Accepted Manuscripts

Technical Brief  
Marc Hodes, Toby Kirk and Darren Crowdy
J. Heat Transfer   doi: 10.1115/1.4039993
There is a substantial and growing body of literature which solves the Laplace equation governing the velocity field for a linear shear flow of liquid in the unwetted (Cassie) state over a superhydrophobic surface. Usually, no-slip and shear-free boundary conditions are applied at liquid-solid interfaces and liquid-gas interfaces (menisci), respectively. When the menisci are curved, the liquid is said to flow over a "bubble mattress.'' We show that the dimensionless apparent hydrodynamic slip length determined by such studies equals a dimensionless spreading (constriction) resistance for a flat, isothermal heat source (sink) surrounded by arc-shaped (including flat) adiabatic boundaries. Furthermore, we show that this parameter also equals a dimensionless thermal contact resistance between mating surfaces with (flat) contacts surrounded by arc-shaped adiabatic regions in the nominal plane of contact. Since real surfaces are rough rather than smooth this yields more accurate analytical results for thermal contact resistance than in the literature. We also provide formulae for the case when each period window includes a finite number of no-slip (or isothermal) and no-shear (or adiabatic) regions and extend them to the case when the latter are weakly curved. Finally, we discuss other areas of mathematical physics to which our results are directly relevant.
TOPICS: Contact resistance, Shear (Mechanics), Shear flow, Bubbles, Boundary-value problems, Laplace equations, Flow (Dynamics), Heat, Surface roughness, Mathematical physics
Tasawar Hayat, Ikram Ullah, Ahmed Alsaedi and Bashir Ahmad
J. Heat Transfer   doi: 10.1115/1.4039994
This article addresses non-linear mixed convection flow due to Riga plate with double stratification. Heat transfer analysis is reported for heat generation/absorption and non-linear thermal radiation. Physical problem is mathematically modeled and non-linear system of partial differential equations (PDEs) is achieved. Transformations are then utilized to obtain non-linear system of ordinary differential equations. Graphical descriptions for velocity, temperature and concentration distributions are captured and argued for several set of physical variables. Features of skin friction and Nusselt and Sherwood numbers are also illustrated. Our computed results indicates that the attributes of buoyancy ratio and modified Hartman number enhance the velocity distribution.
TOPICS: Flow (Dynamics), Mixed convection, Nonlinear systems, Partial differential equations, Buoyancy, Heat, Temperature, Heat transfer, Absorption, Skin friction (Fluid dynamics), Thermal radiation, Differential equations
Kahina Bachir Cherif, Djamal Rebaine, Fouad E. Erchiqui, Issouf Fofana and Nabil Nahas
J. Heat Transfer   doi: 10.1115/1.4039990
This paper addresses the problem of distributing uniformly the energy flux intercepted by a thermoplastic sheet surface during the infrared radiation. To do so we discritized this problem and then formulated it as an integer linear programming problem, for which we applied two meta-heuristic algorithms namely the simulated annealing and harmony search algorithms, in order to minimize the corresponding objective function. The results produced by the numerical study we conducted on the performance of both algorithms are presented and discussed.
TOPICS: Infrared radiation, Algorithms, Integer programming, Simulated annealing, Heating
michele chiumenti, Miguel Cervera, Emilio Salsi and Andrea Zonato
J. Heat Transfer   doi: 10.1115/1.4039991
In this work a novel phenomenological model is proposed to study the liquid-to-solid phase change of eutectic and hypoeutectic alloy compositions. The objective is to enhance the prediction capabilities of the solidification models based on a-priori definition of the solid fraction as a function of the temperature field. However, the use of models defined at the metallurgical level is avoided to minimize the number of material parameters required. This is of great industrial interest because, on the one hand, the classical models are not able to predict recalescence and undercooling phenomena, and, on the other hand, the complexity as well as the experimental campaign necessary to feed most of the microstructure models available in the literature make their calibration difficult and very dependent on the chemical composition and the treatment of the melt. Contrarily, the proposed model allows for an easy calibration by means of few parameters. These parameters can be easily extracted from the temperature curves recorded at the hot spot of the Quick-Cup test, typically used in the Differential Thermal Analysis (DTA) for the quality control of the melt just before pouring. The accuracy of the numerical results is assessed by matching the temperature curves obtained via DTA of eutectic and hypoeutectic alloys. Moreover, the model is validated in more complex casting experiments where the temperature is measured at different thermocouple locations. The remarkable agreement with the experimental evidence validates the predicting capabilities of the proposed model.
