Forced Convection

This paper deals with the correlation of the heat transfer coefficient and friction factor at a constant heat flux in forced convection for helical pipes. The study was based on experiments and two correlation equations for heat transfer coefficient and friction factor were developed by using the least square method. The relative errors and the correlation coefficients for both correlation equations were calculated. Air was used in the study. The correlation equations for the heat transfer coefficient and friction factor are in accordance with the experiment results, for intervals given of Reynolds number( 17.103<Red<135.103). The relative error and the correlation coefficient for the heat transfer coefficient and friction factor are %3,7, 0,94 ; %9,83 and 0,94 respectively.

Major desalination processes consume a large amount of energy derived from oil and natural gas as heat and electricity. Solar desalination, although researched for over two decades, has only recently emerged as a promising renewable energy-powered technology for producing fresh water. Solar desalination based on the humidificationdehumidification cycle presents the best method of solar desalination due to overall high-energy effkiency. This paper provides a comprehensive technical review of solar desalination with a multi-effect cycle providing a better understanding of the process. Discussion on methods to improve system performance and efftciency paves the way towards possible commercialisation of such units in the future.

Energy (DOE), Cooperative Agreement No. However, any opinions, findings, conclusions, or recommendations expressed herein are those of t h e author(s) and do n o t necessarily reflect the views of DOE, Thb work was conducted through t h e Amarillo National Resource Center for P lult o n i u m , DE-FC04-9 5AL8 583 2. ication of a New Time Scale This report was prepared as an account of work sponsored by an agency of the United States Government Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or impliai. or assumes any legal liability or responsibility for the accuracy, oompletentss, or usefulness of any information, apparatus, product, or procus disclosed, or represents that its usc would not infringe privately o w m i rights. Reference h& to any specific commercial product. proctss, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recornmendation, or favoring by the United States Goyernmtnt or any agency themf. The views and opinions of authors cxprcsd herein do not n d y state or reflect those of the United States Government or any agency thereof.

Presented in this paper is an analytic approximation to the thermal-fluid problem involving mixed and forced convective heat transfer from a rotating isothermal cylinder placed in a non-uniform stream shear-flow. The approximation is obtained using a series expansion of the scaled boundary layer equations in terms of a boundary layer variable which is directly proportional to the time variable and inversely proportional to the Reynolds number. Therefore, the resulting approximation is valid both for small time and for moderate and large times for which the Reynolds number of the flow is sufficiently large.

Abstract: Presented in this paper is an analytic approximation to the thermal-fluid problem involving mixed and forced convective heat transfer from a rotating isothermal cylinder placed in a non-uniform stream shear-flow. The approximation is obtained using a series expansion ...

Due to the low total cost of production, Photovoltaic energy constitutes an important part of the renewable energy installed in the world. However, photovoltaic energy is volatile in nature because it depends on weather conditions, which makes the integration, control and exploitation of this type of energy difficult for grid operators. In the traditional grid architecture, system operators have accumulated enough experience that enables them to determine how much operating reserves are required to maintain system reliability based on statistical tools. Still, with the introduction of renewable energy (wind and photovoltaic), the grid structure has changed, and to maintain grid stability, it is becoming fundamental to know renewable energy state and production that can be combined with other less variable and more predictable sources to satisfy the energy demand. Therefore, renewable energy forecasting is a straightforward way to integrate safely this kind of energy into the current electric grid, especially photovoltaic power forecasting, which is still at a relative infancy stage compared to wind power forecasting, which has reached a relatively mature stage. The goal of this work is to present, first, a short-term offline forecasting model that uses only in-situ (local) collected data. Also, the performances of several pure non-linear auto-regressive models are investigated against those of non-linear auto-regressive models with exogenous inputs. For this purpose, two well-known statistical learning techniques, namely Feed Forward Neural Network and Least Square Support Vector Regression, have been used. To test the performance of the models, the results obtained are compared with those of a benchmark model. In this paper, we used the persistent model as well as a multivariate polynomial regression model as benchmark. Photovoltaic • Power forecasting • Renewable energy integration • Statistical learning techniques • Support vector regression • Feed forward neural network Abbreviations List of symbols (w, b, e) Empirical risk functional in the feature space N Number of training instances b Bias w Sepparation margin Regularization parameter of LSSVM e Vector of errors e = e 1 , … , e N x Training data x = x 1 , … , x N y Vector of labels with y = y 1 , … , y N 1 v Vector of ones w T w Inner product of w i Lagrange multipliers (w, b, e, ) Lagrangian objective function Kernel matrix K Bimodal kernel function Nonlinear mapping from input to feature space W Vector of FFNN weights W = w 1 , … , w p x o Vector of computed values of output neurons xo Vector of required values of output neurons Abbreviations PV PhotoVoltaic AR Auto-regressive ARX Auto-regressive with exogenous input NAR Nonlinear auto-regressive * Ayoub Fentis

