Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic （MHD） fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.

Hall and ion slip effects on peristaltic flow and heat transfer analysis with Ohmic heating

The peristaltic transport of a magnetohydrodynamic （MHD） fluid is exam- ined for both symmetric and asymmetric channels. Hall and ion slip effects are taken into account. The heat transfer is analyzed by considering the effects of viscous and Ohmic dissipations. The relevant flow problems are first modeled, and then the closed form solutions are constructed under the assumptions of long wavelength and low Reynolds number. The solutions are analyzed through graphical illustration. It is noted that the velocity increases but the temperature decreases with the increases in the Hall and ion slip parameters. The axial pressure gradient is less in magnitude in the presence of Hall and ion slip currents. The Hall and ion slip effects are to decrease the maximum pres- sure against which peristalsis works as a pump. The free pumping flux decreases with the increases in the Hall and ion slip parameters. The increases in the Hall and ion slip parameters result in an increase in the size of the trapped bolus.

Effects of slip, viscous dissipation and Joule heating on the MHD flow and heat transfer of a second grade fluid past a radially stretching sheet

The flow and heat transfer of an electrically conducting non-Newtonian second grade fluid due to a radially stretching surface with partial slip is considered. The partial slip is controlled by a dimensionless slip factor, which varies between zero （total adhesion） and infinity （full slip）. Suitable similarity transformations are used to reduce the resulting highly nonlinear partial differential equations into ordinary differential equations. The issue of paucity of boundary conditions is addressed and an effective numerical scheme is adopted to solve the obtained differential equations even without augmenting any extra boundary conditions. The important findings in this communication are the combined effects of the partial slip, magnetic interaction parameter and the second grade fluid parameter on the velocity and temperature fields. It is interesting to find that the slip increases the momentum and thermal boundary layer thickness. As the slip increases in magnitude, permitting more fluid to slip past the sheet, the skin friction coefficient decreases in magnitude and approaches zero for higher values of the slip parameter, i.e., the fluid behaves as though it were inviscid. The presence of a magnetic field has also substantial effects on velocity and temperature fields.

Second-order slip MHD flow and heat transfer of nanofluids with thermal radiation and chemical reaction

The effects of the second-order velocity slip and temperature jump boundary conditions on the magnetohydrodynamic （MHD） flow and heat transfer in the presence of nanoparticle fractions are investigated. In the modeling of the water-based nanofluids containing Cu and A1203, the effects of the Brownian motion, thermophoresis, and thermal radiation are considered. The governing boundary layer equations are transformed into a system of nonlinear differential equations, and the analytical approximations of the solutions axe derived by the homotopy analysis method （HAM）. The reliability and efficiency of the HAM solutions are verified by the residual errors and the numerical results in the literature. Moreover, the effects of the physical factors on the flow and heat transfer are discussed graphically.

Dual solutions of MHD stagnation point flow and heat transfer over a stretching/shrinking sheet with generalized slip condition

An analysis was made to study the steady momentum and heat transfer characteristics of a viscous electrically conducting fluid near a stagnation point due to a stretching/shrinking sheet in the presence of a transverse magnetic field and generalized slip condition. Two flow problems corresponding to the planar and axisymmetric stretching/shrinking sheet were considered. By means of similarity transformations, the obtained resultant nonlinear ordinary differential equations were solved numerically using a shooting method for dual solutions of velocity and temperature profiles. Some important physical features of the flow and heat transfer in terms of the fluid velocity, the temperature distribution, the skin friction coefficient and the local Nusselt number for various values of the controlling governing parameters like velocity slip parameter, critical shear rate, magnetic field, ratio of stretching/shrinking rate to external flow rate and Prandtl number were analyzed and discussed. An increase of the critical shear rate decreases the fluid velocity whereas the local Nusselt number increases. The comparison of the present numerical results with the existing literature in a limiting case is given and found to be in an excellent agreement.

