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Abstract: In this paper, the problem of boundary layer flow of a nanofluid past a stretching sheet has been investigated analytically by using the Homotopy Analysis Method. Both the effects of Brownian motion and thermophoresis are considered simultaneously. An analytical solution is presented which depends on the Prandtl number Pr, Lewis number Le, Brownian motion number Nb and thermophoresis number Nt. The results show that the reduced Nusselt number is a decreasing function of each dimensionless number, while the reduced Sherwood number is an increasing function of higher Pr and a decreasing function of lower Pr number for each Le, Nb and Nt numbers like the results presented by Khan and Pop. Contrary the results presented by Khan and Pop, It is found that the reduced Nusselt number decreases with the increase in Pr for many Nb numbers. However for a special Nb, there are conversely interesting results that are clearly discussed in this paper. [Copyright &y& Elsevier]

This paper presents the results of numerical modeling of the evolution of thermal plumes in a fluid layer heated locally from below. Special attention is paid to the development of a boundary layer that precedes thermal plume generation. Equations for natural convection are solved using the ANSYS Fluent software package. The calculated temperature fields are compared with the results of a full-scale experiment. The variation of parameters of the numerical model gives two mechanisms of heat transfer from a local heat source – conductive and convective. In the first case, uniform heating of fluid above the heater surface leads to the formation of a single plume. In the second case, the boundary layer near the heater edges experiences deformation that causes a convective jet to bifurcate. The purpose of the present work is to study the effect of heat source shapes (triangular, square, pentagonal and circular) on the boundary layer structure. For each heater shape, the critical value of the Rayleigh number determined. It is shown that bifurcation of a thermal plume is initiated when the Rayleigh number exceeds a critical value. [ABSTRACT FROM AUTHOR]

In this paper, a scaling analysis using a simple three-region structure was used to develop scalings for the unsteady natural convection boundary layer (NCBL) of a homogeneous Newtonian fluid with Pr>1 adjacent to a finite vertical plate evenly heated with a time-varying sinusoidal temperature, where Pr is the Prandtl number. Three distinct sub-stages are identified in the heating stage, i.e. , a start-up stage, a transitional stage, and a quasi-steady stage. After the heating stage, there is a very short cooling stage, in which a double thermal boundary layer structure is developed, which leads to a new, thinner thermal boundary layer adjacent to the plate co-existing with the original thermal boundary layer. A series of scalings are developed for the thermal and viscous boundary thicknesses, the maximum vertical velocity within the boundary layer, and the Nusselt number which are the major parameters representing the flow behavior, in terms of the governing parameters of the flow, i.e. , the Rayleigh number Ra , Pr , and the dimensionless natural frequency of the time-varying sinusoidal temperature at various flow development stages. These scalings are tested by full numerical solutions of the governing equations and are shown to, in general, provide an accurate description of the flow. [ABSTRACT FROM AUTHOR]

