanofluid

The Cattaneo–Christov heat flux is first utilized to explore the heat transfer characteristics of Marangoni boundary layer flow in a copper–water nanofluid. The Marangoni boundary layer flow is driven by exponential temperature. Five different types of nanoparticle shapes including sphere, hexahedron, tetrahedron, column and lamina are considered for the copper–water nanofluid. The nonlinear system of partial differential equations is reduced by similarity transformations and then solved numerically by the shooting method. It is found that sphere nanoparticle has better heat transfer enhancement than other nanoparticle shapes and both the temperature and the thickness of the thermal boundary layer are lower for the Cattaneo–Christov heat flux model than the classical Fourier's law of heat conduction.     

The study of buoyancy influence on mean flow and heat transfer under conditions of mixed convection in annular channels

Laser Doppler anemometry (LDA) measurements are reported on mean flow and turbulence in water as it flows downwards through a long vertical passage of annular cross‐section having an inner surface which can be uniformly heated and an outer one which is adiabatic. Under buoyancy‐opposed conditions, which can be achieved by heating the core and operating at a reduced mass flow rate, the flow near the inner surface is retarded, turbulent velocity fluctuations and turbulent shear stress are increased and the effectiveness of heat transfer is enhanced. When the influence of buoyancy is very strong, flow reversal occurs near the inner surface. Under such conditions, turbulence is produced very readily and the heat transfer process remains very effective, even when the Reynolds number is reduced to values at which the flow is laminar in the absence of heating. The measurements of turbulence in buoyancy‐opposed flow made in this study provide direct confirmation of the validity of the ideas currently used to explain the influences of buoyancy on mixed convection in vertical passages. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(1): 9–17, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20041     

Studying the effect of radiation on thin‐film sprayed nanofluid flow with heat transfer

In this paper, we discuss thin‐film nanofluid sprayed in non‐Darcian, magnetohydrodynamic, embedding in a porous medium flow and thermal radiation with heat transfer generation on a stretching cylinder. The spray rate is a function of film size. A comparative study is made for the nanoparticles, namely, copper oxide , alumina oxide (), and iron oxide . The governing continuity, momentum, and energy equations of the nanofluid are reduced using similarity transformation and converted into a system of nonlinear ordinary differential equations, which are solved numerically. Numerical solutions are obtained for the velocity and temperature fields as well as for the skin‐friction coefficient and Nusselt number. The pressure distribution and spray rate are also calculated. The results are presented in graphical forms to study the effects of various parameters.     

Radiation and slip effects on MHD point flow of nanofluid towards a stretching sheet with melting heat transfer

In the present paper, the melting heat transfer of a nanofluid over a stretching sheet is investigated. Magnetohydrodynamic stagnation point flow with thermal radiation and slip effects is considered for this study. The governing model of the flow is solved by Runge–Kutta fourth-order method using appropriate similarity transformations. Temperature and velocity fields are presented for various flow pertinent parameters. Nondimensional physical parameters such as Prandtl number, radiation parameter, Brownian motion parameter, Lewis number, thermophoresis parameter, magnetic parameter, and melting parameter on fluid velocity, heat, concentration, skin friction, Sherwood number, and Nusselt number are presented graphically and discussed numerically. Heat transfer rate can be increased by increasing slip, melting, or radiation parameter. Mass transfer increases for greater values of melting parameter or slip parameter while radiation parameter shows the opposite impact on mass transfer.     

Unsteady squeezing flow of water‐based nanofluid between two parallel disks with slip effects: Analytical approach

The squeezing flow of an unsteady water‐based nanofluid between two parallel disks has been analyzed in the current study. Thermal and solutal buoyancy along with heat source enhance the flow phenomena of free convective flow through a porous medium. In addition to that velocity slip and temperature slip are also accounted for in the boundary conditions. The similarity transformation is adopted to formulate the governing equations that convert the complex partial differential equations (PDEs) to nonlinear ordinary differential equations (ODEs). These transformed equations are handled analytically by using the variation parameter method (VPM). For computational purposes, the fixed numeric values of physical parameters are used and their behaviors are shown by means of graphs. The calculated results for the physical quantities of interest are shown in tables. The conformity of the solution is obtained in comparison to an earlier study in a particular case. The major findings are (i) the velocity profile has distinct variations, which are separated by the middle layer of the channel and (ii) enhancement in the heat transfer coefficient is noted due to the interaction of buoyancy parameter.     