TOPICS: Supercooling, Solidification, Alloys, Temperature, Calibration, Thermal analysis, Thermocouples, Casting, Quality control
Sina Khayyam and Seyed M. Hosseini Sarvari
J. Heat Transfer   doi: 10.1115/1.4039992
An inverse radiation-conduction analysis is performed for simultaneous estimation of the thermal properties in an absorbing, emitting, and linear-anisotropically scattering media with spatially variable refractive index. The discrete ordinates method in conjugation with finite volume method is adopted to solve the direct problem. The conjugate gradient method is employed to simultaneously estimate the conduction-radiation parameter, optical thickness, single scattering albedo, scattering phase function, and the wall emissivities, from the knowledge of the exit radiation intensities over the boundaries. The effects of these parameters and the measurement errors on the precision of the inverse analysis are investigated. Results show that the proposed inverse approach can successfully retrieve the unknown parameters for different refractive index profiles.
TOPICS: Heat transfer, Radiation (Physics), Heat conduction, Thermal properties, Transparency, Radiation scattering, Electromagnetic scattering, Scattering (Physics), Refractive index, Albedo, Errors, Finite volume methods, Gradient methods
Jing-zhi Zhang and Wei Li
J. Heat Transfer   doi: 10.1115/1.4039902
Heat transfer and flow characteristics of Taylor flows in vertical capillaries with tube diameters ranging from 0.5 mm to 2 mm were studied numerically with the Volume of Fluid (VOF) method. Streamlines, bubble shapes, pressure drops, and heat transfer characteristics of the fully-developed gas-liquid Taylor flow were investigated in detail. The numerical data fitted well with experimental results and with the predicted values of empirical correlations. The results indicate that the dimensionless liquid film thickness and bubble rising velocity increase with increasing capillary number. Pressure drops in liquid slug region are higher than the single-phase flow because of the Laplace pressure drop. The flow pattern dependent model and modified separate model which taking Bond number and Reynolds number into account can predict the numerical pressure drops well. Compared with the single-phase flow, less time is needed for the Taylor flow to reach a thermal fully-developed status. The Nusselt number of Taylor flow is about 1.16~3.5 times of the fully-developed single-phase flow with a constant wall heat flux. The recirculation regions in the liquid and gas slugs can enhance the heat transfer coefficient and accelerate the development of the thermal boundary layer.
TOPICS: Flow (Dynamics), Nitrogen, Water, Pressure drop, Bubbles, Heat transfer, Slug flows, Heat flux, Heat transfer coefficients, Thermal boundary layers, Fluids, Reynolds number, Liquid films, Shapes
Jiannan Chen, Rui-Na Xu, Zhen Zhang, Xue Chen, Xiaolong Ouyang, Gaoyuan Wang and Peixue Jiang
J. Heat Transfer   doi: 10.1115/1.4039903
Enhancing spray cooling with surface structures is a common, effective approach for high heat flux thermal management to guarantee the reliability of the many high power, high speed electronics and to improve the efficiency of new energy systems. However, the fundamental heat transfer enhancement mechanisms are not well understood especially for nanostructures. Here, we fabricated six groups of nanowire arrayed surfaces with various structures and sizes that show for the first time how these nanostructures enhance the spray cooling by improving the surface wettability and the liquid transport to quickly rewet the surface and avoid dry out. These insights into the nanostructure spray cooling heat transfer enhancement mechanisms are combined with microstructure heat transfer mechanism in integrated microstructure and nanostructure hybrid surface that further enhances the spray cooling heat transfer.