The feasibility of achieving microscale heat transfer effects in macro geometries using conventional fabrication methods has recently been demonstrated. This paper looks at passive techniques, using nature-inspired Inverted Fish Scale geometrical design, to improve the heat transfer performance of the newly proposed system. In this study, an annular microchannel, with gap size of 300 μm, is formed by securing a cylindrical insert of mean diameter 19.4 mm within a cylindrical pipe of internal diameter 20 mm. The Inverted Fish Scale profile is introduced on the insert surface, so as to improve heat transfer through increasing the convective heat transfer coefficient of the flow, for a constant heat transfer area. Both experimental and numerical investigations are carried out to study the effect of the Inverted Fish Scale enhancement profile on the heat transfer and flow characteristics of the microscale flow. Single-phase liquid flow using distilled water is examined, with Reynolds number ranging from 1300 to 4600. The microchannel is considered hydraulically smooth, with length of 30 mm and hydraulic diameter of 600 μm. Results show that the Inverted Fish Scale (IFS) profile indeed has positive effect in enhancing heat transfer. The maximum convective heat transfer coefficient achieved in the whole study is 52.8 kW/m 2 ·K, using IFS insert with scale height of 0.21 mm and pitch length of 2.1 mm, at Reynolds number of 4300. This is more than twice the value using Plain insert at the same flow condition. The possible enhancement mechanisms include re-initialization of velocity and thermal boundary layers, flow recirculation and higher turbulence intensity. In addition, the thermo-hydraulic performance factor, which incorporates the undesirable increment in friction factor, is examined. The thermo-hydraulic enhancement of the IFS profile is generally found to be more effective for 1300≲Re≲3250. In particular, the IFS insert with scale height of 0.21 mm and pitch length of 2.1 mm performs 43% better than the Plain insert, at Reynolds number of 1700. New correlations for the average Nusselt number and friction factor are proposed for the IFS microchannel, to be used in the design of compact heat exchangers. Based on calculations, the present system is able to remove heat flux of up to 375 W/cm 2 . The pressure drop values of the system are all less than 3.3 bars, which may be overcome by a commercially available pump. The present study reiterates the feasibility of achieving microscale heat transfer effects in macro geometry systems, and demonstrates the effectiveness of the Inverted Fish Scale profile in enhancing heat transfer performance. [ABSTRACT FROM AUTHOR]

Towards a higher turbine inlet temperature, full coverage film cooling or effusion cooling is an effective way to cool the hot cascade. The interaction between upstream and downstream film cooling rows becomes more and more important for the evaluation of cooling effectiveness. In this paper, film cooling effectiveness distributions and aero-thermal fields of one film cooling row and two in-line film cooling rows with spacing ratio S/D = 6 are compared and investigated to reveal the row-to-row interaction. The LES model is first validated by a flat plate experiment in which the mainstream velocity equal to 25 m/s, then the LES model is used to analyze the flow field and heat transfer. The results show that the upstream ejection would thickens the downstream boundary layer, making the downstream coolant flow penetrate deeper into the main flow, thus causing poor coolant coverage of the rear film cooling ejection. On the other hand, the lifted kidney vortices of the second row ejection entrain first row ejection to the wall, making the coolant flow from the first row contribute significantly to the coolant coverage on the wall downstream of the second row. The turbulence intensity has great impact on the film cooling effectiveness after the first row, but very small influence on the second row. • The cooling performance of the second hole ejection is very different from single row, and strong row-to-row interaction can be found. • Case 3 in this paper reveals the cooling performance of the second row ejection, and found that the first row coolant jet has large lateral coverage due to deflection and entrainment. • The main flow turbulence intensity has big influence on single row film cooling, but it has little effect on the second row film cooling performance. [ABSTRACT FROM AUTHOR]

This paper numerically explored the influence of the film cooling hole locations and blowing ratios on the thermal performance both in the latticework duct and film cooling. The Realizable k − ε turbulence model and polyhedral mesh were utilized to conduct this study. The film cooling hole was successively installed from the jet region to turning region for different cases. The blowing ratio included 0.2, 0.8, 1.0 and 1.25. These results suggested that the different film hole locations could induce the different flow and cooling performance both in the latticework duct and film cooling channel. The film cooling hole destroyed the boundary layer and was conducive to heat exchange enhancement in the latticework duct. The film cooling hole configured near the turning region had more remarkably effect on the thermal performance. The different location means the different inlet condition for the film cooling. Maximum value of film cooling effectiveness was reached as the film cooling hole installed near the jet region because of the small counter-rotating vortex. [ABSTRACT FROM AUTHOR]

