Space-averaged Nusselt Number Research Articles

THREE-DIMENSIONAL NATURAL CONVECTION OF AIR IN AN INCLINED CUBIC CAVITY

Three-dimensional steady and transient natural convective flow in a differentially heated inclined cubic cavity of air was numerically simulated by the projection method combined with the power law scheme. Various three-dimensional flow structures were induced, depending on the Rayleigh number and inclined angle, although the main flow is nearly two-dimensional. It is of interest to note that the flow is stronger when a vertical cavity is inclined, implying significant flow acceleration by the buoyancy component normal to the hot and cold walls. Change in the flow structure during the transient causes wavy variation of the space-averaged Nusselt number with time.

Heat transfer from a fully-developed pulsating flow in a curved pipe

Numerical studies are made of the flow and heat transfer characteristics of a fully-developed pulsating flow in a strongly curved pipe. Emphasis is placed on delineating the effects of the Reynolds number, and pulsation amplitude and frequency. By using a toroidal coordinate system, the complete, time-dependent incompressible Navier—Stokes equations are formulated. The peripherally-uniform temperature condition is imposed on the pipe wall. Particular attention is given to heat transfer properties over substantially extended parameter ranges of the Reynolds number Re and the Womersley number Wo. Use is made of a well-established numerical solution procedure, with minor amendments. The computed results on the flow field are in close agreement with the existing data in the overlapping parameter ranges. The spatial distributions of axial and secondary flows are depicted. The time variations of flow structure are displayed. The numerical results on the spatial and temporal variations of the thermal field are presented. The circumferential profiles of local Nusselt number are plotted at selected instants. When Wo is small, the time- and space-averaged Nusselt numbers, Num, is lower for a pulsating flow than for a corresponding non-pulsating flow. At moderate and high Wo, however, the difference in Num between a pulsating and a non-pulsating flow is insignificant.

Heat transfer past particles entrained in an oscillating flow with and without a steady velocity

In order to investigate the heat transfer past particles entrained in an oscillating flow with and without a steady velocity, the two-dimensional, unsteady conservation equations of mass, momentum and energy for laminar flow in the gas phase are solved numerically in spherical coordinates. The particle momentum equation is also solved simultaneously with the gas phase equations in order to consider the effect of the particle entrainment on the heat transfer past particles. The numerical solution gives the particle velocity variation as well as the gas phase velocity and temperature distribution as a function of time. The local and space-averaged Nusselt number with particle entrainment is compared with that without particle entrainment. In the case of an oscillating flow with a steady velocity, the values of the space-averaged Nusselt number with particle entrainment are lower than those without particle entrainment at frequencies of 50 and 2000 Hz, since the moving particle is entrained in the steady velocity. In the case of an oscillating flow without a steady velocity, the space-averaged Nusselt number with entrainment at a frequency of 50 Hz is slightly lower than that without particle entrainment, with a phase lag. At 2000 Hz, the space-averaged Nusselt number with and without particle entrainment is almost the same, due to very small particle entrainment.

A theoretical investigation of acoustic enhancement of heat and mass transfer—I. Pure oscillating flow

Effects of an oscillating flow induced by a high intensity acoustic field on heat and mass transfer to and from particles and droplets such as pulverized coal particles and coal-water slurry fuel droplets are investigated. Numerical solutions of two-dimensional, unsteady, laminar conservation equations for mass, momentum and energy transport in the gas phase give the velocity and temperature fields around a particle for different oscillating flows without superposed steady component as a function of time. The local and space-averaged Nusselt numbers depend on the change of imposed oscillating velocity U due to body curvature and flow acceleration. At low frequency (~50 Hz), curvature effects are dominant, resulting in increasing values of Nusselt numbers with increasing U. The Nusselt numbers can be approximated by the quasi-steady analysis. The effects of flow acceleration increase with increasing frequencies (~2000 Hz). The combined effects of curvature and flow acceleration result in the maximum difference of 9% in the space- and time-average Nusselt number for frequencies of 50, 1000 and 2000 Hz for the acoustic Reynolds number varying between 10 and 100. The present results show about 290% increase in the space- and timeaveraged Nusselt number for an acoustic Reynolds number of about 100 compared to that without an acoustic field.