Effects of chemical reactions on MHD micropolar fluid flow past a vertical plate in slip-flow regime

Heat and mass transfer effects on the unsteady flow of a micropolar fluid through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime are studied taking into account a homogeneous chemical reaction of the first order. A uniform magnetic field acts perpendicular to the porous surface absorb micropolar fluid with a suction velocity varying with time. The free stream velocity follows an exponentially increasing or decreasing small perturbation law. Using the approximate method, the expressions for the velocity microrotation, temperature, and concentration are obtained. Futher, the results of the skin friction coefficient, the couple stress coefficient, and the rate of heat and mass transfer at the wall are presented with various values of fluid properties and flow conditions.

Boundary Layer Stagnation-Point Slip Flow and Heat Transfer towards a Shrinking/Stretching Cylinder over a Permeable Surface

In this paper, the boundary layer stagnation-point slip flow and heat transfer towards a shrinking/stretching cylinder over a permeable surface is considered. The governing equations are first transformed into a system of non-dimensional equations via the non-dimensional variables, and then into self-similar ordinary differential equations before they are solved numerically using the shooting method. Numerical results are obtained for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles for some values of the governing parameters, namely the velocity slip parameter (α), the thermal slip parameter (β), the curvature parameter (γ) and the velocity ratio parameter (c/a). The physical quantities of interest are the skin friction coefficient and the local Nusselt number measured by f’’(0) and –θ’(0), respectively. The numerical results show that the velocity slip parameter α increases the heat transfer rate at the surface, while the thermal slip parameter β decreases it. On the other hand, increasing the velocity slip parameter α causes the decrease in the flow velocity. Further, it is found that the solutions for a shrinking cylinder (c/ac/a>0) case. Finally, it is also found that the values of f’’(0) and –θ’(0) increase as the curvature parameter γ increases.

Effects of Velocity and Thermal Slip Conditions with Radiation on Heat Transfer Flow of Ferrofluids

To analyze the thermal convection of ferrofluid along a flat plate is the persistence of this study. The two-dimensional laminar, steady, incompressible flow past a flat plate subject to convective surface boundary condition, slip velocity in the presence of radiation has been studied where the magnetic field is applied in the transverse direction to the plate. Two different kinds of magnetic nanoparticles, magnetite Fe3O4 and cobalt ferrite CoFe2O4 are amalgamated within the base fluids water and kerosene. The effects of various physical aspects such as magnetic field, volume fraction, radiation and slip conditions on the flow and heat transfer characteristics are presented graphically and discussed. The effect of various dimensionless parameters on the skin friction coefficient and heat transfer rate are also tabulated. To investigate this particular problem, numerical computations are done using the implicit finite difference method based Keller-Box Method.

Numerical Modeling of Non-Similar Mixed Convection Heat Transfer over a Stretching Surface with Slip Conditions

In this paper, the heat transfer effect on the steady boundary layer flow of a Casson fluid past a stretching surface in the presence of slip conditions was analyzed. The stretching surface is maintained at a constant temperature. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. The resulting equations are solved numerically by using the Kellerbox finite-difference method, and the expressions for velocity and temperature are obtained. They satisfy all imposed initial and boundary conditions and reduce to some well-known solutions for non-Newtonian fluids. Numerical results for velocity, temperature, skin friction and Nusselt number are shown in various graphs and discussed for embedded flow parameters. It is found that both velocity and temperature decrease with an increase of the Casson fluid parameter.

Scaling group transformation for MHD boundary layer flow over permeable stretching sheet in presence of slip flow with Newtonian heating effects

Taking into account the slip flow effects, Newtonian heating, and thermal radiation, two-dimensional magnetohydrodynamic （MHD） flows and heat transfer past a permeable stretching sheet are investigated numerically. We use one parameter group transformation to develop similarity transformation. By using the similarity transformation, we transform the governing boundary layer equations along with the boundary conditions into ordinary differential equations with relevant boundary conditions. The obtained ordinary differential equations are solved with the fourth-fifth order Runge-Kutta- Fehlberg method using MAPLE 13. The present paper is compared with a published one. Good agreement is obtained. Numerical results for dimensionless velocity, temperature distributions, skin friction factor, and heat transfer rates are discussed for various values of controlling parameters.