Emmons' solution does not include a development length in front of the flame, which causes the thermal and velocity boundary layers to have different starting locations. In this paper, the effect of the unheated starting segment on solid burning was first experimentally investigated over a horizontal 10 cm × 10 cm × 1.5 cm Poly (methyl methacrylate) sample under 0.75 m/s concurrent airflow with varying unheated lengths L 0 (5, 10, 20 cm). The flow field, flame structure, and gas-phase temperature profile were experimentally recorded, and the subsequently produced flame standoff distance and dimensionless temperature gradient were combined to reveal the effect of the unheated segment on the boundary layer combustion. The parameters directly related to fire hazard, like heat transfer coefficient (burning rate), and mass loss rate were also measured and theoretically deduced, to obtain the effect of the unheated segment on wind-driven fire development. Results demonstrated that owing to the presence of the unheated segment, the pressure gradient is misaligned with the density gradient to be prone to produce vortices and form streaky flames. The streak structure distributed in the flame is associated with a stronger heat transfer, resulting in a larger convective heat transfer coefficient than the theoretical ones. Due to the viscous drag effect, with increasing unheated length, the flame standoff distance increases while the convective heat transfer coefficient decreases. Additionally, coupled effects of the unheated length and forced airflow, solid burning is a transient process. As time progresses, with the valley and vortex effect, the flame standoff distance increases and decreases in the leading and trailing section, respectively, and the differences in flame standoff distance and heat transfer coefficient for varying unheated lengths are enlarged. Eventually, the mass-loss rate has an increasing tendency accompanied by a decreasing burning contribution of the leading section. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigate theoretically the problem of steady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid at a stagnation point over an exponentially shrinking vertical sheet with suction. In this study, we assume that the shrinking velocity and wall temperature have specific exponential function form. An appropriate similarity transformation is employed to transform the governing equations in partial differential equations form to similarity equations in ordinary differential equations form. The resulting equations are then solved numerically using shooting technique with Maple implementation. The influence of mixed convection/buoyancy parameter λ, suction parameter s and shrinking variable c/a on the flow and heat transfer characteristics is examined and discussed. Numerical results indicate that the presence of buoyancy force would contribute to the presence of triple solutions to the flow and heat transfer for particular value of pertinent parameters. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate theoretically the problem of steady laminar two-dimensional boundary layer flow and heat transfer of an incompressible viscous fluid in the presence of buoyancy force over an exponentially shrinking vertical sheet with suction. The shrinking velocity and wall temperature are assumed to have specific exponential function forms. The governing equations are first transformed to similarity equations using an appropriate similarity transformation. The resulting equations were then solved numerically using shooting technique involving fourth-order Runge–Kutta method and Newton–Raphson method. The influence of mixed convection/buoyancy parameter λ, suction parameter s and Prandtl number Pr on the flow and heat transfer characteristics is examined and discussed. Numerical results indicate that the presence of buoyancy force would contribute to the existence of triple solutions to the flow and heat transfer for particular value of pertinent parameters. It is different for the non-buoyant flow case i.e. when the buoyancy force is absent, the problem admits only dual solutions. Further, this study also reveals that the features of flow and heat transfer characteristics are significantly affected by buoyancy parameter λ, suction parameter s and Prandtl number Pr. [Copyright &y& Elsevier]

Abstract: This paper presents a numerical investigation for examining the secondary vortex motion and associated heat transfer process in fluid flow through curved passages. Overcoming current modelling limitations, the study formulates an improved simulation model based on 3-dimensional vortex structures for describing secondary flow and its thermal characteristics. For developing laminar fluid flow through curved rectangular ducts, the analysis performs a detailed parametric study involving the contours of helicity and outer duct wall pressure gradient for a range of flow rates, duct aspect ratios, duct flow curvatures and external wall heat fluxes. The flow conditions leading to hydrodynamic instability and Dean vortex generation in curved passages are carefully analysed, identifying the flow and geometrical parametric influences. Active interaction of buoyancy force on fluid motion arising from wall heating is considered where aspects of boundary layer separation is used in recognising thermal enhancement due to secondary flow. The simulated results are validated with the available experimental data. Surpassing precision and reliability of current practise, the study develops two numerical approaches offering improved capabilities for capturing the onset of hydrodynamic instability and resulting Dean vortices. These techniques are compared and assessed for their merits of application in determining the onset of secondary flow hydrodynamic instability with and without external wall heating. [Copyright &y& Elsevier]

