Semi-analytical solution of the extended Graetz problem for combined electroosmotically and pressure-driven microchannel flows with step-change in wall temperature

Analytical solutions are obtained for the temperature and Nusselt number distribution in the thermal entrance region of a parallel plate microchannel under the combined action of pressure-driven and electroosmotic transport mechanisms, by taking into account the effects of viscous dissipation, Joule heating and axial conduction simultaneously, in the framework of an extended Graetz problem. Step changes in wall temperature are considered to represent physically conceivable thermal entrance conditions. The solution of the temperature distributions at the various channel sections essentially involves the determination of a set of eigenvalues and eigenfunctions corresponding to a Sturm Liouiville problem with non self-adjoint operators. The resultant eigenfunctions are non orthogonal in nature, and are obtained in the forms of hypergeometric functions. Parametric variations on the effects of the relative strengths of the pressure gradients and the electric field, ratio of the rate of heat generation to the rate of wall heat transfer, and the Peclet number are analyzed in details, in terms of their influences on the temperature field as well as the Nusselt number distribution.     

Micro-scale thermo-fluidic transport in two immiscible liquid layers subject to combined electroosmotic and pressure-driven transport

A theoretical analysis is presented for fully developed convective heat transfer in two immiscible fluid layers confined within parallel plate microchannels subject to combined effects of axial pressure gradients and imposed electrical fields. Assuming desperate zeta potentials at the interfaces thus formed, closed-form expressions are derived for the velocity and temperature distributions under fully developed conditions, with uniform wall heat flux boundary conditions. For the heat transfer analysis, the viscous dissipation effects are neglected as compared to the Joule heating effects. Results are subsequently obtained for different ranges of the ratios of various electrical properties of the two fluid layers and various relative strengths of the ratios of the electrical fields and the imposed pressure gradients. These results demonstrate the effects of the applied electric fields and pressure gradients, presence of external heat source or sink and interfacial positions on the temperature distributions in the two layers and the corresponding Nusselt numbers.     

The extended Graetz problem with piecewise constant wall temperature for pipe and channel flows

Axial heat conduction effects within the fluid can be important for duct flows if the Prandtl number is relatively low (liquid metals). In addition, axial heat conduction effects within the flow might also be important, if the heating zone is relatively short in length. The present paper shows an entirely analytical solution to the extended Graetz problem with piecewise constant wall temperature boundary conditions. The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is as simple to compute as the one without axial heat conduction. The analytical results are compared to available numerical calculations and good agreement is found.     

Extended Graetz problem including streamwise conduction and viscous dissipation in microchannel

Extended Graetz problem in microchannel is analyzed by using eigenfunction expansion to solve the energy equation. The hydrodynamically developed flow is assumed to enter the microchannel with uniform temperature or uniform heat flux boundary condition. The effects of velocity and temperature jump boundary condition on the microchannel wall, streamwise conduction and viscous dissipation are all included. From the temperature field obtained, the local Nusselt number distributions are shown as the dimensionless parameters (Peclet number, Knudsen number, Brinkman number) vary. The fully developed Nusselt number for each boundary condition is obtained also in terms of these parameters.     

The effect of wall conduction for the extended Graetz problem for laminar and turbulent channel flows

Axial heat conduction effects within the fluid can be important for duct flows if either the Prandtl number is relatively low (liquid metals) or if the dimensions of the duct are small (micro heat exchanger). In addition, axial heat conduction effects in the wall of the duct might be of importance. The present paper shows an entirely analytical solution to the extended Graetz problem including wall conduction (conjugate extended Graetz problem). The solution is based on a selfadjoint formalism resulting from a decomposition of the convective diffusion equation into a pair of first order partial differential equations. The obtained analytical solution is relatively simple to compute and valid for all Péclet numbers. The analytical results are compared to own numerical calculations with FLUENT and good agreement is found.     

Variation of momentum and thermal boundary layers for oscillatory flows in a channel

Zero mean oscillatory flow over a heated plate mounted on the bottom wall of a channel, is analysed by solving two dimensional time dependent governing equations using control volume based pressure correction procedure. A uniform sinusoidally varying velocity profile is applied at the inlet, and temperature of the heated plate is kept constant. The numerical solutions are compared with experimental values and the effects of Reynolds and Wormersly numbers on the velocity and temperature profiles are presented for the same Prandtl number.     