Heat and Momentum Transport in Self-Sustained Oscillatory Viscous Flows

Heat and momentum transport in-self-sustained oscillatory viscous flows is investigated by direct numerical simulation using the spectral element method. Above a critical Reynolds number, these flows bifurcate to a time-periodic, self-sustained oscillatory state. Traveling waves are observed, even at moderately low Reynolds numbers, inducing self-sustained oscillations that result in very well-mixed flows, which, in turn, lead to convective heat transfer augmentation. These oscillatory states are investigated and correlations between the time- and space-averaged Nusselt and Reynolds numbers are obtained. The transport phenomena of heat and momentum due to the oscillatory components of the flow are analyzed by looking at the phase portraits of velocity and temperature, investigating the behavior of the terms involving their fluctuations, as well as considering the correlation coefficients between the fluctuating components. Results are presented for laminar and transitional incompressible flows in communicating channels, composed of interrupted surfaces, leading to relatively thin thermal boundary layers that further contribute to heat transfer augmentation.

Effects of particle entrainment on heat transfer past particles in an oscillating flow

In order to investigate the effect of the particle entrainment on the heat transfer past paricles entrained in an oscillating flow with and without a steady velcoity, the two dimensional, unsteady, laminar conservation equations for mass, momentum and energy transport in the gas phase are solved numerically in spherical coordinates. The particle momentum equation is also solved simultaneously with the gas phase equations. The numerical solution gives the particle velocity variation as well as the gas phase velocity and temperature distribution as a function of time. The local and space-averaged Nusseit number with particle entrainment is compared with that without particle entrainment. In the case of an oscillating flow with a steady velocity, the values of the space-averaged Nusselt number with particle entrainment are lower than those without particle entrainment at frequencies of 50 and 2000 Hz since the moving particle is entrained in the steady velocity. In the case of an oscillating flow without a steady velocity, the space-averaged Nusselt number with entrainment at a frequency of 50 Hz is slightly lower than that without particle entrainment, with a phase lag. At 2000 Hz, the space-averaged Nusselt number with and without particle entrainment is almost the same, due to very small particle entrainment.

Numerical investigation of incompressible flow in grooved channels. Part 2. Resonance and oscillatory heat-transfer enhancement

Modulatory heat-transfer enhancement in grooved channels is investigated by direct numerical simulation of the Navier–Stokes and energy equations using the spectral element method. It is shown that oscillatory perturbation of the flow at the frequency of the least-stable mode of the linearized system results in subcritical resonant excitation and associated transport enhancement as the critical Reynolds number of the flow is approached. The Tollmien–Schlichting frequency theory that was presented in Part 1 of this paper is shown to accurately predict the optimal frequency for transport augmentation for small values of the modulatory amplitude, and the effect of the excited travelling-wave channel modes on the resulting temperature distribution is described. The importance of (non-trivial) geometry in the forced response of a flow is discussed, and grooved-channel flow is compared to (straight-channel) plane Poiseuille flow, for which no resonance excitation occurs owing to a zero projection of the forcing inhomogeneity on the dangerous modes of the system. For the particular grooved-channel geometry investigated, resonant oscillatory forcing at modulatory amplitudes as small as 20% of the mean flow results in a doubling of transport as measured by a time, space-averaged Nusselt number.

Heat transfer in curved tubes with pulsating flow

Effects of pulsatile flow upon heat transfer characteristics are studied for fully developed, laminar, and pulsating flow in curved tubes. The heat transfer boundary conditions are taken to be axially uniform heat flux with peripherally uniform wall temperature. Temperature distribution, and local and peripherally averaged Nusselt numbers are calculated for different values of frequency and amplitude ratio parameters, Reynolds number, curvature ratio. Dean and Prandtl numbers. The result shows that there is considerable variation in local and peripherally averaged Nusselt number. The time and space averaged Nusselt number approaches the corresponding steady state flow case at frequency parameter α = 6 and decreases as α decreases. A further decrease is associated with increasing amplitude ratio at low frequencies.