Kek-Kiong Tio

Boundary conditions for stokes flows near a porous membrane

A theoretical development is carried out to model the boundary conditions for Stokes flows near a porous membrane, which, in general, allows non-zero slip as well as normal flow at the surface. Two types of models are treated: an infinitesimally thin plate with a periodic array of circular apertures and a series of parallel slits. For Stokes flows, the mean normal flux and slip velocity are proportional to the pressure difference across the membrane and the average shear stress at the membrane, respectively. The appropriate proportionality constants which depend on the membrane geometry are calculated as functions of the porosity. An interesting feature of the results is that the slip at the membrane has, in general, a direction different from that of the applied shear for these models.

The dynamics of small, heavy, rigid spherical particles in a periodic Stuart vortex flow

The equation of motion of small, heavy, rigid spherical particles in a periodic Stuart vortex flow is studied as a four‐dimensional nonlinear dynamical system with a parametric space of five dimensions. The five parameters are a scaled Reynolds number, the Stokes number, the fluid‐to‐particle density ratio, the vorticity distribution in the flow, and a gravitational parameter. Depending on the values of these parameters, heavy particles may either settle or remain indefinitely suspended against gravity. When suspension occurs, suspended particles asymptotically collect along periodic, quasiperiodic, or chaotic open trajectories located above or below the vortices. The nature of these asymptotic paths is investigated using the standard tools of power spectrum and bifurcation diagram (Poincare sections). Furthermore, the basins of attraction in the physical and parametric spaces are also computed for both types of suspensions (above and below the vortices). In addition to the two types of upper and lower as...

Thermal Analysis of Inclined Micro Heat Pipes

The effect of gravity is investigated for the case of inclined-triangular- and trapezoidal-shaped micro heat pipes (MHPs). The study is limited to the case of positive inclination, whereby the condenser section is elevated from the horizontal position. The results show that the axial distribution of the liquid phase is changed qualitatively. While the liquid distribution still increases monotonically starting from the evaporator end, it reaches its maximum value not at the condenser end but at a certain point in the condenser section, beyond which the liquid distribution decreases monotonically. This maximum point, where potentially flooding will first take place, results from the balance between the effects of gravity and the heat load on the MHPs. As the liquid distribution assumes its greatest value at the maximum point, a throat-like formation appears there. This formation is detrimental to the performance of MHPs, because it hinders, and at worst may block, the axial flow of the vapor phase. The results also show that the maximum point occurs further away from the condenser end for a triangular-shaped MHP compared to a trapezoidal-shaped MHP.

Thermal Analysis of a Water-Filled Micro Heat Pipe With Phase-Change Interfacial Resistance

The progressive evaporation and condensation processes in a micro heat pipe, with which high heat fluxes at the liquid–vapor interface are associated, render it a device of high thermal conductance. By coupling the phase-change interfacial resistance model with a mathematical model based on first principles for fluid flow and heat transfer, the axial temperature variations of the liquid and vapor phases as well as those of other field variables are characterized and analyzed. The findings provide a well-defined exposition of the validity of uniform-temperature assumption for the liquid and vapor phases in the analysis of micro heat pipes. In conjunction with the acquisition of liquid and vapor temperature profiles, the heat transfer characteristics of the evaporation process can be analyzed. The local evaporative heat transfer coefficient and heat flux are evaluated. The results indicate that both heat transfer coefficient and heat flux are of considerably high values, confirming that the heat transport capability of a micro heat pipe is dominated by the phase-change heat transfer at the liquid–vapor interface. [DOI: 10.1115/1.4006898]

Analysis of Microheat Pipes With Axial Conduction in the Solid Wall

A one-dimensional, steady-state model of a triangular microheat pipe (MHP) is developed, with the main purpose of investigating the thermal effects of the solid wall on the heat transport capacity of an MHP. The energy equation of the solid wall is solved analytically to obtain the axial temperature distribution, the average of which over the entire length of the MHP is simply its operating temperature. Next, the liquid phase is coupled with the solid wall by a heat transfer coefficient. Then, the continuity, momentum, and energy equations of the liquid and vapor phases are, together with the Young― Laplace equation, solved numerically to yield the heat and fluid ftow characteristics of the MHP. The heat transport capacity and the associated optimal charge level of the working fluid are predicted for different operating conditions. Comparison between the models with and without a solid wall reveals that the presence of the solid wall induces a change in the phase change heat transport by the working fluid, besides facilitating axial heat conduction in the solid wall. The analysis also highlights the effects of the thickness and thermal conductivity of the solid wall on its axial temperature distribution. Finally, while the contribution of the thermal effects of the solid wall on the heat transport capacity of the MHP is usually not dominant, it is, nevertheless, not negligible either.

