Entropy generation on MHD flow and convective heat transfer in a porous medium of exponentially stretching surface saturated by nanofluids

This paper examines the unsteady boundary layer magnetohydrodynamic flow and convective heat transfer of an exponentially stretching surface saturated by nanofluids in the presence of thermal radiation. The combined effect of stratifications (thermal and concentration) in the unsteady boundary layer flow past over a stretching surface embedded in a porous medium is analyzed. The system of coupled nonlinear differential equations are solved numerically by developing finite difference scheme together with the Newton’s linearization technique, which allows us to control nonlinear terms smoothly. The study shows that the thermal boundary layer thickness significantly increases with the increase of Brownian motion, thermophoresis number and magnetic field strength. The unsteadiness behavior of the flow of nanofluid has reducing effect on both momentum and thermal boundary layer thickness. The Brownian motion has controlling effect on nanoparticle migration. The entropy generation by means of Bejan number has strong impact on the applied magnetic field, dissipation of energy, thermal radiation and Biot number.     

Flow and boundary layer development in straight core annular diffusers

This paper is mainly concerned with a numerical study of flow and boundary layer development in straight core annular diffusers using a finite difference method and marching integration technique. To this end, predictions have been made for four cone angles. Velocity profiles, displacement thickness, momentum thickness, shape factor, kinetic energy flux parameter, pressure recovery coefficients and effectiveness have been computed. The predicted pressure recovery coefficients have been compared with an experimental investigation. It is found that the agreement between predicted and experimental results is quite satisfactory.     

多孔泡沫金属中指数规律变热流平板表面的层流对流传热分析

采用Brinkman-Forchheimer-extended Darcy流动模型和局部非热平衡传热模型(双温度模型),对指数规律变热流密度条件下的多孔泡沫金属中平板表面的层流对流传热进行了分析,并得出了平板表面的热边界层的厚度和局部的对流传热系数的表达式。结果发现:平板表面的热边界层的厚度发展沿流动方向逐渐增大,但是增大的趋势由迅速趋向平缓;局部对流传热系数沿流动方向逐渐减小,而后趋于稳定。最后推导出了局部的对流传热Nusselt数的准则方程。     

Finite difference analysis for developing laminar flow in circular tubes applied to forced and combined convection

The complete two-dimensional partial differential equations for developing laminar flow in a circular tube have been treated by a finite difference analysis. Property variation with temperature, especially that of viscosity, is allowed for in a flexible manner. The continuity and momentum equations, and then the energy equations, are solved by direct elimination at each axial step, and marching procedure used in the axial direction. A new technique is that the stepwise energy balance is rigidly satisfied throughout by using it as a constituent equation in place of the ‘explicit’ wall thermal boundary condition normally used. The analysis predicts the complete developing hydrodynamic and thermal fields, together with friction factors and heat transfer coefficients. It has been tested for a range of fluid velocity and thermal boundary conditions and for various fluids, including high viscosity oils, water and air. Data for constant wall heat flux have already been published. ^1,2 Predictions for constant wall temperature presented here are for forced and combined convection and are compared with experimental data of Test³ and Zeldin and Schmidt⁴.     

Flat plate drag reduction by turbulence manipulation

The major objective of the present paper is to delineate the conditions under which a turbulent boundary layer manipulated by the insertion of a passive object may lead to a lower overall drag than in the unmanipulated flow. It is pointed out that almost any device inserted in the boundary layer will lead to a lowerskin friction drag. Experimental evidence is presented to support this conclusion, which is most easily thought of as characterizing “wall wakes”. However when the streamwise extent of the manipulator is not small, the no-slip condition forced on the manipulator boundary modifies the flow through what is here described as the “blade” effect. The presence of this effect may be inferred from experimental data which unambiguously show that a flat plate with a chordc of the order of the boundary layer thicknessδ produces the same order of skin friction reduction as a cylindrical rod with a higher wake momentum thicknessϑ _w . As in general both blade and wake effects are operating simultaneously, available data are analysed in the plane formed by the two variablesc/δ andϑ _w /δ. This analysis shows that the net drag reduction, if it occurs at all, is quite small, and that its realization demands a blade chord (at zero incidence) larger than about 40ϑ _w . Finally, it is pointed out that if, as often claimed, such manipulators effect a permanent decrease in boundary layer momentum thickness, then sufficiently far downstream where the boundary layer may be expected to have returned to equilibrium, the local skin friction coefficient at any station must be higher than in the unmanipulated flow at the same station because of the lower momentum thickness Reynolds number. It therefore follows that any possible reduction in drag due to the manipulator can only be achieved for certain limited downstream lengths behind the manipulator.     