Stability Scrutinization of Agrawal Axisymmetric Flow of Nanofluid through a Permeable Moving Disk Due to Renewable Solar Radiation with Smoluchowski Temperature and Maxwell Velocity Slip Boundary Conditions

The utilization of solar energy is essential to all living things since the beginning of time.In addition to being a constant source of energy,solar energy(SE)can also be used to generate heat and electricity.Recent technology enables to convert the solar energy into electricity by using thermal solar heat.Solar energy is perhaps the most easily accessible and plentiful source of sustainable energy.Copper-based nanofluid has been considered as a method to improve solar collector performance by absorbing incoming solar energy directly.The goal of this research is to explore theoretically the Agrawal axisymmetric flow induced by Cu-water nanofluid over a moving permeable disk caused by solar energy.Moreover,the impacts of Maxwell velocity and Smoluchowski temperature slip are incorporated to discuss the fine points of nanofluid flow and characteristics of heat transfer.The primary partial differential equations are transformed to similarity equations by employing similarity variables and then utilizing bvp4c to resolve the set of equations numerically.The current numerical approach can produce double solutions by providing suitable initial guesses.In addition,the results revealed that the impact of solar collector efficiency enhances significantly due to nanoparticle volume fraction.The suction parameter delays the boundary layer separation.Moreover,stability analysis is performed and is found that the upper solution is stable and physically trustworthy while the lower one is unstable.

Condensation Heat Transfer in Horizontal Non-Circular Microchannels

This investigation contributes to a better understanding of condensation heat transfer in horizontal non-circular microchannels. For this purpose, the conservation equations of mass, momentum and energy have been numerically solved in both phases (liquid and vapor), and all the more, so the film thickness analytical expression has been established. Numerical results relative to variations of the meniscus curvature radius, the condensate film thickness, the condensation length and heat transfer coefficients, are analyzed in terms of the influencing physical and geometrical quantities. The effect of the microchannel shapes on the average Nusselt number is highlighted by studying condensation of steam insquare, rectangular and equilateral triangular microchannels with the same hydraulic diameter of 250 μm.

不同分数导数下Maxwell杂化纳米流体流动和传热变化的灵敏度分析

研究多孔介质中垂直拉伸板引起的分数阶Maxwell杂化纳米流体流动与传热现象,并考虑二阶滑移边界条件.利用分数阶剪应力和分数阶Fourier定律构建边界层控制方程.然后采用有限差分结合L1算法进行数值求解,并详细讨论分数导数参数增大时,各物理参数对该流体流动与传热影响的灵敏度变化.结果表明,Darcy数和滑移参数对平均表面摩擦系数的影响,以及滑移参数对平均Nusselt数的影响,对速度分数导数比对温度分数导数更敏感.Darcy数对平均Nusselt数的影响只对温度分数导数敏感,与速度分数导数几乎无关.此外,一阶滑移参数比二阶滑移参数对流动和传热的影响更大.

Analysis of the heat transfer in unsymmetrically heated triangular microchannels in slip flow regime

A theoretical analysis of heat transfer characteristics is presented for the fully developed laminar flow of the incompressible gas in the triangular microchannels heated unsymmetrically with constant axial heat flux. Through solving the energy equation with temperature jump boundary conditions in slip flow regime by virtue of a computation- oriented method of the orthonormal function analysis, the dimensionless temperature profiles and the average Nusselt number for various thermal boundary conditions are obtained. The effects of Knudsen number, aspect ratio, and thermal boundary conditions on the heat transfer are discussed. The calculated results show that the orthonormal function method can be used to study the heat transfer characteristics of the unsymmetrically heated triangular microchannels. The average Nusselt number in triangular microchannels is lower for slip flow than for no-slip flow, and decreases with increasing Knudsen number. The aspect ratios and thermal boundary conditions of triangular microchannels have significant influences on the change of average Nusselt numbers with the increase in the Knudsen number. For the equilateral triangular microchannels, the decrease of the Nusselt number ratio due to temperature jump is smaller at large Knudsen number and larger at small Knudsen number on the boundary condition of bottom wall heated alone as compared with the one on the boundary condition of two heated hypotenuse walls. The correlations of the average Nusselt number with the Knudsen number for equilateral triangular microchannels are obtained.