TOPICS: Cooling, Sprays, Nanowires, Heat transfer, Nanostructures , Reliability, Energy / power systems, Thermal management, Electronics, Heat flux
S Mamatha U, Mahesha and C.S.K. Raju
J. Heat Transfer   doi: 10.1115/1.4039904
This is a theoretical exploration of the magnetohydrodynamic Carreau fluid in a suspension of dust and graphene nanoparticles. Graphene is a two-dimensional singe-atom thick carbon nanosheet. Due to its high thermal conductivity, electron mobility, large surface area and stability it has remarkable material, electrical, optical, physical and chemical properties, in this study a simulation is performed by mixing of Graphene+water and Graphene+Ethylene glycol into dusty non-Newtonian fluids. Dispersion of graphene nanoparticles in dusty fluids finds applications in biocompatibility, bio-imaging, biosensors, detection and cancer treatment, in monitoring stem cells differentiation etc. Graphene+water and Graphene+Ethylene glycol mixtures are significant in optimizing the heat transport phenomena. Initially arising set of physical governing partial differential equations (PDEs) are transformed to ordinary differential equations (ODEs) with the assistance of similarity transformations. Consequential highly nonlinear ODEs are solved numerically through Runge-Kutta Fehlberg Scheme (RKFS). The computational results for Non-dimensional temperature, velocity, profiles are presented through graphs. Additionally, the numerical values of friction factor and heat transfer rate are tabulated numerically for various physical parameter obtained. We also validated the present results with previous published study and found to be highly satisfactory. The formulated model in this study reveals that heat transfer rate and wall friction is higher in mixture of graphene +Ethylene glycol when compared to graphene +water.
TOPICS: Fluids, Dust, Nanoparticles, Graphene, Unsteady flow, Heat flux, Heat transfer, Friction, Heat, Temperature, Stability, Magnetohydrodynamics, Simulation, Electron mobility, Thermal conductivity, Chemical properties, Non-Newtonian fluids, Carbon, Differential equations, Transport phenomena, Biosensors, Cancer, Atoms, Partial differential equations, Stem cells, Imaging, Biocompatibility
G Janardhana Reddy, Hussain Basha and Venkata Narayanan N. S.
J. Heat Transfer   doi: 10.1115/1.4039905
Present research article investigates the transient laminar free convective supercritical carbon dioxide flow past a semi-infinite vertical cylinder using numerical methods. Two new thermodynamic models for the supercritical fluid (SCF) have been considered. Based on these proposed models, for supercritical carbon dioxide two new equations for thermal expansion coefficient is obtained on the basis of Redlich-Kwong equation of state (RK-EOS) and Van der Waals equation of state (VW-EOS). Based on the calculated values of thermal expansion coefficient, it is shown that not only RK-EOS is closer to experimental values but also gives greater accuracy when compared to VW-EOS validating RK-EOS as suitable model for predicting natural convective properties of carbon dioxide under supercritical condition. The governing equations for the SCF flow over a vertical cylinder are obtained and they are unsteady, non-linear and coupled. Since the equations are highly complex, it is clear from the available literature survey that, there are no analytical or direct numerical techniques existed to simplify the fluid flow equations and hence, they are solved using the computational techniques such as Crank-Nicolson implicit finite difference scheme. Numerical simulations are performed for carbon dioxide in the region of its critical point. Results in subcritical, supercritical and near critical regions are shown graphically and discussed for different physical parameters. From the obtained graphical data, it is clear that, the steady-state time increases for the increasing values of reduced temperature and reduced pressure for carbon dioxide in supercritical region.