In the present work heat transfer and friction factor properties were experimentally investigated by using copper wavy twisted tape inserts with circular holes in forced convection. The turbulent flow was created by inserting the wavy twisted tape inserts into the test pipe creating high rate of turbulence in pipe, which results in increasing heat transfer enhancement and pressure drop. The tape consists of the circular holes and the twisting with various twist ratios (TR=5.5, 6.5, 8.5). The length and width of insert was 500 mm and 16 mm respectively. The outside diameter & inside diameter of test pipe is 32 mm & 28 mm respectively. The length of test section is 500 mm. The bulk mean temperatures at various positions are used for different flow rate of air. From the obtained results the new Correlations for Nusselt number and friction factor are developed for twisted tape inserts. The Reynolds number is varied from 2000 to 12000. The results of varying twists in wavy twisted tape inserts with different pitches have been compared with the values for the smooth tube. It showed that the highest heat transfer rate was achieved for the wavy twisted tape with twist ratio 5.5.

The transient generalized Couette flow with heat transfer through a porous medium between two infinite parallel porous plates is studied considering the Hall effect and temperature dependent physical properties. The upper plate is moving with a uniform velocity while the lower plate is kept stationary. An exponential decaying pressure gradient is imposed in the axial direction and an external uniform magnetic field as well as a uniform suction and injection are applied perpendicular to the horizontal plates. A numerical solution for the governing non-linear coupled set of equations of motion and the energy equation including the viscous and Joule dissipations is adopted. The effect of the porosity of the medium, the Hall current and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is investigated.

In the current work, a numerical analysis of the thermodynamic second law is investigated for the laminar forced convection flow in a duct adjacent to two inclined backward facing steps. For calculation of entropy generation from the second law of thermodynamics in a laminar forced convection flow, the velocity and temperature distributions are primarily needed. For this purpose, the governing equations including mass, momentum and energy equations are solved by computational fluid dynamic (CFD) techniques to obtain the temperature and velocity fields. For simulating the inclined surface, the blocked-off method is used. The effects of the inclination angle on the entropy generation and Bejan number are also presented. Comparison of numerical results with the available data published in open literature shows a good consistency.

In the current work, a numerical analysis of the thermodynamic second law is investigated for the laminar forced convection flow in a duct adjacent to two inclined backward facing steps. For calculation of entropy generation from the second law of thermodynamics in a laminar forced convection flow, the velocity and temperature distributions are primarily needed. For this purpose, the governing equations including mass, momentum and energy equations are solved by computational fluid dynamic (CFD) techniques to obtain the temperature and velocity fields. For simulating the inclined surface, the blocked-off method is used. The effects of the inclination angle on the entropy generation and Bejan number are also presented. Comparison of numerical results with the available data published in open literature shows a good consistency.

Theoretical analysis of magnetohydrodynamic fully developed forced convective flow and heat transfer characteristics of a non-Newtonian electrically conducting Casson fluid through a porous channel filled with anisotropic porous material bounded by two impermeable horizontal walls subject to constant heat flux applied to the outer walls is investigated. The extended Darcy-Brinkmann model govern the flow inside the porous channel and accounts for the presence of the inertia term, which allows for the no-slip boundary conditions at the walls. The principal axis of anisotropic permeability is oriented from 𝟎 to 𝝅 𝟐 radians. The equations governing the system are solved using the inbuilt "DSolve" in Mathematica 11.1 for the velocity and temperature profiles as well as the Nusselt number (𝑵𝒖), which characterizes the rate of heat transfer in the system. The effects of various parameters on the velocity, temperature and heat transfer profiles are displayed through graphs and discussed quantitatively. From the results we observed that the velocity profile reduced as the Casson parameter (𝛽), anisotropic ratio (𝐾 𝑟 ), orientation angle (𝜑), and Hartmann number (𝐻𝑎) increased, whereas the velocity profile increased when the Darcy number (𝐷𝑎) and apparent viscosity (𝜆) increased. Similarly, these variables also had similar effect on the temperature profile of the fluid. On the other hand, the heat transfer profile, as measured by Nusselt number, increased when the Casson parameter (𝛽), anisotropic ratio (𝐾 𝑟 ) and Hartmann number (𝐻𝑎) increased, while increasing the orientation angle (𝜑) and apparent viscosity (𝜆) decreased the Heat Transfer Profile. Upon further investigation, the heat transfer profile was shown to be maximum along the path of least permeability in the anisotropic porous media under investigation.

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In this paper, author solve numerically, using the method of finite differences, the transfer equations, laminar, three-dimensional, between inclined isothermal ellipsoid of revolution, and a newtonian fluid in vertical upward flow generated by the natural convection. In the boundary layer, the results concerning the dimensionless velocity fields and temperatures as well as the Nusselt number and the friction coefficients, are represented graphically. With respect to the angle of inclination of the ellipsoid, the author put in evidence of the privileged points on the partition of the body. Secondly, the influence of the geometry of the body was also considered, in order to assess the adherence of the fluid on the wall and locate the boundary layer separation points.