Numerical study of ferrofluid flow and heat transfer in the presence of a non‐uniform magnetic field in rectangular microchannels

This paper presents a numerical investigation of the hydro‐thermal behavior of a ferrofluid in rectangular minichannels in the presence of a non‐uniform magnetic field using a two‐phase mixture model and control volume technique. Effects of increasing the diameter of nanoparticles, and channel aspect ratio have also been studied. It is concluded that the magnetic field with a negative gradient increases the Nusselt number and the rate of this increment depends on the channel aspect ratio. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21004     

An experimental study of heat transfer in an open thermosyphon

An experimental study was performed on heat transfer of an open thermosyphon with constant wall heat flux. Water and aqueous glycerin were used as working fluids. The experimental range of modified Rayleigh number was 1 × 10³ < Ra_m < 3 × 10⁵. The average and local heat transfer coefficients, vertical temperature distributions of the tube wall and fluid at the centerline of the tube, and temperature fluctuations of the fluid were measured. Flow patterns were observed by adding tracer powder to the fluid. Fluid velocities were measured by laser Doppler velocimeter. Experimental results indicate that, for a water thermosyphon, there are three regimes where different heat transfer characteristics and flow patterns occur. For 1 × 10³ < Ra_m < 3 × 10³, the flow was laminar and the thermal boundary layer reached the center of the tube. Heat was exchanged between the wall and descending flow. Wall temperature increased in the downward direction. For 4 × 10³ < Ra_m < 3 × 10⁴, no turbulence was observed in the flow and the thermal boundary layer was localized in the vicinity of the wall. The wall temperature increased upward. For 3 × 10⁴ < Ra_m < 3 × 10⁵, flow was considerably disturbed by the mixing of upward and downward flow in the upper part of the tube. However, the flow was laminar in the lower part of the tube. Reduction of the flow rate induced by the flow mixing at high Ra_m can be one of the major causes of the deterioration of heat transfer from Lighthill's theory. © 2001 Scripta Technica, Heat Trans Asian Res, 30(4): 301–312, 2001     

Differential transform solution for Hall and ion‐slip effects on radiative‐convective Casson flow from a stretching sheet with convective heating

Magnetohydrodynamic (MHD) materials processing is becoming increasingly popular in the 21st century as it offers significant advantages over conventional systems, including improved manipulation of working fluids, reduction in wear, and enhanced sustainability. Motivated by these developments, the present work develops a mathematical model for Hall and ion‐slip effects on non‐Newtonian Casson fluid dynamics and heat transfer toward a stretching sheet with a convective heating boundary condition under a transverse magnetic field. The governing conservation equations for mass, linear momentum, and thermal (energy) are simplified with the aid of similarity variables and Ohm's law. The emerging nonlinear‐coupled ordinary differential equations are solved with an analytical technique known as the differential transform method. The impact of different emerging parameters is presented and discussed with the help of graphs and tables. Generally, aqueous electroconductive polymers are considered, for which a Prandtl number of 6.2 is employed. With increasing Hall parameter and ion‐slip parameter, the flow is accelerated, whereas it is decelerated with greater magnetic parameter and rheological (Casson) fluid parameter. Skin friction is also decreased with greater magnetic field effect, whereas it is increased with stronger Hall parameter and ion‐slip parameter values.     

Magnetohydrodynamic boundary layer flow of nanofluid with variable chemical reaction in a radiative vertical plate

The nanotechnology-based nanofluid has extraordinary prospects in heat transfer engineering. Analysis of these applied nanofluids can yield the appropriate combinations of various useful physical parameters. In the present study, the incompressible boundary layer flow of a nanofluid in the presence of the variable chemical reaction, temperature-dependent viscosity, hydromagnetic force, and the radiation past an infinite vertical plate has been investigated. The governing nanofluid equations are simplified to ordinary differential equations, which are solved using the function bvp4c from MATLAB. The effects of the physical parameters including the similarity parameter, magnetic field, two dimensionless constant temperatures, Schmidt number, local Grashof number, radiation parameter, local chemical reaction parameter, kinematic diffusion parameter, and temperature-independent kinematic diffusion parameter on the velocity, temperature, concentration and the local Nusselt number are demonstrated. The results show that as the magnetic field parameter increases, the heat transfer decreases, and the increase of the radiation parameter yields the opposite effect. The kinematic diffusion and the chemical reaction parameters greatly stimulate the concentration of nanofluid and reduce the heat transfer.