SCPPVC系统新翼型空气涡轮机性能数值模拟

为提高立式太阳能热气流发电系统(SCPPVC)的能量转换效率,基于Wilson理论,结合两种原空气涡轮机翼型优势表面,设计并建立了新翼型物理模型;采用数值模拟方法,探究了新翼型空气涡轮机在SCPPVC系统中的性能。结果表明:双翼型结合的新翼型空气涡轮机的能量转换效率大幅提高;当叶片数目为6,风速为5 m/s,尖速比为2时,该空气涡轮机性能相较原有模型分别提高了21.1%和29.2%。     

A novel cathode structure with double catalyst layers and low Pt loading for proton exchange membrane fuel cells

A novel cathode structure (NCS) was developed, which consisted of an inner and an outer catalyst layer (CL). It showed an improved platinum (Pt) utilization (above 50%), a lowered CL/gas diffusion layer interfacial resistance, and a decreased mass transport polarization compared with the traditional cathode structure (TCS). A hydrogen/air proton exchange membrane fuel cell employing NCS yielded an output power density up to 0.76 W cm⁻² with cathode Pt loading as low as 0.28 mg cm⁻². The enhanced performance of NCS is attributed to synergistic effect of the two catalyst supports in outer CL, which provides abundant pores to relieve water flooding and facilitates heat-induced proton conductor migration from the inner to outer CL, forming a hydrophilic proton conduction network. Moreover, the thin and compact inner CL can meet the demand of rich active sites and catalyst migration toward the regions nearest to the membrane under high current densities.     

A novel optimization model for combined wind power accommodation and electric boiler with thermal storage

As the installed capacity of wind power continues to increase, the problem of curtailed wind power is becoming serious in China, especially in the northern region during the winter heating season. To solve the problem of wind‐heat conflict during the heating period in the Three North area, an electric boiler with thermal storage (EBTS) is installed at the end of the grid where wind power is difficult to accommodate and using curtailed wind power to supply heat promotes local accommodation. In this paper, a multi‐objective optimization model of wind power accommodation based on the wind power–EBTS system for heating is established. The goals of maximizing wind power accommodation, minimizing the number of times EBTS must be adjusted, and minimizing operating costs are presented, and a bi‐level optimization scheme is designed. An improved multi‐objective particle swarm optimization algorithm is used to solve these functions, and an optimal compromise solution from the generated Pareto solution set is filtered using the fuzzy membership method. Based on actual data from a demonstration project in China's Jilin Province, the simulation results verify that this method can effectively reduce operating costs and improve wind power accommodation.     

Analytical solutions of Nusselt number for thermally fully developed flow in microtubes under a combined action of electroosmotic forces and imposed pressure gradients

Closed form expressions are developed for Nusselt number variation in a thermally fully developed microtube flow, under a combined influence of electroosmotic forces and imposed pressure gradients. The analysis takes care of the interaction amongst pressure driven convection and Joule heating effects, in order to obtain the pertinent rate of heat transfer. While separate limiting conditions on the asymptotic Nusselt number can be obtained for pure electroosmotic and solely pressure driven flows, relative influences of electrical potential gradients and imposed pressure gradients acting in tandem are also critically analyzed, as a function of the tube radius normalized with respect to the Debye length. Significant insights are also developed regarding the influence of adverse pressure gradients on the thermal transport, in presence of aiding electroosmotic effects.     

Analysis of Entropy Generation of Combined Heat and Mass Transfer in Internal and External Flows with the Assumption of Local Thermodynamic Equilibrium

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Convective heat transfer in helical coils for constant-property and variable-property flows with high Reynolds numbers

Forced convection heat transfer of single-phase water in helical coils was experimentally studied. The testing section was constructed from a stainless steel round tube with an inner diameter of 10 mm, coil diameter of 300 mm, and pitch of 50 mm. The experiments were conducted over a wide Reynolds number range of 40000 to 500000. Both constant-property flows at normal pressure and variable-property flows at supercritical pressure were investigated. The contribution of secondary flow in the helical coil to heat transfer was gradually suppressed with increasing Reynolds number. Hence, heat transfer coefficients of the helical tube were close to those of the straight tube under the same flow conditions when the Reynolds number is large enough. Based on the experimental data, heat transfer correlations for both incompressible flows and supercritical fluid flows through helical coils were proposed.     