BACKGROUND: Conidia from Metarhizium are part of the commercial formulations used worldwide for insect pest control. Among the alternatives proposed to improve conidia production, the use of packed column bioreactors allows controlled processes with higher levels of production and productivity than those obtained with the traditional process in plastic bags. However, problems associated with overheating, low CO 2 removal, and inadequate oxygen supply in packed columns limit the scale-up and operation at an industrial scale. RESULTS: Packed densities, up to 1.5 times higher than those obtained in lab-scale column bioreactors, negatively affected growth and conidia production by Metarhizium robertsii (ENCB-MG-81). Therefore, a spherical-style packing was added to decrease packed density and improve the culture conditions in packed column bioreactors. The addition of spherical-style packing reduced the axial temperature gradient (up to 50%), increased the maximum CO 2 production rate and the total CO 2 production (up to 2.5 times), and enhanced the volumetric conidia productivity in packed column bioreactors from 5.28 ± 1.36 to 6.77 ± 0.89 × 10 8 conidia cm-3. CONCLUSION: The use of spherical-style packing within the culture bed in column bioreactors improves the production of conidia by Metarhizium robertsii, as well as the gas exchange and heat removal from the bed.

The increasing complexity and miniaturization of electronic applications necessitate the development of efficient and compact heat sink designs for effective heat dissipation. This study presents a numerical investigation of heat transfer performance in circular pin-fin heat sinks featuring notches of varying sizes. Five distinct heat sink models are analyzed, with the first model comprising a solid fin, while the remaining four incorporate notched fins of different dimensions. Results indicate a significant influence of notch size on heat transfer performance, particularly for larger notches. The Nusselt number for a heat sink with a 4 mm notch size exhibits an increase of approximately 9% compared to that of a solid-fin heat sink. Additionally, the average temperature of heat sinks decreases with the introduction of notched fins, resulting in a temperature difference of 2.15℃ between solid-fin and 4 mm-sized notch heat sinks. An assessment of overall efficiency and overall effectiveness reveals that all notched heat sinks are viable options, with the 4 mm-sized notch heat sink demonstrating optimal performance in this study. This investigation provides valuable insights for the design of highperformance heat sinks in compact electronic applications.

The heat transfer and flowing resistance characteristics of air flow crossing over pin finned tube heat exchanger was studied numerically and experimentally. The purpose of this study is to improve the heat transfer characteristics of a pin finned-tube for better performance. A plain and solid pin finned tube heat exchanger models were fabricated and used to examine the heat transfer coefficient enhancement. In the numerical study, the finite volume mesh generation was performed using ANSYS Design modular and Fluent 18.0. Plain, solid and perforated pin finned tubes were studied numerically. The experimental results showed that Nusselt number is approximately 27% higher than that of the plain tube, while, the pressure drop value is 17% higher than that of the plain tube. The numerical results showed that perforated finned tube provides a good reduction in surface temperatures. The use of perforated pin finned tube results in increasing Nusselt number by 26% and increasing pressure drop by 22% in comparison with solid pin finned tube. A comparison between the numerical and experimental results showed a good agreement between them. Finally, correlation equations were developed for the heat transfer and friction factor.

A downburst index has been developed to assess the magnitude of convective downbursts associated with heavy precipitation-producing (HP) convective systems. The index, designed for use during the warm season over the central and eastern continental United States, is composed of relevant parameters that represent the simultaneous physical processes of convective updraft development and downburst generation, incorporating positive buoyant energy or convective available potential energy (CAPE) and the vertical equivalent potential temperature (θ e ) gradient between the surface and the midtroposphere. Since convective storm updrafts require buoyant energy, a very important parameter used in the analysis of convection is CAPE, computed from real-time Geostationary Operational Environmental Satellite (GOES) sounding data. Since updraft strength is proportional to CAPE, large CAPE would result in strong updrafts that could lift a precipitation core within a convective storm to a dry air layer in the midtroposphere. CAPE also plays a major role in the formation of precipitation by resulting in strong updrafts that increase the size of precipitation particles, which, in turn, enhances the effect of precipitation loading. The amount of mid-level water vapor relative to the low-level water vapor, represented by the θ e deficit (θ emax -θ emin ) is important in the determination of downdraft strength due to evaporational cooling as dry air is entrained into the convective system. In addition to large CAPE and the presence of a vertical (θ e ) gradient, previous research has identified other favorable conditions for downburst generation during cold-season convection events. Strong forcing by a vigorous upperlevel troughs and rapidly moving cold-frontal systems as well as strong and diffluent winds aloft have been associated with severe wind-producing convective systems that develop during the cold season. A primary mechanism in downburst generation associated with synoptically forced convective systems is the downward transport of higher momentum possessed by winds in the mid-troposphere. This paper will investigate the role of downward momentum transport in the production of convective winds observed on the Earth's surface. A literature review of the current understanding of momentum transport in convective systems as well as the types of convective systems that produce downbursts on a large scale will be presented. The paper will then feature case studies comparing a typical warm-season downburstproducing convection event to an early cold-season that occurred on 23 and 24 November 2004 in which it is believed that downward momentum transfer was a major factor in the magnitude of convective winds observed at the surface. Finally, based on a review of previous research and the case studies presented, a modification to the use of the downburst index will be explored to apply to cold-season forecasting situations.