TOPICS: Heat transfer, Transients (Dynamics), Natural convection, Carbon dioxide, Cylinders, Equations of state, Supercritical carbon dioxide, Thermal expansion, Flow (Dynamics), Temperature, Fluid dynamics, Numerical analysis, Computer simulation, Supercritical fluids, Pressure, Steady state
Rajib Biswas and Sarder Firoz Ahmmed
J. Heat Transfer   doi: 10.1115/1.4039909
In this paper we have reported the effects of Hall current on MHD unsteady heat and mass transfer of Casson nanofluid flow through a vertical plate in the presence of radiation and chemical reaction. The model used for the nanofluid includes the effects of thermophoresis and Brownian motion. Then the model equations are transformed into non-dimensional form by the as usual mathematical procedure of transformation and the resultant non-dimensional coupled partial differential equations are solved by applying explicit finite difference technique. The obtained results are plotted after stability test by using graphics software tecplot-9.Then the results indicate the fluid flow, temperature and concentration distributions are significantly invaded by the various dimensionless parameters such as Magnetic parameter, Schmidt number, Grashof number, Lewis number, Prandtl number, modified Grashof number, Dufour number, thermophoresis parameter, Brownian motion parameter, Chemical reaction and Radiation parameter on velocity, temperature and concentration profiles along with the local Skin friction, local Nusselt number and Sherwood number. We have also discussed the results with the help of graphs. An increase in the Casson parameter is to put down the velocity and Dufour number parameter cut back the velocity profile whereas increasing the heat generation parameter increases the temperature profiles.
TOPICS: Flow (Dynamics), Magnetohydrodynamics, Heat, Mass transfer, Nanofluids, Vertical plates, Chemical reactions, Radiation (Physics), Brownian motion, Temperature, Skin friction (Fluid dynamics), Computer software, Stability, Fluid dynamics, Partial differential equations, Prandtl number, Temperature profiles
Jin Shang, Chaoran Jiang, Liujun Xu and Jiping Huang
J. Heat Transfer   doi: 10.1115/1.4039910
Invisibility has recently been achieved in optics, electromagnetics, acoustics, thermotics, fluid mechanics, and quantum mechanics; it was realized through a properly designed cloak structure with unconventional (anisotropic, inhomogeneous, and singular) material parameters, which limit practical applications. Here we show, directly from the solution of Laplace's equation, that two or more conventional (isotropic, homogeneous, and nonsingular) materials can be made thermally invisible by tailoring the many-particle local-field effects. Our many-particle thermal invisibility essentially serves as a new class of invisibility with a mechanism fundamentally differing from that of the prevailing cloaking-type invisibility. We confirm it in simulation and experiment. As an application, the concept of many-particle thermal invisibility helps us propose a class of many-particle thermal diodes: the diodes allow heat conduction from one direction with invisibility, but prohibit the heat conduction from the inverse direction with visibility. This work reveals a different mechanism for thermal camouflage and thermal rectification by using composites, and it also suggests that besides thermotics, many-particle local-field effects can be a convenient and effective mechanism for achieving similar controls in other fields, e.g., optics, electromagnetics, acoustics, and fluid mechanics.
TOPICS: Particulate matter, Acoustics, Heat conduction, Fluid mechanics, Electromagnetism, Optics, Electromagnetic force, Laplace equations, Thermal rectification, Quantum mechanics, Composite materials, Simulation, Anisotropy
Huayong Zhao and Colin P. Garner
J. Heat Transfer   doi: 10.1115/1.4039911
This paper presents the corrections for existing hydrodynamic instability based Critical Heat Flux (CHF) models in pool boiling by taking into account the effect of the viscosity, geometry and size of the liquid-vapour interface. Based on the existing literature, the Kelvin - Helmholtz theory used by the most commonly adopted CHF models can lead to noticeable errors when predicting the instability conditions. This is due to neglecting the effects of fluids viscosity and its oversimplification of the interface geometry. In addition, the literature suggests the most unstable condition predicted by the Viscous Correction for Viscous Potential Flow (VCVPF) theory for cylindrical interface best matches the observed vapour column breakup condition. In this paper, the most unstable instability conditions predicted by the VCVPF theory are used to correct for the existing CHF models. The comparison between the existing and corrected CHF models suggests the corrected models always predict a higher CHF value. In addition, the corrected Zuber model predicts similar CHF value to the Lienhard and Dhir model. Comparison with experimental data suggests the corrections to the Zuber's model can increase its prediction accuracy in most cases, but not necessary for the Lienhard and Dhir model. When compared to experimental CHF data for boiling cryogens at different pressures, the introduced corrections consistently help to improve the accuracy of both the Zuber model and the Lienhard and Dhir model.