Abstract: This paper presents a self-similar solution of the coupled problem of magneto-hydrodynamic free convection flow of an electrically conducting fluid arising from melting of a semi-infinite solid substrate. At steady state, buoyancy induced free convection of the electrically conducting fluid is influenced by the Lorentz force. A set of governing PDEs is developed for a two dimensional boundary layer problem including phase change which is simplified to a set of ODEs using a similarity transformation and are solved iteratively using an implicit Keller-box method. An asymptotic analytical solution for melting and heat transport rates is also presented for the case of small Prandtl numbers. The effect of each of the three characteristic parameters, viz., the Prandtl number, the melting parameter and the Lykoudis number on the similarity velocity and temperature profiles in the boundary layer over melting substrate is studied. It is observed that increasing the Lykoudis number or decreasing the Prandtl number lowers the melting rate and heat transfer at the substrate–melt interface. The use of magnetic field in controlling the free convection heat transfer, the melting rate and the thickness of the velocity and thermal boundary layers over melting substrate is elucidated and discussed. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to show the possibility to increase small wind turbine performances using a Micro Electro Mechanical System (M.E.M.S.) placed inside the blade. In particular its effects on the Laminar Separation Bubble (LSB) phenomenon are presented. This is a local boundary layer separation, that may occur on aerodynamic bodies operating at low Reynolds numbers as the root blade sections of small horizontal axis wind turbine rotors. Its presence induces an aerodynamic efficiency drop-off due to a drag increase and a lift decrease. Tests are performed on an airfoil designed for the root section of a small wind turbine having a 10 kW nominal power. A M.E.M.S. was placed internally the wing section to produce mechanical disturbances directly inside the boundary layer; M.E.M.S.’ lower face is clamped to the wing structure, while the upper one is glued to a PVC movable strip aligned with the airfoil upper surface. M.E.M.S. was electrically supplied at different amplitudes and frequencies in order to vary vibration modes. Preliminary measurements, performed by using a pressure distribution analysis, were carried out to qualitatively locate the LSB presence. Laminar separation, transition and turbulent reattachment points positions are quantitatively detected by means of a thermographic approach: the heated thin foil technique is used to observe temperature distribution on the airfoil surface and a numerical energy balance approach was employed to evaluate the local convective heat transfer coefficient h. Afterward the local Stanton number distribution was calculated and a first and second derivatives analysis allowed to localize the LSB characteristic points positions. Results showed a very effective M.E.M.S. action for frequencies about 175 Hz and a Reynolds number of 105. A lift increases about 50%, was showed with a consequent increase of the wind turbine Cp values. [Copyright &y& Elsevier]

Abstract: This paper is primely devoted to numerical treatment and derivation of analytical expressions for the solution of steady, laminar, incompressible, viscous and electrically conducting fluid of the boundary layer flow due to a rotating sphere subjected to a uniform suction and injection through the surface in the presence of a uniform radial magnetic field. The fluid and body rotate either in the same direction or in opposite directions. Particular attention is the vicinity of equator of the sphere for which the governing mean flow and temperature equations are derived using the similarity transformations. These are first solved numerically by a spectral Chebyshev collocation integration scheme and later are treated via the recently popular homotopy analysis method to obtain the exact solutions. The homotopy series are mathematically proven to rapidly converge to the numerical solutions, provided that auxiliary convergence control parameters are selected optimally as described here. The resulting flow pattern, temperature distribution, surface shear stresses, infinite radial velocity and heat transfer characteristics are presented and discussed for the various parameter cases. Explicit formulas are also derived for some parameters of physical significance. [Copyright &y& Elsevier]