Spatial and temporal behavior in the theory of thermoelasticity for solids with double porosity

In this article, we study the spatial and the temporal behavior of solutions to the initial boundary value problem associated with the linear theory of thermoelastic materials with a double porosity structure. We consider two appropriate time-weighted integral measures and we deduce some exponential estimates that describe the spatial behavior of solutions. For bounded bodies, we obtain estimates of Saint-Venant type, while for unbounded bodies we deduce some alternatives of Phragmén–Lindelöf type. The temporal behavior of solutions is described using the Cesáro means of various parts of the total energy.     

Methodology for modelling plug-in electric vehicles in the power system and cost estimates for a system with either smart or dumb electric vehicles

The article estimates the costs of plug-in electric vehicles (EVs) in a future power system as well as the benefits from smart charging and discharging EVs (smart EVs). To arrive in a good estimate, a generation planning model was used to create power plant portfolios, which were operated in a more detailed unit commitment and dispatch model. In both models the charging and discharging of EVs is optimised together with the rest of the power system. Neither the system cost nor the market price of electricity for EVs turned out to be high (36-263 €/vehicle/year in the analysed scenarios). Most of the benefits of smart EVs come from smart timing of charging although benefits are also accrued from provision of reserves and lower power plant portfolio cost. The benefits of smart EVs are 227 €/vehicle/year. This amount has to cover all expenses related to enabling smart EVs and need to be divided between different actors. Additional benefits could come from the avoidance of grid related costs of immediate charging, but these were not part of the analysis.     

Fundamental solution and uniqueness theorems in the linear theory of thermoviscoelasticity for solids with double porosity

In this article, the linear theory of thermoviscoelasticity for Kelvin–Voigt materials with double porosity is considered. The fundamental solution of the system of equations of steady vibrations is constructed by elementary functions and its basic properties are established. The Green’s first identity in the considered theory is obtained. A wide class of the internal and external boundary value problems (BVPs) of steady vibrations is formulated. Finally, on the basis of the Green’s identity, the uniqueness theorems for regular (classical) solutions of these BVPs are proved.     

Uncertainty and differences in GHG emissions between electric and conventional gasoline vehicles with implications for transport policy making

There is a huge uncertainty in the GHG emissions reduction potential with transport electrification. The typical Life Cycle Assessment (LCA) practice of modeling a pathway by reducing what is known about a model parameter to a single value to produce a single-point GHG emissions estimate has led to reports in literature on the GHG emissions differences between Electric Vehicles (EV) and conventional Internal Combustion Engines (ICE) to range significantly from below 10% to above 60%. In this study we performed a LCA, combined with a Monte Carlo stochastic simulation, to determine the uncertainty in GHG emission differences between EVs and gasoline ICEs, by taking into account of all the possible variations that may affect the lifecycle GHG emissions estimates for EVs and ICEs based on the technologies already available in the market today. This study provides insights into the relative importance of the factors driving the lifecycle GHG emissions difference between the EVs and ICEs, and a measure of the probability for EVs providing benefits over ICEs globally today and projected to 2040. This paper offers critical perspective to inform the global debates on the role of transport electrification as means to a low carbon mobility future, and the implications for policy makers.     

Falkner-Skan problem for a static and moving wedge with prescribed surface heat flux in a nanofluid

An analysis is carried out to study the problem of the steady flow and heat transfer over a static or moving wedge with a prescribed surface heat flux in a nanofluid. The governing partial differential equations are transformed into a set of nonlinear ordinary differential equations using similarity transformation, before being solved numerically by the Keller box method and the Runge-Kutta-Fehlberg method with shooting technique. The features of the flow and heat transfer characteristics are analyzed and discussed. Three different types of nanoparticles are considered, namely copper Cu, alumina Al₂O₃ and titania TiO₂ with water as the base fluid. It is found that the skin friction coefficient and the heat transfer rate at the surface are highest for copper-water nanofluid compared to the alumina-water and titania-water nanofluids. Moreover, the heat transfer rate at the surface increases with the Falkner-Skan power law parameter m.     

Chebyshev collocation spectral approach for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index

The Chebyshev collocation spectral method for discrete ordinates equation is presented to solve combined radiation and conduction heat transfer problem in semitransparent graded index media. The angular dependence of the problem is discretized by discrete ordinates method, and the space dependence is expressed by Chebyshev polynomial and discretized by collocation spectral method. The exponential convergence characteristic of the spectral methods is studied. The comparisons between the present results and those available in references indicate that, the Chebyshev collocation spectral-discrete ordinates method (SP-DOM so called) for combined radiation and conduction heat transfer in one-dimensional semitransparent medium with graded index is accurate and efficient.