This investigation explores heat transfer enhancement in shell and tube heat exchangers using a tri-hybrid nanofluid suspension consisting of copper (Cu), iron oxide (Fe 3 O 4), and multiwall carbon nanotubes (MWCNT) dispersed in water as the base fluid. The numerical simulation employs a novel Galerkin finite element method (GFEM) to study turbulent convection influenced by Reynolds number, tube radius, and nanoparticle volume fraction. The complex interactions among these physical parameters are analyzed in terms of average Nusselt number, entropy generation, and flow behavior. Results demonstrate that increasing nanoparticle concentration and fluid velocity significantly improve heat exchanger efficiency. Visualization tools such as streamlines, entropy contours, and isotherms provide comprehensive insight into optimizing thermal management systems.

A study was conducted to develop an efficient indirect forced convection solar dryer for the purpose of drying 40 kg of cashews per batch. The system consists of a solar flat plate collector, drying chamber and a blower. Performance test was conducted in active and passive mode on different solar days in the Department of Mechanical Engineering, PRIST University, Puducherry. Dryer performance parameters like moisture content, drying rate, thermal efficiency of collector, system efficiency and dryer efficiency were evaluated based on the experimental data. The performance study indicates that the required moisture reduction from 10% to 5% was achieved within 6 hours in active mode, 10 hours in passive mode and 14 hours in open sun drying. Thermal efficiency of the solar collector varied between 65-70% in active mode and 30-45% in passive mode. The quality evaluation of the products proved that the developed system is suitable for drying of cashew. The dryer can be used to replace ele...

Nanofluids offer a significant advantage over conventional heat transfer fluids and consequently, they have attracted much attention in recent years. The engineered suspension of nano-sized particles in a base liquid alters the properties of these nanofluids. Many researchers have measured and modeled the thermal conductivity and viscosity of nanofluids. The estimation of forced convective heat transfer coefficients is done through experiments with either metal or nonmetal solid particles dispersed in water. Regression equations are developed for the determination of the thermal conductivity and viscosity of nanofluids. The parameters influencing the decrease in convection heat transfer, observed by certain investigators, is explained.

This paper presents a numerical study of fully developed turbulent heat transfer in a flat channel half filled with porous material; the simulated fluid is air while an aluminium foam represents the solid matrix. The main focus is on heat transfer performances of a porous wall, the interface between a saturated porous medium and the clear fluid, in forced convection conditions; in the fluid portion a turbulent regime with a Reynolds number based on the mean velocity and the hydraulic diameter Re=9•10 3 is sustained. The Nusselt number and the efficiency computed on the porous wall is sensibly higher than the flat wall value and this is in direct relation with the presence of a higher peak of the wallnormal turbulent heat flux.

The considerable quantities of heat transfer are dissipated during the operating electronic/electrical systems and have harmful effects on the operating time. So; to keep these systems in good working condition, the location of efficient mechanical cooling systems is essential. The heat transfer rate in an enclosure intensely depends on the combination of geometrical and physical parameters. For this purpose, a 3D Numerical simulation of turbulent mixed convection in a cubical cavity containing an internal heat source in its middle was carried out. The cavity has an inlet port at the lower left face area and an outlet port located in the upper right face area. The analyses are performed for air at ambient circumstances (Pr = 0.71) and the variation of interval for Richardson number (Ri) is chosen between 0.01 and 30 to investigate three situations: dominated forced convection, natural convection, and mixed convection for a fixed dimension of the enclosure in turbulent regimes (Gr = 10 9 ). The effects of the variation of Ri, the dimensionless time, and the dynamic parameters on the thermal flow and fluid flow phenomena are presented and discussed. The obtained results show an exchange between the forces of pressure and of buoyancy in the studied interval and a strong dependence between the geometrical parameters and the heat transfer rate, and then the correlations of the combination of the parameters were proposed.

In This paper we investigate the MHD natural convective boundary layer flow of electrically-conducting nanofluids from a stationary vertical porous surface in a permable porous medium. The mathematical model is formulated by considering water-based nanofluids containing metallic Nano-particles for stationary plate cases. Three nanofluids are examined, namely copper, aluminum oxide or titanium oxide in water. Validation of finite element solutions for skin friction and Nusselt number is achieved via comparison with the previously published work, Primary and secondary velocities are consistently elevated with increasing Soret, thermal Grashof and solutal Grashof numbers. Increasing Schmidt number, chemical reaction and suction parameter both suppress Nano-particle concentration whereas the converse behavior is computed with increasing Soret number.

The dissolution rate of dense magnesia specimen in calcium aluminate based melts was measured in air over the temperature range of 1 450-1 600°C, using a rotating disk/cylinder technique. The measured dissolution rates were strongly dependent on the rotation speed with the results indicating mass transfer in the slag phase to be the rate-limiting step. At a given rotation speed, the dissolution rate was strongly dependent on the slag chemistry and temperature. The diffusivity of MgO in the slag was calculated from the dissolution rate and solubility data, using known mass transfer correlations. Addition of FeO x and CaF 2 and increasing the temperature, resulted in substantial increase in the dissolution rate and deduced diffusivity of MgO in the slag.