TOPICS: Viscosity, Heating, Critical heat flux, Hydrodynamic stability, Geometry, Pool boiling, Boiling, Errors, Flow (Dynamics), Fluids
Moussa Mirehei and Jose L. Lage
J. Heat Transfer   doi: 10.1115/1.4039914
The steady-periodic natural convection phenomenon inside a heated enclosure filled with disconnected, discrete solid blocks, and under horizontal, time-periodic heating is investigated numerically. This configuration is akin to several practical engineering applications, such as oven baking in food processing, heat treating of metal parts in materials processing, and storage and transportation of discrete solid goods in containerization. Because of the relative large size, and limited number of solid bodies placed inside the enclosure, the solid and fluid constituents are viewed separately and the process modeled using continuum balance equations for each with suitable compatibility conditions imposed at their interfaces. The periodic heating is driven by a sinusoidal in time hot-wall temperature, while maintaining the cold wall temperature constant, with top and bottom surfaces adiabatic. Results are presented in terms of hot and cold wall-averaged Nusselt numbers, time-varying energy capacity of the enclosure, and periodic isotherms and streamlines, for Ra varying from 10^3 to 10^7, Pr equal to 1, and 36 uniformly distributed, conducting and disconnected solid square blocks. The results explain why and how the effect of varying Ra on the convection process is significantly affected by the presence of the solid blocks. An analytical equation, valid for time-periodic heating, is proposed for anticipating the block interference effect with great accuracy, substantiating the distinct features of Nusselt versus Rayleigh observed when the blocks are present inside the enclosure.
TOPICS: Rayleigh number, Fluids, Heating, Metals, Heat, Temperature, Convection, Engineering systems and industry applications, Materials processing, Natural convection, Transportation systems, Food products, Ovens, Storage, Wall temperature
Hao Wu, Nan Gui, Xingtuan Yang, Jiyuan Tu and Shengyao Jiang
J. Heat Transfer   doi: 10.1115/1.4039913
For the heat transfer of pebble or granular beds (e.g. high temperature gas-cooled reactors (HTGR)), the particle thermal radiation is an important part. Using the sub-cell radiation model (SCM) which is a generic theoretical approach to predict effective thermal conductivity (ETC) of particle radiation, particle-scale investigation of the nuclear packed pebble beds filled with mono-sized or multi-component pebbles is performed here. When the radial porosity distribution is considered, the ETC of the particle radiation decreases significantly at near-wall region. It is shown that radiation exchange factor increases with the surface emissivity. The results of the SCM under different surface emissivity are in good agreement with the existing correlations. The discrete heat transfer model in particle scale is presented, which combines discrete element method (DEM) and particle radiation model, and is validated by the transient experimental results. Compared with the discrete simulation results of polydisperse beds, it is found that the SCM with the effective particle diameter can be used to analyse the behaviour of the radiation in polydisperse beds.
