Laminar forced convection in elliptic ducts

The problem of laminar forced convection heat transfer in short elliptical ducts with (i) uniform wall temperature and (ii) prescribed wall heat flux is examined in detail with the well known Lévêque theory of linear velocity profile near the wall. Moreover, consideration is given to the variation of the slope of the linear velocity profile with the position on the duct wall. A correction factor for the temperature dependent viscosity is included. Expressions for the local and average Nusselt numbers and wall temperatures are obtained. For the case of constant heat flux the Nusselt numbers are higher than for constant wall temperature.The results corresponding to the classical Graetz and Purday problems are deduced as special cases.Nomenclature a, b semiaxes of ellipse, b Graetz number (average), Re Pr D _e/Z - h _i ^o local heat transfer coefficient - J _n(x) Bessel function of order n - K thermal conductivity of the fluid - [X] Laplace transform of X - N _u ^o local Nusselt number, h _i ^o D _e/K - perimeter average Nusselt number - overall average Nusselt number - Nu _w wall Nusselt number - Nu Nusselt number at large distance from the inlet - p Laplace transform parameter - Pr Prandtl number, C _a/K - Re Reynolds number, D _e / _a - T temperature of the fluid - T ₁, T _W inlet and wall temperatures, respectively - u _z local isothermal velocity along the axis of the duct - average fluid velocity - x, y, z Cartesian coordinates, z-axis parallel to the axis of the duct (z=0 at duct inlet) - Z length of the duct - thermal diffusivity, K/C - * correction factor for the temperature dependent viscosity - (x) gamma function - coordinate measured normal to the wall of the duct - _a, _w viscosity of fluid at average and wall temperatures - , , z elliptic cylindrical coordinates - density of fluid - (z) heat flux     

Convective heat transfer characteristics of microencapsulated phase change material suspensions in minichannels

A comparative experimental study was conducted in order to investigate the convective heat transfer characteristics of water-based suspensions of microencapsulated phase change material (MEPCM) flowing through rectangular copper minichannels. The hydraulic diameter of the channels was 2.71 mm. MEPCM particles with an average size of 4.97 μm were used to form suspensions with mass concentrations ranging from 0 to 20%. The comparative experiments were performed for varying mass flow rates in the laminar region and varying thermal conditions. The cooling performance of the MEPCM suspensions strongly depended on the mass flow rate and the MEPCM mass concentration. The 5% suspension always showed a better cooling performance than water resulting in lower wall temperatures and enhanced heat transfer coefficients within the whole range of mass flow rates. The suspensions with higher mass concentrations, however, were more effective only at low mass flow rates. At higher mass flow rates they showed a less effective cooling performance than water.     

The effects of counter anions on the dynamic mechanical response in polymer networks crosslinked by metal–ligand coordination

Metal–ligand coordination has been proven to be an attractive strategy to tune a polymer network's dynamic mechanical properties, such as self-healing ability. Nonetheless, the role of counter anions is often overlooked. To address this, a series of polydimethylsiloxane (PDMS) films crosslinked through lanthanide metal cations (Eu³⁺, Tb³⁺)–bipyridine interactions have been prepared and studied. Neutral 2,2'-bipyridine ligands were embedded into the linear polydimethylsiloxane (PDMS) chain through polycondensation. With nitrate ( ) as the coordinating anions, metal salts Eu(NO₃)₃ and Tb(NO₃)₃ were found to be ineffective crosslinkers. With noncoordinating anions, such as triflate (OTf^-: CF₃ ), metal salts Eu(OTf)₃ and Tb(OTf)₃ showed improved interaction strength with bipyridine ligands. Surprisingly, the addition of Eu(OTf)₃ and Tb(OTf)₃ salts also increased the d-spacing distances of the phase-segregated domains between metal–ligand complexes and the PDMS polymer backbone. For the Eu(OTf)₃-, Tb(OTf)₃-PDMS films, the much-improved self-healing abilities are attributed to the crosslinker dynamics and the enhanced chain mobility. This work underlines the importance of counter anions on the mechanical properties, and provides further guidance on the future design of self-healing metal−ligand crosslinked polymers.) © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 3110–3116     

Infinite Horizon Sparse Optimal Control

A class of infinite horizon optimal control problems involving nonsmooth cost functionals is discussed. The existence of optimal controls is studied for both the convex case and the nonconvex case, and the sparsity structure of the optimal controls promoted by the nonsmooth penalties is analyzed. A dynamic programming approach is proposed to numerically approximate the corresponding sparse optimal controllers.     

Measurement of damping in structures by the power input method

Experimental Techniques -     

Photoelastic investigation of metal-forming processes using new sapphire dies

Experimental Techniques -     

Flow boiling heat transfer on a heating element restricted by an interference sleeve

The flow boiling phenomenon over a heated tube restricted by an interference sleeve, which is a passive enhancement technique, has been analysed using a semi-empirical approach. The liquid boiled was water flowing through an annular cross-section. A model developed earlier for the case of pool boiling over porous surfaces has been adapted after modification to pool boiling with interference surfaces using equivalent geometrical parameters and a modified permeability factor. This was further extended to saturated flow boiling situation using an additive mechanism. The single phase heat transfer coefficient required for the additive mechanism is obtained from an experimental correlation developed in the present study. The suppression factors evaluated for the eight sleeve geometries used in the present investigation are expressed in terms of the single phase Reynolds number and the Martinelli parameter. Very good agreement was observed between the model predictions and experimental data validating the mechanisms postulated. Further, a purely empirical correlation based on the present experimental data has been proposed to estimate the two-phase heat transfer coefficient. While the empirical correlation shows a better fit with the experimental data, the additive model has a physical basis.     

Bending of a uniformly loaded clamped sector plate

The paper involves the expansion of the biharmonic deflection function in a series of non-orthogonal functions satisfying the condition of clamped edges. Each of these non-orthogonal functions is expanded in a series of orthogonal functions which satisfy a certain fourth order differential equation and the boundary conditions implied by the fact that the edges are clamped. This reduces the bending of a uniformly loaded clamped sector plate to the solution of a linear algebraic system of equations. Numerical results for the deflection of the central line are obtained when the semi-sector angle is 15 degrees.     

Point force in a MHB rotating fluid

We consider the steady flow of an inviscid, rotating fluid confined in a cylinder under the influence of a uniform axial magnetic field, in the presence of an isolated point force. It is found that, the wave-like terms, infinite in number, occurring on the downstream side are not persistent and decay at far distances, in contrast to the non-magnetic case. Also the presence of a uniform magnetic field induces an additional finite number of decaying modes on the upstream side and an infinite number of similar modes on the downstream side, which reduce to the geostrophic terms, in the corresponding non-magnetic case. The downstream solution reveals that discontinuities occur in the velocity gradients inside the fluid region.