This is a numerical investigation of the coupled laminar ¯ow and heat transfer in the space between a pair of disks attached to a hub rotating about a vertical axis in a ®xed cylindrical enclosure. A temperature variation is imposed in the ¯uid by setting the disks at dierent uniform temperatures, the temperature of the bottom disk being higher than that of the top disk. The Boussinesq approximation is used to characterize buoyancy forces in the momentum conservation equations. The dierent types of interdisk ¯ow that arise as a function of angular velocity are described. At low Reynolds numbers the ¯ow is primarily driven by gravity-induced buoyancy. As the Reynolds number increases, free convection yields to centrifugally-induced buoyancy. At suciently high Reynolds numbers, convection patterns induced by the strong shear at the enclosure wall dominate the interdisk ¯ow and heat transfer but centrifugal buoyancy continues to in¯uence the 3-D ¯ow structure with respect to the isothermal case. One of the eects of buoyancy is the appearance of a new transition in the bifurcation diagram previously investigated by the authors for the isothermal ¯ow case. Here, centrifugal buoyancy favors the generation of a 3-D ¯ow which features a strong breaking of its symmetry properties with respect to the interdisk midplane, as in the isothermal case. Heat transfer rates are calculated for a range of Reynolds numbers and interdisk spacings. Special attention is paid to the high Reynolds number forced convection regime which is of practical interest. It is shown that the scales derived from heat and mass transfer analyses of the freely rotating disk apply to the present problem. In many of the present cases, 2-D (axisymmetric) and 3-D calculations yield very similar values for the overall heat transfer rates. This is especially the case for those ¯ows with a wavy 3-D structure, meaning ¯ows which, on average, are symmetrical with respect to the interdisk midplane. However, examples are also provided where the ¯ow is strongly 3-D, requiring computationally intensive calculations to obtain accurate predictions of the corresponding heat transfer rates.

One of the most important disadvantages of solar air heaters is their low thermal performance. The use of porous plates, doubleglazed glass, and geometric changes to the absorber plate is methods for improving the heat transfer and thermal performance of solar air heaters. In this numerical study, an attempt is made to investigate the geometric changes made to the solar air heater using the computational fluid dynamics method, and the results are compared with previous research and the optimal state is selected. The maximum thermal efficiency of 82% is related to the presence of three baffles in the solar air heater. The most optimal thickness for the flat plate solar air heater is about 15 to 18 cm thick. The thermal efficiency of double-glazed glass is 20% higher than that of single-glazed glass. Increasing the number of baffles by more than 3 leads to an increase in pressure drop.

Thermoacoustic engines have been subjected to numerous studies for the past ten years. Our current research focus on the transient regime in an annular thermoacoustic primemover. It appears that several phenomena can play a role in the amplification and saturation regimes. Indeed, we can quote acoustically induced conductivity, forced convection due to acoustic streaming, heat conduction in different parts of the thermoacoustic prime-mover, and saturation due to harmonic generation. The experiments presented here show for the first time a double-threshold phenomenon during the amplification regime. The first threshold, which corresponds to the setting of the thermoacoustic instability, is followed by a saturation regime. Then without any changes in the control parameters, a second threshold has been observed after a time delay, corresponding to an additional amplification. Other interesting results are also presented.

In a recent paper we developed a Theoretical model built on the assumption that current transients that occur during the electrochemical deposition of species arise from the simultaneous contribution of three basic mechanisms: reaction, diffusion and convection. The theory provided an explanation for the different effects exhibited by voltammograms when natural and irregular convective movements are supposed to develop inside the electrolytic cell. In this paper we examine the underlying physics and the effectiveness of the theoretical model in describing electrochemical processes under forced convection conditions, particularly the effect of hydrodynamic conditions on the current-potential and current-time curves. We also examine the connection among diffusion layer thickness, convective velocity and stationary concentration on the electrode surface, regarding the role they play in the current yields. A comparative study of our model and the one introduced by Hyde and Compton [M.E. Hyde, R.G. Compton, J. Electroanal. Chem. 581 (2005) 224-230.] is performed, revealing similar results despite fundamental differences in the approaches of both theoretical models. The present work shows, from a basic point of view how the stationary current yield results from the interplay of convective velocity and diffusion layer thickness.