Effects of flow and colony morphology on the thermal boundary layer of corals

The thermal microenvironment of corals and the thermal effects of changing flow and radiation are critical to understanding heat-induced coral bleaching, a stress response resulting from the destruction of the symbiosis between corals and their photosynthetic microalgae. Temperature microsensor measurements at the surface of illuminated stony corals with uneven surface topography (Leptastrea purpurea and Platygyra sinensis) revealed millimetre-scale variations in surface temperature and thermal boundary layer (TBL) that may help understand the patchy nature of coral bleaching within single colonies. The effect of water flow on the thermal microenvironment was investigated in hemispherical and branching corals (Porites lobata and Stylophora pistillata, respectively) in a flow chamber experiment. For both coral types, the thickness of the TBL decreased exponentially from 2.5 mm at quasi-stagnant flow (0.3 cm s⁻¹), to 1 mm at 5 cm s⁻¹, with an exponent approximately 0.5 consistent with predictions from the heat transfer theory for simple geometrical objects and typical of laminar boundary layer processes. Measurements of mass transfer across the diffusive boundary layer using O₂ microelectrodes revealed a greater exponent for mass transfer when compared with heat transfer, indicating that heat and mass transfer at the surface of corals are not exactly analogous processes.     

Non-similarity solution and correlation of transient heat transfer in laminar boundary layer flow over a wedge

With a comprehensive and rigorous method, this paper has successfully examined the transient heat transfer in a steady and two-dimensional (2D) laminar boundary layer flow on a wedge with sudden change of thermal boundary conditions of uniform wall temperature (UWT) and heat flux (UHF). Additionally, a correlation of unsteady forced convection was also formulated through an exact solution of transient heat conduction (ξ=0) and the similarity solutions of a steady forced convection on a wedge (ξ=1) in this study. Particularly, for the wedge with −0.198838?ξ?1, the deviation of the wall temperatures estimated by correlation is less than 7.5% within full time of 0?ξ?1 comparing with numerical results in the case of UHF ranging from Pr=10⁻⁴ to 10⁴.     

Suppressing a Laminar Flow Separation Zone by Spark Discharge at Mach Number M = 1.43

The influence of flow perturbations generated by an electric discharge on the region of interaction between a shock wave and laminar boundary layer in the flow on a flat plate at a Mach number of M = 1.43 has been experimentally studied. The oblique shock wave generated by a wedge mounted above the plate induced separation of the flow, while perturbations in the flow were introduced by a spark discharge on the model plate surface. It is established that the discharge leads to the formation of turbulent and thermal spots. The turbulent spot suppresses the separation zone, while the thermal spot leads to a local increase in the boundary layer thickness in the interaction zone.

     

Thermal interaction between laminar film condensation and forced convection along a conducting wall

Summary A theoretical analysis is presented to investigate the thermal interaction between laminar film condensation of a saturated vapor and a forced convection system separated by a heat conducting wall. In this work, the effect of the wall thermal resistance is considered. It is assumed that the countercurrent boundary layer flow is formed on the two sides. Governing boundary layer equations together with their corresponding boundary conditions for film condensation and forced convection are all cast into dimensionless forms by using the non-similarity transformation. The resulting system of equations is solved by using the local non-similarity method in conjunction with the fourth order Runge-Kutta method in conjunction with the Nachtsheim-Swigert iteration scheme. The total heat flux through the wall and the wall temperature distribution are determined. The present results show that the effect of the forced convection Prandtl number Pr _c is not negligible for large values of the thermal resistance ratioA ^*, and the effect ofA ^* and Pr _c on the overall heat transfer through the wall is more pronounced than that of the Jakob number and film Prandtl number.     