Abstract: The problem of steady laminar mixed convection boundary layer flow past an isothermal horizontal circular cylinder placed in a viscous and incompressible fluid of temperature-dependent viscosity is theoretically considered in this paper. The partial differential equations governing the flow and heat transfer are shown to be non-similar. Full numerical solutions of these governing equations are obtained using an implicit finite-difference scheme known as the Keller-box method. The solutions are obtained for various values of the Prandtl number Pr, the mixed convection parameter λ and the viscosity/temperature parameter θr . The obtained results show that the flow and heat transfer characteristics are significantly influenced by these parameters. [Copyright &y& Elsevier]

Abstract: Individual terms in the entropy transport equation are used today to analyse entropy production and dissipation within the flow. The underlying idea is that the local entropy production tells us where a particular design can be improved. However, very little attention has been paid up to now to the analysis of the full entropy transport equation. The present paper focuses on this topic and shows similarity solutions of the entropy transport equation. Two cases have been investigated as examples: laminar flow over a flat plate and flow between converging and diverging parallel plates, so called Jeffery–Hamel flows. Thus, similarity solutions have been derived for the boundary layer equations as well as for an analytical solution of the Navier–Stokes equations. These solutions show nicely the variation of all different terms in the entropy transport equation and highlight also restrictions under which such solutions can be obtained. [Copyright &y& Elsevier]

With the development of heat engines, in some fields the heat wall suffers from dynamic heat flux, thus some cooling control techniques are needed to meet this dynamic cooling requirement. The traditional stationary vortex generators have not met the cooling demand in these cooling fields with dynamic heat flux. Existing studies have shown that the capacity of convective heat transfer depends on the distribution characteristics of the velocity and temperature field of the cooling fluid. Therefore, considering to the factors of single-side heat transfer and fluid flow boundary layer, new and efficient mixing heat technology is increasingly demanded for many industrial fields. In this paper, the dynamic turbulence generator such as spherical cylinder is adopted to study the influence of flow vortexes on heat transfer and achieves a better distribution of velocity field and facilitates the enhancement of convective heat transfer. Research results indicate that compared to traditional stationary vortex generator technologies, vibration spherical cylinder can effectively improve heat transfer performance and leads to a lower flow resistance. As a conclusion, the flow and heat transfer performance increase with the vibration frequency increasing. When Re = 7255, the thermal hydraulic performance is increased by a maximum 24.55% than traditional stationary vortexes generator. When Re = 14510, the performance is better than stationary cylinder structure. And the vibration frequency can be adjusted timely according to cooling demand. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the momentum and heat transfer in an unsteady separated stagnation-point flow of a viscous fluid over a plane surface advancing towards or receding from the normal stagnation flow which impinges on the surface with a variable strain rate s (t) , causing the unsteadiness in this flow problem. The flow and heat transfer characteristics are therefore governed by the flow strength (stagnation) parameter a , unsteadiness parameter β , plate velocity (normal) parameter α and Prandtl number P r. The current analysis ensures the existence of the self-similar solutions to this flow problem only when the plate velocity varies directly to the square root of the strain rate s (t). A closed form analytic solution of this flow problem is found for the specific relational values of β = 2 a. The solutions of this flow problem are non unique only under the negative values of β. When the plate surface is advancing towards the normal stagnation flow (i.e., when α > 0), the self-similar boundary layer solution continues for any given values of a and β , whereas for receding of the plate surface from the incoming flow (i.e., for α < 0) the boundary layer solution does not exist after a certain value of α depending upon the values of a and β. In the case where receding of the plate surface occurs, the features of the boundary layer flows depend highly on the sum values of the parameters a and β. For (a + β) > 0, the boundary layer solution ends with an attached flow solution, while it gets terminated at a reverse flow solution for (a + β) < 0. And for (a + β) = 0, the governing boundary layer equations provide us with the trivial (zero) solutions which are unable to capture the free boundary conditions. • Transformation of basic equations. • Analytic solution. • Heat transfer solution. • Asymptotic analysis for large values of the plate velocity. [ABSTRACT FROM AUTHOR]