TOPICS: Particulate matter, Thermal radiation, Radiation (Physics), Alpha particles, Emissivity, Heat transfer, Discrete element methods, Very high temperature reactors, Porosity, Simulation results, Thermal conductivity, Transients (Dynamics)
Marcelo J.S. de Lemos and Paulo Carvalho
J. Heat Transfer   doi: 10.1115/1.4039915
This work presents a study of double-diffusive free convection in a porous square cavity under turbulent flow regime and with aiding drive. The thermal non-equilibrium model was employed to analyze the energy and mass transport across the enclosure. Governing equations were time- and volume averaged according to the double-decomposition concept. Analysis of a modified Lewis number, Lem, showed that for porous media this parameter presents opposite behavior when varying the thermal conductivity ratio or the Schmidt number, while maintaining the same value for Lem. Differently form free flow, the existence of the porous matrix contributes to the overall thermal diffusivity of the medium, whereas mass diffusivity is only effective within the fluid phase for an inert medium. Results indicated that increasing Lem through an increase in Sc reduces flow circulation inside porous cavities, reducing Nuw and increasing Shw. Results further indicate that increasing the buoyancy ratio N promotes circulation within the porous cavity, leading to an increase in turbulence levels within the boundary layers. Partial contributions of each phase of the porous cavity (solid and fluid) to the overall average Nusselt number becomes independent of N for higher values of the thermal conductivity ratio, ks/kf. Further, for high values of ks/kf, the average Nusselt number drops as N increases.
TOPICS: Porous materials, Turbulence, Equilibrium (Physics), Buoyancy, Convection, Cavities, Flow (Dynamics), Fluids, Thermal conductivity, Boundary layers, Thermal diffusivity, Natural convection
Technical Brief  
S Saravanan and N Raja
J. Heat Transfer   doi: 10.1115/1.4039912
This paper reports the changes made in the ?ow and heat transfer characteristics of a closed enclosure in the presence of sidewalls with symmetrical linear heating. The ?ow inside the enclosure is primarily driven by a centrally placed discrete heater with thermal radiation included at all surfaces involved. Finite volume method based computational results corresponding to the resulting steady state were obtained. The factors causing augmentation and suppression of heat transfer are discussed for two types of sidewall heating. Moreover it is found that the role of radiation is well stronger than convection in determining the total heat transfer rate when the side wall heating is decreasing with height.
TOPICS: Temperature, Radiation (Physics), Convection, Heating, Heat transfer, Symmetry (Physics), Thermal radiation, Finite volume methods, Steady state
Christopher F. Cirenza, Thomas E. Diller and Christopher B. Williams
J. Heat Transfer   doi: 10.1115/1.4039759
A two-year study was conducted to engage undergraduate mechanical engineering students to approach heat transfer education in an active, hands-on manner and excite them to pursue research and graduate studies in the field. Physical workshops were designed and implemented into junior level heat transfer classes, allowing students to feel and observe heat transfer using heat flux and temperature sensors that provided real-time data. These instruments, coupled with open-ended, challenge-based pedagogy, provided opportunities for students to explore important heat transfer concepts, such as the differences between heat and temperature. The conceptual knowledge of the students was assessed through concept-specific questions. These results were compared to those of a control group who took the traditional lecture without the workshops. The results yielded significantly higher scores for the experimental group in the first year but much less of a difference in the second year, which added video-enhanced workshops in place of the purely hands-on workshops. In addition to concept questions, surveys taken by the students reveal that the students much preferred the workshops over not having them. They also believed the workshops strongly enhanced their learning by giving them a real, hands-on experience.