Geometrical size effect on the interface diffusion of micro solder joint in electro-thermal coupling aging

This paper investigates the influence of diffusion layer (solder layer) thickness (δ) on interface diffusion in both thermal aging and electro-thermal coupling aging. The different δ (δ = 60, 120 and 240 μm) of Cu/Sn–3.0Ag–0.5Cu (SAC305)/Cu butt solder joints are used. The results indicate that the geometrical size (solder layer thickness) of solder joint has significant effect on element diffusion behavior. The diffusion coefficient, time exponent, element concentrations and diffusion flux are greatly dependent upon δ. The effects of δ on the interface diffusion is different between thermal aging and electro-thermal coupling aging, due to driving force for diffusion is different. During thermal aging, concentration gradient is the main driving force of diffusion, and diffusion coefficient, time exponent and diffusion flux are relatively low for a thin solder layer. However, under electro-thermal coupling condition, the electron wind force provides the dominating driving force for diffusion, and diffusion coefficient and diffusion flux of thin δ are significantly larger than the thick ones. The Cu concentration of the area near interface is relatively high for a thin solder layer in both tests. Under the same experimental temperature, the effects of δ on the electro-thermal coupling aging are more obvious than thermal aging.     

An experimental study of frost formation on a horizontal cylinder under cross flow

Frost layers formed on the front and rear surfaces of a horizontal cylinder during cross flow are found to be thicker than those at the top and bottom surfaces where the flow separation is nearly initiated. This observation was obtained in an experimental study carried out to examine frost formation on a horizontal cylinder given a cross flow condition. The thickness of the frost layer and the temperature distribution in the cylinder were measured for various experimental conditions. The local heat flux around the cylinder and the effective thermal conductivity of the frost layer were likewise evaluated, while thickness and surface temperature of the frost layer around the cylinder were measured periodically. These measurements were obtained by varying the Reynolds number, temperature, and humidity. The dew point temperature of the inlet air, however, was kept below the freezing point throughout the experiment. Results also reveal that inlet air velocity, temperature, and humidity affect thickness and thermal conductivity of the frost layer.     

Analysis of Film Condensation Along a Vertical Flat Plate Under Sinusoidal G-Jitter

Transient phenomenon of laminar film condensation along a vertical flat plate under sinusoidal g-jitter has been analyzed, based on the same assumptions of Nusselt’s analysis of film condensation where the heat transfer within the liquid film is by pure conduction. The momentum equation retains the transient term. The perturbed acceleration due to gravity has been assumed to be a sinusoidal function of time and frequency of oscillation for the simplicity. The resultant equation has been solved analytically and the velocity profiles and mass flow rate under such g-jitter has been simulated. It has been observed that at the different heights the velocity response with time is purely sinusoidal with different amplitude. Last but not the least; boundary layer thickness is also oscillating with time, hence heat transfer coefficient. However, the entire analysis is an extension of Nusselt’s analysis of film condensation which includes transient response.     

Heat transfer in boundary layer flow of a micropolar fluid past a curved surface with suction and injection

Van Dyke's singular perturbation technique has been used to study the heat transfer in the flow of a micropolar fluid past a curved surface with suction and injection. The conditions for similar solutions of the thermal boundary layer equations have been obtained. In addition to the usual “no slip” condition for velocity, the two types of boundary conditions used for microrotation are: (i) no relative spin on the boundary; (ii) the anti-symmetric part of the stress tensor vanishes at the boundary. The effect of suction or injection on velocity, microrotation, temperature, skin friction coefficient, wall couple stress coefficient, displacement and momentum thicknesses, rate of heat transfer and adiabatic wall temperature have been studied. It is observed that with the increase of injection velocity, the thickness of the boundary layer is increased and the local drag is reduced. A comparison with the results obtained for a Newtonian fluid reveals that the microelements present in the fluid reduce the velocity and frictional drag, and cool the boundary.     

Calculation of the Boundary Layer of a Two-Phase Medium

Results are given of the calculations of the turbulent boundary layer of a two-phase mixture consisting of a gas and spherical particles 10^–6 m in size. The problem formulation is presented, and the concentration of particles on the wall and the heat flux to the wall are determined. The two-phase mixture is treated as Newtonian liquid, and the gas and solid particles which form this mixture are calculated as continuous flows. The calculation of a two-phase flow in the boundary layer is performed with due regard for the effect of the concentration of solid particles on the viscosity and thermal conductivity of a binary mixture in the presence of the forces of interfacial interaction.     