Molten salts are used in a wide range of engineering platforms, with particular niche involving high-temperature thermo-fluidic applications. Molten salts are employed as industrial working fluids for several high temperature processing applications, including: as a catalytic medium for fuel production, for synthesis of exotic ceramic materials, and pyrolysis of waste products. Molten salts are of particular interest as materials for energy related applications, such as in the fields of Concentrated Solar Power (CSP), enhanced oil recovery, advanced nuclear reactors and nuclear fuel cycles. Industry wide applications include molten salt eutectics as materials for Thermal Energy Storage (TES) and as Heat Transfer Fluids (HTF), typically for enhancing the commercial gridscale reliability of utilities that utilize CSP. Molten salts offer unique advantages such as low vapor pressure, extended operating temperature ranges, safe operation, minimal environmental footprint and moderate cost (compared to conventional heat transfer oils and ionic liquids). The scope of this literature review is limited to forced convective heat transfer data for a variety of molten salt formulations. The motivation of this study is guided by the promising role of molten salts in energy related applications, since the knowledge of the range of forced-convective heat transfer coefficients accruing from leveraging this class of working fluids are going to be crucial for determining (as well designing) the size and performance of the thermal devices. This review reveals that there is still a need for characterizing the heat transfer performance for various commercial molten salt eutectics and the available heat transfer data can be predicted reasonably well with available standard correlations. In addition, the goal of this review is to analyze the available literature data for the purpose of identifying the future research directions on this topic. science publication database (ISI, 0000). As seen from the plot, there is

The kinetics of colour and fluorescence development were studied in aqueous systems containing whole milk powder (WMP) and sucrose (S) at three WMP/S ratios (R ¼ 0.30, 0.68, 1.06) and three temperatures (T ¼ 105, 122.5, 140 1C). At each testing time, the colour parameters Kubelka-Munk index (K/S), lightness (L), optical density (OD), absorption coefficient (K), dominant wavelength (DWL) and fluorescence (F) were determined. F and 100/L were the most appropriate parameters to study non-enzymatic browning in concentrated milk systems. Adequate models (r 2 40.96) developed to analyse the effect of T and R on the rate constants, showed that colour parameters and their kinetic coefficients were mainly affected by temperature. The influence of R was more relevant at high temperatures. The activation energies and Q 10 values obtained for K/S, 100/L, F and OD were in the range 81-159 kJ mol À1 and 1.8-3.8, respectively. F and reflectance properties showed different dependence on temperature and R, reflecting that although related, they do not have the same origin and significance.

All electronics components generates heat during their operation which must get dissipated to the surrounding to ensure satisfactory performance of device and to avoid the damage to the components. One of the promising way to dissipate this heat is attaching heat sink to the device, i.e. transferring heat by convection. How much heat will get transferred by Convection depends upon geometrical parameter such as fin length, height, width, spacing, thickness ,operating parameter like heat supplied to device, temperature difference between surface and surrounding and few other parameters like fin material, fin array orientation, number of fins etc. Day by day size of electronic devices is reducing but amount of heat generated within device is increasing as surface area exposed to surrounding is reducing due to decrease in size of device. This paper reviews the parameter which affects convective heat transfer most for a constrained dimensions of heat sink. Also, this paper focuses on ass...

In this paper, forced convective heat transfer in a water based nanofluid has experimentally been compared to that of pure water in an automobile radiator. Five different concentrations of nanofluids in the range of 0.1e1 vol.% have been prepared by the addition of Al 2 O 3 nanoparticles into the water. The test liquid flows through the radiator consisted of 34 vertical tubes with elliptical cross section and air makes a cross flow inside the tube bank with constant speed. Liquid flow rate has been changed in the range of 2e5 l/min to have the fully turbulent regime (9 Â 10 3 < Re < 2.3 Â 10 4 ). Additionally, the effect of fluid inlet temperature to the radiator on heat transfer coefficient has also been analyzed by varying the temperature in the range of 37e49 C. Results demonstrate that increasing the fluid circulating rate can improve the heat transfer performance while the fluid inlet temperature to the radiator has trivial effects. Meanwhile, application of nanofluid with low concentrations can enhance heat transfer efficiency up to 45% in comparison with pure water.

This paper presents mathematical models of thin layer forced convection solar drying of Cuminum cyminum using two drying methods (mixed and indirect) at different operating conditions. The average initial moisture content of the seeds for all tests was about 43% d.b. and the drying was performed continuously, in each test, for a uniform period of 90 minutes drying time in a solar cabinet dryer to obtain an average final moisture content of 8% d.b. Three airflow rates (0.084, 0.127 and 0.155 m 3 s -1 ) were adopted and the experiments were run each sunny day from 11:30 to 13:00 with an average solar intensity of 750 W m -2 (±50 W m -2 ), ambient air temperature of 27°C (±1°C) and relative humidity of 30% (±1%). In order to find the most suitable form of thin layer solar drying model, eleven different mathematical models were selected using the experimental data to determine the pertinent coefficients for each model by applying the non-linear regression analysis technique. The goodness of fit was evaluated by calculating and comparing the statistical values of the coefficient of determination (R 2 ), reduced chi-square (χ 2 ) and root of mean square error (RMSE) for any model and for the two drying methods. The best results were found for the approximation of diffusion model with R 2 = 0.995, 0023 . 0 2 = χ and RSME= 0.0199 in mixed mode type, and the Midilli model with R 2 = 0.994, 0.0045 2 = χ and RSME= 0.0225 in indirect mode type thin layer solar drying.

