1,720,984 research outputs found
Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci
No full textThis paper presents new asymptotic formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.</jats:p
Explicit formulas for forced convection in a shrouded longitudinal-fin heat sink with clearance
No full textWe consider laminar forced convection in a shrouded longitudinal-fin heat sink (LFHS) with tip clearance, as described by the pioneering study of (Sparrow, Baliga & Patankar 1978 J. Heat Trans. 100). The base of the LFHS is isothermal but the fins, while thin, are not isothermal, i.e. the conjugate heat transfer problem is of interest. Whereas Sparrow et al. numerically solved the fully developed flow and thermal problems for a range of geometries and fin conductivities, we consider the physically realistic asymptotic limit where the fins are closely spaced, i.e. the spacing is small relative to their height and the clearance above them. The flow problem in this limit was considered by (Miyoshi et al. 2024, J. Fluid Mech. 991, A2), and we consider the corresponding thermal problem. Usingmatched asymptotic expansions, we find explicit solutions for the temperature field (in both the fluid and fins) and conjugate Nusselt numbers (local and average). The structure of the asymptotic solutions provides further insight into the results of Sparrow et al.: the flow is highest in the gap above the fins, hence heat transfer predominantly occurs close to the fin tips. The new formulas are compared with numerical solutions and are found to be accurate for practical LFHSs. Significantly, existing analytical results for ducts are for boundaries that are either wholly isothermal, wholly isoflux or with one of these conditions on each wall. Consequently, this study provides the first analytical results for conjugate Nusselt numbers for flow through ducts
Longitudinal thermocapillary slip about a dilute periodic mattress of protruding bubbles
Full text linkA common realization of superhydrophobic surfaces comprises of a periodic array of cylindrical bubbles which are trapped in a periodically grooved solid substrate. We consider the thermocapillary animation of liquid motion by a macroscopic temperature gradient which is longitudinally applied over such a bubble mattress. Assuming a linear variation of the interfacial tension with the temperature, at slope , we seek the effective velocity slip attained by the liquid at large distances away from the mattress. We focus upon the dilute limit, where the groove width is small compared with the array period . The requisite velocity slip in the applied-gradient direction, determined by a local analysis about a single bubble, is provided by the approximation wherein is the applied-gradient magnitude, is the liquid viscosity and , a non-monotonic function of the protrusion angle , is provided by the quadrature, \begin{align*}& I(\alpha) = \frac{2}{\sin\alpha} \int_0^\infty\frac{\sinh s\alpha}{ \cosh s(\pi-\alpha) \sinh s \pi} \, \textrm{d} s
On spreading resistance for an isothermal source on a compound flux channel
No full textRecently, Jain [ASME J. Heat Mass Transfer, 220 (2024)] provided spreading-resistance formulas for an isothermal source on compound, orthotropic, semi-infinite, two-dimensional (axisymmetric) flux channels (tubes). The boundary condition (BC) in the source plane was a discontinuous convection (Robin) one. Along the source, a sufficiently large heat transfer coefficient was imposed to approximate an isothermal condition; elsewhere, it was set to zero, imposing an adiabatic BC. An eigenfunction expansion resolved the problem. Distinctly, we impose, precisely, a mixed isothermal-adiabatic BC in the source plane and use conformal maps to resolve the spreading resistance for the limiting case of a compound, isotropic flux channel. Our complimentary approach requires more time to compute the spreading resistance. However, it converges uniformly rather than pointwise, converges to the exact spreading resistance rather than one with an error, eliminates the Gibbs phenomenon at the edges of the source and fully resolves the square-root singularities in heat flux as the discontinuity in the BC is approached
Fully developed flow through shrouded-fin arrays: exact and asymptotic solutions
No full textThe flow resistance, i.e. friction factor times Reynolds number , of longitudinal-fin heat sinks with or without clearance between a shroud and the tips of the fins is an important parameter in thermal design. This is because it dictates the caloric resistance of the heat sink, i.e. change in bulk temperature of the fluid flowing through it. When there is no clearance and the common and oft-valid assumption of negligible fin thickness is invoked, corresponds to simply that of a rectangular duct. However, with clearance, only numerical results are available as per the well-known study by Sparrow, Baliga and Patankar (ASME J. Heat Transfer, vol. 100, 1978). We develop analytical formulae for for fully developed flow with clearance. The exact solution is provided by an integral formula derived via conformal mappings. Additionally, simple formulae are derived via asymptotic expansions in three cases: (1) the fin spacing is small compared to the fin height and clearance; (2) the clearance is small compared to the fin spacing, which is small compared to the fin height; (3) the same as case (2) but valid for larger clearances. The different asymptotic formulae are compared to the exact formula, and together cover almost the entire relevant parameter range (for fin spacing and clearance) with errors of less than 15 %. A formula for the limiting case of no clearance is shown to be more accurate, for any fin spacing, than a widely used correlation from the literature.</p
Physical modelling of the slow voltage relaxation phenomenon in lithium-ion batteries
Full text linkIn the lithium-ion battery literature, discharges followed by a relaxation to
equilibrium are frequently used to validate models and their parametrizations.
Good agreement with experiment during discharge is easily attained with a
pseudo-two-dimensional model such as the Doyle-Fuller-Newman (DFN) model. The
relaxation portion, however, is typically not well-reproduced, with the
relaxation in experiments occurring much more slowly than in models. In this
study, using a model that includes a size distribution of the active material
particles, we give a physical explanation for the slow relaxation phenomenon.