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.

Study at Two Dimensions of Thermal Transfer through a Fibers Panel Subjected to Climatic Constraints in Dynamic Frequency Regulations Established

From resolution of two-dimensional equation of heat in dynamic frequency regime, we have plotted evolution curves of temperature according to depth of material or in lateral direction. They will allow us to evaluate thermal behavior of towed material. Aim of study is to use fibers as a thermal insulating material by proposing a method for determining effective thermal insulation layer in dynamic frequency regime.

Soil Nature Effect Investigation on the Ground-to-Air Heat Exchanger for the Passive Cooling of Rooms

The building sector consumes much energy either for cooling or heating and is associated to greenhouse gas emissions. To meet energy and environmental challenges, the use of ground-to-air heat exchangers for preheating and cooling buildings has recently received considerable attention. They provide substantial energy savings and contribute to the improvement of thermal comfort in buildings. For these systems, the ground temperature plays the main role. The present work aims to investigate numerically the influence of the nature of soil on the thermal behavior of the ground-to-air heat exchanger used for building passive cooling. We have taken into account in this work the influence of the soil nature by considering three types of dry soil: clay soil, sandy-clay soil and sandy soil. The mixed convection equations governing the heat transfers in the earth-to-air heat exchanger have been presented and discretized using the finite difference method with an Alternate Direction Implicit (ADI) scheme. The resulting algebraic equations are then solved using the algorithm of Thomas combined with an iterative Gauss-Seidel procedure. The results show that the flow is dominated by forced convection. The examination of the sensitivity of the model to the type of soil shows that the distributions of contours of streamlines, isotherms, isovalues of moisture are less affected by the variations of the nature of soil through the variation of the diffusivity of the soil. However, it is observed that the temperature values obtained for the clay soil are higher while the sandy soil shows lower temperature values. The values of the ground-to-air heat exchanger efficiency are only slightly influenced by the nature of the soil. Nevertheless, we note a slightly better efficiency for the sandy soil than for the sandy-clayey silt and clayey soils. This result shows that a sandy soil would be more suitable for geothermal system installations.

Transient Hydromagnetic Stagnation-Point Flow across a Vertical Surface with Partial Slip in a Chemically Reactive Medium

A numerical study of partial slip boundary condition is investigated. The stagnation-point flow problem involving some physio-chemical parameters has been elucidated. The process involves developing a multivariate mathematical model for the flow and transforming it into a coupled univariate equation. Key parameters of interest in the study are the buoyancy force, the surface stretching, the unsteadiness, the radiation, the dissipation effects, the slip effects, the species reaction and the magnetic field parameters. It is concluded that the impact of physio-chemical factors significantly alters the kinematics of the flow in order to optimally achieve desired product characteristics.

分数阶Maxwell纳米流体二阶滑移流动与热传递分析

在考虑二阶滑移边界的影响下,对多孔介质中垂直拉伸板引起的分数阶Maxwell纳米流体流动与热传递特性开展分析研究。利用分数阶剪切应力和分数阶Cattaneo热通量模型构建二维边界层控制方程,采用有限差分和L1算法进行数值求解。对不同物理参数下的速度、温度、平均表面摩擦系数和平均Nusselt数的变化趋势进行图形化分析。研究结果表明,牛顿流体的流动性能和热传递优于粘弹性流体;速度分数阶导数参数和温度松弛时间会恶化对流和热传递,而温度分数阶导数参数和速度松弛时间则促进对流和热传递;滑移参数降低了流体初始速度,一阶滑移参数对流动和热传递的影响大于二阶滑移参数;流动和热传递对各物理参数的敏感度随该物理参数的增大而下降。