This paper aims to provide a novel enhanced heat transfer method for the internal tip surface of a U bend channel of relevance for a gas turbine rotor blade. The DWVGs (delta-winglet vortex generators) pair is arranged at multiple locations on the tip surface. Two types of vortex generators are studied, including common-flow-up and common-flow-down configurations. The inlet channel Reynolds number varies from 10,000 to 50,000. The topological analysis method is used to determine the formation and evolution of the vortices and to better understand the mechanism of the heat transfer enhancement. Results of skin-friction lines, topological portrait, Nusselt number, friction factor, thermal performance are included. The results show that due to the interaction among the vortices surrounding the vortex generators, the DWVGs pair in common-flow-up configuration has a slight heat transfer improvement, and is not sensitive to the tip location. However, the DWVGs pair in common-flow-down configuration placed at the downstream of the tip surface improved the heat transfer significantly as the induced vortices between the turbulator pairs effectively reduce the thickness of the boundary layer. Compared with the smooth U bend channel, the optimal design shows that the heat transfer and overall thermal performance can be increased by up to 7.4% and 6.8%, respectively. This study elaborates the flow and heat transfer processes from the perspective of topology, which is helpful in the design of cooling procedures of turbine blades. [ABSTRACT FROM AUTHOR]

It is established that large errors would be incurred if the average Nusselt number for natural convection above heated horizontal plates of finite size is determined by the similarity or integral theories which assume the plate is semi-infinite. Recognizing that boundary layers grow from both edges of a finite plate, correction factors are mathematically deduced for the isothermal case ( F t = 2 2 / 5 ) and for the case of constant heat flux ( F q = 2 1 / 3 ). Correction factors are also developed for near-horizontal orientations of the heated plate. The semi-infinite assumption does not alter the computation of the overall heat transfer rate for inclination angles at which the vertical mechanism of natural convection is dominant since then, even in the case of a finite plate, a single boundary layer covers the entire length of the plate. The theoretical rationalization developed in the paper brings the predictions of explicit algebraic expressions for average Nusselt number in line with those determined accurately by computational fluid dynamics (with extensive experimental verification), and provides physical explanation of the subtle thermo-fluid-dynamics of natural convection established by the present CFD simulations. • CFD study of natural convection around heated inclined plates. • Correction of theoretical average Nusselt number for horizontal and near-horizontal orientations. • Corrective theories developed for both isothermal and iso-heat-flux boundary conditions. • Influence of boundary condition on average Nusselt number explained. • Subtle effect of inclination on heat transfer in near-horizontal and near-vertical cases uncovered. [ABSTRACT FROM AUTHOR]

Existing clothing models assume spatial homogeneity of the enclosed air layer between skin and fabric, which contradicts real-life scenarios. Furthermore, depending on the thickness of enclosed air layer and the temperature difference between skin and fabric, natural convection may occur but it is often neglected in the theoretical models. In this study, we have developed a theoretical model that considers the spatial heterogeneity of enclosed air layer and natural convection. It computes the sensible heat transfer (conduction, radiation and natural convection) in the heterogeneous enclosed and boundary air layers. The heat transfer in the clothing layer is calculated based on the thermal resistance of the fabric. The model presented in this paper is systematically validated for natural convection and spatial heterogeneity using a thermal cylinder and a thermal manikin with increasing level of spatial complexity. The validation of the model was performed for a wide range of temperatures (−10 °C to 26 °C), enclosed air layer thicknesses (homogeneous and heterogeneous), and ambient air speeds (0.2 m/s, 1 m/s) and demonstrated a good agreement between predicted and measured heat flux with an average error of 3.7% and 9.3% for homogeneous and heterogeneous enclosed air layers, respectively. • Spatial heterogeneity of enclosed air layer influences heat loss by up to 30%. • Clothing model reliability was successfully proven in a systematic validation for realistic clothing and human body shape. • The mean accuracy of the model for heat loss is 3.7% and 9.3% for homogeneous and heterogeneous enclosed air layers. [ABSTRACT FROM AUTHOR]