This model, the Many-Particle-DFN (MP-DFN), is compared against discharge and
relaxation data from the literature, and optimal fits of the size distribution
parameters (mean and variance), as well as solid-state diffusivities, are found
using numerical optimization. The voltage after relaxation is captured by
careful choice of the current cut-off time, allowing a single set of physical
parameters to be used for all C-rates, in contrast to previous studies. We find
that the MP-DFN can accurately reproduce the slow relaxation, across a range of
C-rates, whereas the DFN cannot. Size distributions allow for greater internal
heterogeneities, giving a natural origin of slower relaxation timescales that
may be relevant in other, as yet explained, battery behavior
Stability of a photosurfactant-laden viscous liquid thread under illumination
No full textThis paper investigates the effects of a light-actuated photosurfactant on the canonical problem of the linear stability of a viscous thread surrounded by a dynamically passive fluid. A model consisting of the Navier-Stokes equations and a set of molar concentration equations is presented that capture light-induced switching between two stable surfactant isomer states, trans and cis. These two states display significantly different interfacial properties, allowing for some external control of the stability behaviour of the thread via incident light. Normal modes are used to generate a generalized eigenvalue problem for the growth rate which is solved with a hybrid analytical and numerical method. The results are validated with appropriate analytical solutions of increasing complexity, beginning with a solution to a clean interface, then analytical solutions for one insoluble surfactant, one soluble surfactant and a special case of two photosurfactants with a spatially uniform undisturbed state. Presenting each of these cases allows for a holistic discussion of the effect of surfactants in general on the stability of a liquid thread. Finally, the numerical solutions in the presence of two photosurfactants that display radially non-uniform undisturbed states are presented, and details of the impact of the illumination on the linear stability of the thread are discussed.</p
Asymptotic Nusselt numbers for internal flow in the Cassie state
No full textWe consider laminar, fully developed, Poiseuille flows of liquid in the Cassie state through diabatic, parallel-plate microchannels symmetrically textured with isoflux ridges. Via matched asymptotic expansions, we develop expressions for (apparent hydrodynamic) slip lengths and Nusselt numbers. Our small parameter is the pitch of the ridges divided by the height of the microchannel. When the ridges are oriented parallel to the flow, we quantify the error in the Nusselt number expressions in the literature and provide a new closed-form result. It is accurate to and valid for any solid (ridge) fraction, whereas previous ones are accurate to and breakdown in the important limit when the solid fraction approaches zero. When the ridges are oriented transverse to the (periodically fully developed) flow, the error associated with neglecting inertial effects in the slip length is shown to be, where is the channel-scale Reynolds number based on its hydraulic diameter. The corresponding Nusselt number expressions' accuracies are shown to depend on the Reynolds number, Péclet number and Prandtl number in addition to. Manipulating the solution to the inner temperature problem encountered in the vicinity of the ridges shows that classic results for the thermal spreading resistance are better expressed in terms of polylogarithm functions.</p
Nusselt numbers for Poiseuille flow over isoflux parallel ridges for arbitrary meniscus curvature
No full textWe numerically compute Nusselt numbers for laminar, hydrodynamically, and thermally fully developed Poiseuille flow of liquid in the Cassie state through a parallel plate-geometry microchannel symmetrically textured by a periodic array of isoflux ridges oriented parallel to the flow. Our computations are performed using an efficient, multiple domain, Chebyshev collocation (spectral) method. The Nusselt numbers are a function of the solid fraction of the ridges, channel height to ridge pitch ratio, and protrusion angle of menisci. Significantly, our results span the entire range of these geometrical parameters. We quantify the accuracy of two asymptotic results for Nusselt numbers corresponding to small meniscus curvature, by direct comparison against the present results. The first comparison is with the exact solution of the dual series equations resulting from a small boundary perturbation (Kirk et al., 2017, "Nusselt Numbers for Poiseuille Flow Over Isoflux Parallel Ridges Accounting for Meniscus Curvature," J. Fluid Mech., 811, pp. 315-349). The second comparison is with the asymptotic limit of this solution for large channel height to ridge pitch ratio.</p
Solution of the extended Graetz-Nusselt problem for liquid flow over isothermal parallel ridges
No full textWe consider convective heat transfer for laminar flow of liquid between parallel plates. The configurations analyzed are both plates textured with symmetrically aligned isothermal ridges oriented parallel to the flow, and one plate textured as such and the other one smooth and adiabatic. The liquid is assumed to be in the Cassie state on the textured surface(s) to which a mixed boundary condition of no-slip on the ridges and no-shear along flat menisci applies. The thermal energy equation is subjected to a mixed isothermal-ridge and adiabatic-meniscus boundary condition on the textured surface(s). We solve for the developing three-dimensional temperature profile resulting from a step change of the ridge temperature in the streamwise direction assuming a hydrodynamically developed flow. Axial conduction is accounted for, i.e., we consider the extended Graetz-Nusselt problem; therefore, the domain is of infinite length. The effects of viscous dissipation and (uniform) volumetric heat generation are also captured. Using the method of separation of variables, the homogeneous part of the thermal problem is reduced to a nonlinear eigenvalue problem in the transverse coordinates which is solved numerically. Expressions derived for the local and the fully developed Nusselt number along the ridge and that averaged over the composite interface in terms of the eigenvalues, eigenfunctions, Brinkman number, and dimensionless volumetric heat generation rate. Estimates are provided for the streamwise location where viscous dissipation effects become important.</p
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