The Effects of Working Fluid on the Heat Transport Capacity of a Microheat Pipe

The effects of the thermophysical properties of the working fluid on the performance of a microheat pipe of triangular cross section are investigated. For this purpose, five different working fluids are selected: water, hepthane, ammonia, methanol, and ethanol. For operating temperatures ranging from 20°Cto100°C, it is found that the behavior of the heat transport capacity is dominated by a property of the working fluid, which is equal to the ratio of the surface tension and dynamic viscosity σ∕μl. This property has the same dimension as velocity and can be interpreted as a measure of the working fluid’s rate of circulation, which can be provided by capillarity after overcoming the effect of viscosity. Of the five working fluids selected, ammonia is preferable for operating temperatures below 50°C since it yields the highest heat transport capacity; however, water is the preferred working fluid for temperatures above 50°C.

Thermal analysis of droplet spray evaporation from a heated solid surface

This paper deals with the heat transfer aspects of droplet spray evaporation from a heated solid surface. The analysis is restricted to the low superheat regime, in which the impinging droplets stick onto the solid without bubble nucleations. In this limit of approximation, the heat flow is quasi-steady and conduction dominated. The difficulty arising from droplet thermal interactions is overcome with an approximate model of an evaporating droplet surrounded by a uniform surface heat flux. The size of the droplet changes with time, but the effect of the surrounding droplets, which are treated as a continuum producing the uniform surface flux, is taken into consideration in an average sense. In addition, the analysis also incorporates the effects of droplet contact angle, droplet concentration, and solid conductivity. A transcendental equation has been derived and solved by using the Newton-Raphson method to obtain the Nusselt number.

Analysis of thermal constriction resistance with adiabatic circular gaps

The thermal constriction resistance is studied analytically for the special case of the interface of two simiinfinite solids in partial contact at various contact geometries. A corrective-iterative method is applied to solve the spatially periodic combination of Dirichlet and Neumann equations, and the thermal constriction resistance is expressed in a power series related to the fraction of the interfacial area occupied by the adiabatic disks. An expression for the dimensional resistance is developed which effectively describes discrete circular contacts or gaps on an otherwise isothermal surface. 33 refs.

The Dynamics of Bubbles in Periodic Vortex Flowss

To analyze the dynamics of small, spherical, rigid bubbles in a certain class of turbulent shear flows dominated by large scale coherent vortical structures, we model the plane free shear layer with a periodic array of Stuart vortices. The equation of motion of the bubbles is then integrated numerically to obtain the Lagrangian description of the bubbles, the long-term dynamics of which depends on the free-stream Reynolds number, the Stokes number, the gravitational field, and the strength of the vortices. Depending on the values of these four parameters, it is found that either there exists a stable equilibrium point near the center of each vortex, where bubble accumulation occurs, or all bubbles escape from captivity by the vortices. In the limiting case of dominant viscous drag forces, an Eulerian description of the “bubble flow field” is derived. Furthermore, the divergence of this flow field is negative in the neighborhood of a vortex center, where it achieves its minimum. This indicates that bubbles accumulation may indeed exist, and thus qualitatively confirms the more general numerical results obtained without the assumption of dominant viscous drag forces.

Thermal resistance of two solids in contact through a cylindrical joint

Abstract The steady-state heat-conduction problem of two semi-infinite solids in contact through a cylindrical joint is, by physical symmetry and uniqueness of solution, reduced to the problem of a cylinder of isothermal top surface in contact at its bottom with a semi-infinite solid. An analysis is carried out to investigate the thermal resistance of the system, taking into account the aspect ratio of the cylinder and the thermal conductivity of the solids. The effect of these parameters on the thermal resistance, which consists of the constriction resistance at the interface and the material resistance of the cylinder, is examined and discussed.