Unsteady natural convection in a triangular enclosure under isothermal heating

The fluid flow and heat transfer inside a triangular enclosure due to instantaneous heating on the inclined walls are investigated using an improved scaling analysis and direct numerical simulations. The development of the unsteady natural convection boundary layer under the inclined walls may be classified into three distinct stages including a start-up stage, a transitional stage and a steady state stage, which can be clearly identified in the analytical and numerical results. A new triple-layer integral approach of scaling analysis has been considered to obtain major scaling relations of the velocity, thicknesses, Nusselt number and the flow development time of the natural convection boundary layer and verified by direct numerical simulations over a wide range of flow parameters

On the natural convection boundary layer adjacent to an inclined flat plate subject to ramp heating

An investigation of the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a temperature boundary condition which follows a ramp function up until some specified time and then remains constant is reported. The development of the flow from start-up to a steadystate has been described based on scaling analyses and verified by numerical simulations. Attention in this study has been given to fluids having a Prandtl number Pr less than unity. The boundary layer flow depends on the comparison of the time at which the ramp heating is completed and the time at which the boundary layer completes its growth. If the ramp time is long compared with the steady state time, the layer reaches a quasi steady mode in which the growth of the layer is governed solely by the thermal balance between convection and conduction. On the other hand, if the ramp is completed before the layer becomes steady; the subsequent growth is governed by the balance between buoyancy and inertia, as for the case of instantaneous heating

Numerical and experimental studies of the natural convection within a horizontal cylinder

Numerical solutions are obtained for the quasi-compressible Navier-Stokes equations governing the time-dependent natural convection within a horizontal cylinder. The early flow development and wall heat transfer are obtained after a uniformly cold wall is imposed as a boundary condition on the cylinder. Results are also obtained for a time-varying cold wall as a boundary condition with windward explicit differencing used for the numerical solutions. The viscous truncation error associated with this scheme is controlled so that first-order accuracy is maintained in time and space. Experiments within a small-scale instrumented horizontal cylinder revealed the time development of the temperature distribution across the boundary layer as well as the decay of wall heat transfer with time. Agreement between temperature distributions obtained experimentally and numerically was generally good. The time decay of the dimensionless ratio of the Nusselt number to the one-fourth power of the Grashof number is found both numerically and experimentally, and good agreement is obtained between these two results over most of the cylinder wall

Terminal states of thermocapillary migration of a planar droplet at moderate and large Marangoni numbers

In this paper, thermocapillary migration of a planar droplet at moderate and large Marangoni numbers is investigated analytically and numerically. By using the dimension-analysis method, the thermal diffusion time scale is determined as the controlling one of the thermocapillary droplet migration system. During this time, the whole thermocapillary migration process is fully developed. By using the front-tracking method, the steady/unsteady states as the terminal ones at moderate/large Marangoni numbers are captured in a longer time scale than the thermal diffusion time scale. In the terminal states, the instantaneous velocity fields in the unsteady migration process at large Marangoni numbers have the forms of the steady ones at moderate Marangoni numbers. However, in view of the former instantaneous temperature fields, the surface tension of the top surface of the droplet gradually becomes the main component of the driving force on the droplet after the inflection point appears. It is different from that the surface tension of the bottom surface of the droplet is the main component of the driving force on the droplet for the latter ones. The physical mechanism of thermocapillary droplet migration can be described as the significance of the thermal convection around the droplet is higher than/just as the thermal conduction across the droplet at large/moderate Marangoni numbers.Comment: 8 pages, 6 figure

Definition of parameters useful to describe dynamic thermal behavior of hollow bricks

Dynamic thermal behavior of hollow bricks is attracting much interest nowadays as there is much concern on energy performance of building envelope. In fact, high thermal inertia of outer walls provides mitigation of the daily heat wave, which reduces the cooling peak load and the related energy demand. Different approaches have been used to study dynamic thermal behavior within the papers available on unsteady heat transfer through hollow bricks. Actually, the usually employed methods for calculation of unsteady heat transfer through walls are based on the hypothesis that such walls are composed by homogeneous layers, so they are not suitable for many common building components. In this framework, a study on the dynamic thermal performance of hollow bricks is brought forth in the present paper. A critical review of available data from the literature is provided. Literature data are used to propose a parameter useful to predict dynamic thermal behavior. A finite-volume method is used to solve two-dimensional unsteady thermal fields in some standard bricks with different imposed temperature solicitations, with a numerical code developed by the authors. New results are used to check the effectiveness of the proposed parameters

Dynamic thermal features of insulated blocks: Actual behavior and myths

The latest updates in the European directive on energy performance of buildings have introduced the fundamental “nearly zero-energy building (NZEB)” concept. Thus, a special focus needs to be addressed to the thermal performance of building envelopes, especially concerning the role played by thermal inertia in the energy requirements for cooling applications. In fact, a high thermal inertia of the outer walls results in a mitigation of the daily heat wave, which reduces the cooling peak load and the related energy demand. The common assumption that high mass means high thermal inertia typically leads to the use of high-mass blocks. Numerical and experimental studies on thermal inertia of hollow envelope components have not confirmed this general assumption, even though no systematic analysis is readily available in the open literature. Yet, the usually employed methods for the calculation of unsteady heat transfer through walls are based on the hypothesis that such walls are composed of homogeneous layers. In this framework, a study of the dynamic thermal performance of insulated blocks is brought forth in the present paper. A finite-volume method is used to solve the two-dimensional equation of conduction heat transfer, using a triangular-pulse temperature excitation to analyze the heat flux response. The effects of both the type of clay and the insulating filler are investigated and discussed at length. The results obtained show that the wall front mass is not the basic independent variable, since clay and insulating filler thermal diffusivities are more important controlling parameters

Inverse problems in partial differential equations

Identification in partial differential equations by Laplace equatio

Turbulence, Energy Transfers and Reconnection in Compressible Coronal Heating Field-line Tangling Models

MHD turbulence has long been proposed as a mechanism for the heating of coronal loops in the framework of the Parker scenario for coronal heating. So far most of the studies have focused on its dynamical properties without considering its thermodynamical and radiative features, because of the very demanding computational requirements. In this paper we extend this previous research to the compressible regime, including an energy equation, by using HYPERION, a new parallelized, viscoresistive, three-dimensional compressible MHD code. HYPERION employs a Fourier collocation -- finite difference spatial discretization, and uses a third-order Runge-Kutta temporal discretization. We show that the implementation of a thermal conduction parallel to the DC magnetic field induces a radiative emission concentrated at the boundaries, with properties similar to the chromosphere--transition region--corona system.Comment: 4 pages, 4 figures, Solar Wind 12 proceedings (in press