An experimental study was performed to investigate the heat transfer and pressure drop characteristics of serrated finned tube banks with staggered layouts. The influences of varied fin densities, transversal tube spacing and longitudinal tube spacing were presented. For a constant fin height, an increase in the fin density resulted in an increase in the Euler number, and a gradual decrease in the Nusselt number was observed as the Reynolds number increased. An increase in the transversal tube spacing corresponded to a significant reduction in the Euler number, whereas the Nusselt number essentially remained unchanged. The longitudinal tube spacing had an insignificant effect on the Nusselt and Euler numbers, and the optimum ratio of the transversal tube spacing to longitudinal tube spacing increased with an increase in the transversal tube spacing. Scaling of the tube spacing had little effect on the Nusselt number but had a significant influence on the Euler number. Finally, predictive correlations for Nusselt and Euler numbers were developed based on the data presented here, and comparisons between the test data from this paper and the predictive values from previously published correlations were performed.

From potentiostatic current transients and voltammetry studies, carried out under both stagnant and forced convection conditions, the tenoxicam electrochemical behavior on a bare carbon paste rotating disk electrode was assessed in an aqueous solution (pH = 0.403). It was found that tenoxicam's electrochemical oxidation is a mass transfer-controlled process where a current peak is clearly formed at around 0.74 V when the potential scan was varied in the positive direction. However, when the potential was switched to the negative direction, up to the initial potential value, no reduction peak was formed. Tenoxicam's electrochemical oxidation follows an EC mechanism where the electrodic and chemical kinetics are fast. From sample-current voltammetry both the number of electrons, n, that tenoxicam losses during its electro-oxidation and its half-wave potential, E 1/2 , were determined to be 2 and 0.770 V vs. Ag/AgCl, respectively. Moreover, from differential pulse voltammetry plots it was confirmed that effectively in this case n = 2. Considering 2 electrons and both the Randles-Sevcik and Cotrell equations, the tenoxicam's diffusion coefficient, D, was determined to be (3.745 ± 0.077) × 10 -6 and (4.116 ± 0.086) × 10 -6 cm 2 s -1 , respectively. From linear sweep voltammetry plots recorded under forced convection conditions, it was found that Levich's equation describes adequately the limiting current recorded as a function of the electrode rotation rate, from where the D value was also found to be (4.396 ± 0.058) × 10 -6 cm 2 s -1 . Therefore, the average D value was (4.09 ± 0.33) × 10 -6 cm 2 s -1 . Furthermore, from the radius of the tenoxicam molecule, previously optimized at M052X/6-31 + G(d,p) level of theory, and using the Stokes-Einstein approach, D was also estimated to be 4.54 × 10 -6 cm 2 s -1 which is similar to the experimentally estimated values, under both stagnant and forced convection hydrodynamic conditions.

Compact heat exchangers are of great technological importance in many industries such as automotive, submarine and spacecraft industry. Micro-channel cooling is an area which is providing a new platform for the development of these compact heat exchange devices. Micro-channel flows and heat transfer characteristics are different from what is usually observed in macrochannel flows. In the present work, computational fluid dynamics is used as a tool to study the influence of variable thermophysical properties on the Nusselt number, skin friction and pressure drop for different channel diameter, fluid inlet velocities, and heat fluxes. The Nusselt number and pressure drop is found to be higher for variable properties as compared to constant properties for an increase in diameters, inlet velocities, and heat fluxes. Temperature-dependent specific heat capacity z Radial and axial cylindrical coordinate (m) R Pipe radius (m) Re Reynolds number (-) T m Bulk mean temperature (K) T w Wall temperature (K) T in Inlet temperature (K) B Amjad Ali Pasha