Experimental study on the particle accumulation phenomenon in seeded flows around a near-bottom-wall horizontal cylinder

In experiments of flows around a cylinder in a water channel, an interesting phenomenon is that a particle accumulation line obviously forms on the bottom of the channel. The present paper focuses on this phenomenon, and the formation mechanism of the particle accumulation line is in detail investigated experimentally with particle image velocimetry (PIV). The circular cylinder was set in a fully developed turbulent boundary layer with 12 gap ratios S/D ranging from 0 to 1.5 under two Reynolds numbers (1371 and 902) based on the momentum loss thickness. The possible mechanism of this phenomenon has been demonstrated with the experimental results: the separation takes place due to the interaction between the wake of the cylinder and the boundary layer of the plane wall, the gap flow separates from the wall downstream of the cylinder and causes an attachment vortex of low velocity area at about 1 to 2 cylinder diameters from the cylinder, where the particle accumulation line forms steadily.     

Studies on laminar thin film flow along a vertical wall

Summary The problem of a laminar thin-film flow along a vertical wall is examined here. Using a fourth-degree polynomial velocity profile function inside the boundary layer, the momentum integral equation is solved analytically to determine the boundary layer thickness and the corresponding film-thickness.     

The connection between Ekman and Stewartson layers for a rotating disk

When a disk of finite radius and the surrounding medium rotate coaxially with slightly different angular velocities, a so-called Stewartson layer exists at the edge of the disk. The properties of this layer outside the boundary layer of the disk have been given in a previous publication. In the present paper it is shown how the radial flow of the Ekman boundary layer turns into the axial flow of the Stewartson layer. This happens in a region of which both the radial and axial dimensions are O(E^1/2), where E is the Ekman number.     

Algebraic model of turbulent boundary layer on a convex curvilinear surface

A simple algebraic model of turbulent boundary layer on convex curvilinear surfaces is suggested that is based on the generalization of the two-layer one-parameter algebraic model for a flat plate [ 1 ]. The model is tested in a wide range of variation of the curvature parameter (0.01 ≤ δ₀/R _w ≤ 0.09, where δ₀ is the thickness of the boundary layer at the initial cross section of the curvilinear region andR _w is the curvature radius of the surface), the results of which are indicative of a good agreement between the experimental and calculated data on the integral characteristics of the boundary layer, namely, the friction coefficientC _f , the displacement thickness δ^* and momentum thickness δ^**, and the form parameterH = δ^*/δ^**. Based on the comparison between the calculated and experimental data on the distribution of tangential turbulent stresses, a conclusion is made that the model predicts a much lower effect of the curvature on the suppression of turbulence in the outer region of boundary layers at a mild curvature of the surface (δ ₀ /R _w = 0.01) than in experiments. However, this difference has a tendency to decrease as the surface curvature increases. An analysis of the calculated and experimental velocity profiles plotted in the variables of the wall law leads to a conclusion that the generalized Townsend wall law is partially realized on a curvilinear surface.     

Heat transfer in a viscoelastic boundary layer flow through a porous medium

This paper examines the viscoelastic fluid flow and heat transfer characteristics in a saturated porous medium over an impermeable stretching surface with frictional heating and internal heat generation or absorption. The heat transfer analysis has been carried out for two different heating processes, namely (i) with prescribed surface temperature (PST-case) and (ii) prescribed surface heat flux (PHF-case). The governing equations for the boundary layer flow problem result similar solutions. For the specified five boundary conditions, it is not possible to solve directly the resulting sixth-order nonlinear ordinary differential equation. For the present incompressible boundary layer flow problem with constant physical parameters, the momentum equation is decoupled from the energy equation. Two closed–form solutions for the momentum equation are obtained and identified the realistic solution of the physical problem. Exact solution for the velocity field and the skin-friction are obtained. Also, the solution for the temperature and the heat transfer characteristics are obtained in terms of Kummers function. Asymptotic results for the temperature function for large Prandtl numbers are presented. The work due to deformation in the energy equation, which is essential and escaped from the attention of researchers while formulating the visco-elastic boundary layer flow problems, is considered. Drastic variation in the values of heat transfer coefficient is observed when the work due to deformation is ignored.The authors would like to thank the reviewers for their valuable comments/ suggestions to improve the clarity of the paper.