TOPICS: Heat transfer, Students, Workshops (Work spaces), Instrumentation, Temperature sensors, Education, Heat flux, Undergraduate students, Mechanical engineering, Heat, Temperature
Silvia Ravelli and Giovanna Barigozzi
J. Heat Transfer   doi: 10.1115/1.4039763
Within the framework of scale resolving simulation techniques, this paper considers the application of the Stress-Blended Eddy Simulation (SBES) model to pressure side film cooling in a high pressure turbine nozzle guide vane. The cooling geometry exhibits two rows of film cooling holes and a trailing edge cutback, fed by the same plenum chamber. The blowing conditions investigated were in the range of coolant-to-mainstream mass flow ratio (MFR) from 1% to 2%. The flow regime resembles that in a real engine (exit isentropic Mach number of Ma2is = 0.6), but also low speed conditions (Ma2is = 0.2) were considered for comparison purposes. The predicted results were validated with measurements of surface adiabatic effectiveness and instantaneous off-wall visualizations of the flow field downstream of cooling holes and cutback slot. The focus is on SBES ability of developing shear layer structures, because of their strong influence on velocity field, entrainment mechanisms and, thus, vane surface temperature. Special attention has been paid to the development and dynamics of coherent unsteadiness, since measured values of shedding frequency were also available for validation. SBES provided significant improvement in capturing the unsteady physics of cooling jet-mainstream interaction. The effects of changes in flow regime and blowing conditions on vortex structures were well predicted along the cutback surface. As regards the cooling holes, the high speed condition made it difficult to match the experimental Kelvin-Helmholtz breakdown in the shear layer, in case of high velocity jets.
TOPICS: Pressure, Eddies (Fluid dynamics), Simulation, Stress, Turbines, Film cooling, Cooling, Flow (Dynamics), Shear (Mechanics), Jets, Nozzle guide vanes, Mach number, Temperature, Engines, Physics, Dynamics (Mechanics), Visualization, Vortices, Geometry, Coolants, High pressure (Physics), Layer structure (Solids)
Sugun Tej Inampudi, Baji Marthi and Satyabrata Sahoo
J. Heat Transfer   doi: 10.1115/1.4039764
Natural circulation loop (NCL) based secondary fluid systems are simple, reliable and inexpensive due to the absence of any moving components such as pumps. Water based NCLs are widely used in applications such as solar collectors, nuclear reactors, etc. Also, most of the studies on natural circulation loops do not consider the 3-dimensional variation of the field variables. In the subject work, 3-D steady flow simulation of water based, single-phase rectangular natural circulation loop (NCL) with isothermal source and sink have been carried out to study the effects of different design and operating parameters such as loop height, temperature lift, in plane and out of plane tilt angles on the rate of heat transfer and the rate of entropy generation due to both fluid flow and heat transfer. Rate of entropy generation due to both heat transfer and fluid flow for turbulent flow regimes in a natural circulation loop is calculated for a wide range of design and operating parameters. In turbulent flow regimes the rate of entropy generation due to fluid flow is significant although rate of entropy generation due to heat transfer is dominant. All the above-mentioned design and operating parameters have significant effect on rate of entropy generation and rate of heat transfer as well. With increases in loop height and temperature lift, rate of entropy generation increases. As the tilt angle increases in XY plane, the rate of the entropy generation initially increases but after certain tilt angle it starts decreasing.
TOPICS: Entropy, Water, Heat transfer, Fluid dynamics, Design, Temperature, Turbulence, Fluids, Flow simulation, Pumps, Solar collectors, Nuclear reactors
Lin Liu, Liancun Zheng, Yanping Chen and Fawang Liu
J. Heat Transfer   doi: 10.1115/1.4039765
The paper gives a comprehensive study on the space fractional boundary layer flow and heat transfer over a stretching sheet with variable thickness, and the variable magnetic field is applied. Novel governing equations with left and right Riemann-Liouville fractional derivatives subject to irregular region are formulated. Solutions of the governing equations are obtained using numerical method by introducing new variables to change the boundary as a regular one, and meanwhile, the shifted Gr├╝nwald formulae are applied. By introducing new source items, the exact solutions are constructed and the comparisons between the numerical solutions and the exact ones are presented. Dynamic characteristics with the effects of fractional parameter, magnetic parameter, exponent parameter and weight coefficient on the velocity and temperature distributions are shown and discussed by graphical illustrations.
TOPICS: Flow (Dynamics), Heat transfer, Boundary layers, Numerical analysis, Temperature distribution, Magnetic fields, Weight (Mass)

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