February 1999 Contents * 1.7 Weak solutions * 1.8 More independent variables 1.9 Postscript Exercises 2 First-order quasilinear systems 2.1 Motivation and models 2.2 Cauchy data and characteristics 2.3 The Cauchy-Kowalevski theorem 2.4 Hyperbolicity 2.4.1 Two-by-two systems 2.4.2 Systems of dimension n 2.4.3 Examples * 2.5 Weak solutions and shock waves 2.5.1 Causality 2.5.2 Viscosity and entropy 2.5.3 Other discontinuities * 2.6 Systems with more than two independent variables Exercises 3 Introduction to second-order scalar equations 3.1 Preamble 3.2 The Cauchy problem for semilinear equations 3.3 Characteristics 3.4 Canonical forms for semilinear equations 3.4.1 Hyperbolic equations 3.4.2 Elliptic equations 3.4.3 Parabolic equations 3.5 Some general remarks Exercises vii viii CONTENTS 4 Hyperbolic equations 4.1 Introduction 4.2 Linear equations: the solution to the Cauchy problem 4.2.1 An ad hoc approach to Riemann functions 4.2.2 The rationale for Riemann functions 4.2.3 Implications of the Riemann function representation 4.3 Non-Cauchy data for the wave equation * 4.3.1 Strongly discontinuous boundary data 4.4 Transforms and eigenfunction expansions 4.5 Applications to wave equations 4.5.1 The wave equation in one space dimension 4.5.2 Circular and spherical symmetry * 4.5.3 The telegraph equation * 4.5.4 Waves in periodic media * 4.5.5 General remarks 4.6 Wave equations with more than two independent variables 4.6.1 The method of descent and Huygens' principle 4.6.2 Hyperbolicity and time-likeness * 4.7 Higher-order systems 4.7.1 Linear elasticity 4.7.2 Maxwell's equations of electromagnetism 4.8 Nonlinearity 4.8.1 Simple waves CONTENTS ix 5.6.2 Helmholtz' equation 5.6.3 The modified Helmholtz equation * 5.7 Green's functions, eigenfunction expansions and transforms 5.7.1 Eigenvalues and eigenfunctions 5.7.2 Green's functions and transforms 5.8 Transform solutions of elliptic problems 5.8.1 Laplace's equation with cylindrical symmetry: Hankel transforms 5.8.2 Laplace's equation in a wedge geometry; the Mellin transform * 5.8.3 Helmholtz' equation * 5.8.4 Higher-order problems 5.9 Complex variable methods 5.9.1 Conformal maps * 5.9.2 Riemann-Hilbert problems * 5.9.3 Mixed boundary value problems and singular integral equations * 5.9.4 The Wiener-Hopf method * 5.9.5 Singularities and index *5.10 Localised boundary data 5.11 Nonlinear problems 5.11.1 Nonlinear models 5.11.2 Existence and uniqueness 5.11.3 Parameter dependence and singular behaviour 5.12 Liouville's equation again 5.

In this paper, the effects of the fluid-thermal parameters of a porous medium with different values of porosity and permeability on the fluid flow, heat, and concentration parameters were investigated for solar energy applications. The characteristics of the boundary layer, velocity profiles, pressure drop, and thermal and high heat concentration distribution have been analyzed. A developed Brinkman equation for fluid flow and a power law model for thermal conductivity (considering the porosity and permeability factors) were calculated with constant solar heat flux. The numerical model was developed based on the finite element method by the LU algorithm using the MUMPS solver. The Brinkman equations were solved under steady and unsteady states for velocity, pressure, thermal, and concentration distribution effects, respectively. In a porous medium, the normalized temperature of the presented model had an acceptable agreement with the experimental data, with a maximum error of 3%. At constant permeability, by decreasing the porosity, the velocity profile was extended. This was mainly due to the presence of pores in the collector. With an accelerated flow, the maximum velocity of 2.5 m/s occurred at a porosity of 0.2. It was also found that in the porous collector, the Nusselt number increased where the maximum difference between the porous and the nonporous collectors occurred at the beginning of the collector, with a value of 32%, and the minimum difference was 27%. The results also indicate that in the porous collector, solar energy absorbance was higher and the heat transfer was improved. However, an increase in the pressure drop was noted in the porous collectors.

In this paper, the effects of the fluid-thermal parameters of a porous medium with different values of porosity and permeability on the fluid flow, heat, and concentration parameters were investigated for solar energy applications. The characteristics of the boundary layer, velocity profiles, pressure drop, and thermal and high heat concentration distribution have been analyzed. A developed Brinkman equation for fluid flow and a power law model for thermal conductivity (considering the porosity and permeability factors) were calculated with constant solar heat flux. The numerical model was developed based on the finite element method by the LU algorithm using the MUMPS solver. The Brinkman equations were solved under steady and unsteady states for velocity, pressure, thermal, and concentration distribution effects, respectively. In a porous medium, the normalized temperature of the presented model had an acceptable agreement with the experimental data, with a maximum error of 3%. At...

This paper presents the results of an experimental investigation of transient forced convective heat transfer for turbulent flow of nine circular tubes with baffle plate inserts using different pitch to tube inlet diameter ratios and baffle orientation angles in the range of Reynolds number 3000 Re 20000 in the case of constant heat flux. The characteristic parameters of the tubes are: pitch to tube inlet diameter ratio HaD 1, 2 and 3; baffle orientation angle 45, 90 and 180 degree. Air, having a Prandtl number of 0.71 was used as the working fluid, while stainless steel was considered as the pipe material. The data show that unsteady entropy generation numbers for the baffled tubes are higher than those from the steady one. A generalised correlation for the unsteady entropy generation number relative to the steady dimensional entropy generation number for the baffle inserted tubes has been developed.

Influence of triple helical tapes inserted for turbulent flow through a tube on heat transfer enhancement was studied experimentally. The triple helical tapes made of mild steel with different helix angles, α = 9°, 13°, 17°, and 21°were examined for Reynolds number ranging from 22,000 to 51,000. The experiment showed that the Nusselt number, effectiveness and friction factor for the inserts were found to be up to 4.5, 3.45 and 3.0 times, respectively, over the plain tube. The highest enhancement efficiency achieved was 3.7 for the inserts based on constant blower power. Finally, new correlations for predicting heat transfer and friction factor for turbulent flow through a circular tube fitted with the inserts were proposed.