Time-dependent Heat Transport Research Articles

Experimental investigation of the cryogenic [formula omitted]-cooling performance for an impinging jet configuration for different inflow conditions

This work focuses on the cryogenic impingement cooling performance depending on the given inflow conditions. An experimental setup is presented which allows a detailed observation of the time dependent temperature distribution in a solid body via a thermal imaging camera during the cooling process. The space- and time-dependent heat transport from the solid to the impinging fluid is calculated from the gained temperature data using the so-called inverse global integration method (IGIM). This method allows an accurate determination of the heat flux density without the necessity of a precise calculation of the sensible temperature gradients. An investigation of the LN2-impingement conditions such as mass flow rates and fluid density is conducted to bridge the gap between the inflow conditions and the resulting heat fluxes. Moreover, a variation of the working pressure and the nozzle geometry is also performed to assess the main dependencies of the cooling performance. Thus, some important conclusions regarding the heat flux and its governing physical phenomena can be drawn. In order to simplify the application of the gathered information, the corresponding heat transfer coefficients are calculated as a function of the time dependent surface temperature and the set inflow conditions. It is shown that the usage of a constant value results in a high inaccuracy because the heat flux density and the heat transfer coefficient show no trivial correlation for arbitrary impingement conditions.

Combined magnetic and porosity effects on flow of time-dependent tangent hyperbolic fluid with nanoparticles and motile gyrotactic microorganism past a wedge with second-order slip

This research explores the time-dependent heat transport phenomena for the MHD flow of nanofluids containing motile microorganisms via porous matrix. The fluid flows through a porous stretched wedge with second-order slip and Nield boundary. Different physical and geometric parameters are included to achieve more practicable effects. The developed equations are converted into a non - dimensional form through the use of appropriate similarity functions. The mathematical formulation is built for these transmuted equations using the built-in Matlab software bvp4c. Differences in physical quantities namely skin friction coefficient −f″(0), local Nusselt number −θ′(0), Sherwood number φ′(0)and microorganism organism density −χ′(0) have also been identified under the influences of emerging parameters. Bioconvection caused by microorganisms stabilized nanomaterials, resulting in effective thermal delivery. The findings showed good consistency as compared to the current literature. The higher mixed convection parameter contributes to the quantities of flow viscosity, temperature, and nanoparticle concentration in boundary conditions. The incremented slip parameter γ precedes the flow speed. The skin friction factor −f″(0) reduces against unsteadiness parameter A, Hartree pressure gradient β, velocity ratio parameterλ, bouancy ratio parameterNr but it develops progressively when the parameters M, We, n, λ and bioconvection Rayleigh number Nc are incremented. The elaborated discussion is also presented with graphical and tabular illustrations.

Cylindrical heat conduction models for enclosed thermophones

The efficiency of enclosed thermophones is governed by the time-dependent heat transport between the heating element and the enclosure gas. Efficiency gains have been made by reducing the heat capacitance of the heating elements so that a maximum amount of energy is available for transport. However, efficiency is still limited when there is poor conduction into and out of the enclosure gas. An analytical model for the conduction in an enclosed thermophone with a heating element composed of a regularly spaced linear array of conducting fibers will be presented. The model considers interaction between the individual fibers and treats the enclosure wall as a heat sink. The conduction model will be incorporated into a device model which can calculate steady-state acoustic output. The results are compared against experimental data. In addition, the device model can be used to explore the optimal fiber spacing for enclosed thermophones with regularly spaced linear array heating elements. [Work funded by the Naval Research Laboratory.]

Time resolved heat exchange in driven quantum systems

We study time-dependent heat transport in systems composed of a resonant level periodically forced with an external power source and coupled to a fermionic continuum. This simple model contains the basic ingredients to understand time resolved energy exchange in quantum capacitors that behave as single particle emitters. We analyse the behaviour of the dynamic heat current for driving frequencies within the non-adiabatic regime, showing that it does not obey a Joule dissipation law.

Unconditionally Stable Finite Difference Scheme and Iterative Solution of 2D Microscale Heat Transport Equation

A two-dimensional time-dependent heat transport equation at the microscale is derived. A second order finite difference scheme in both time and space is introduced and the unconditional stability of the finite difference scheme is proved. A computational procedure is designed to solve the discretized linear system at each time step by using a preconditioned conjugate gradient method. Numerical results are presented to validate the accuracy of the finite difference scheme and the efficiency of the proposed computational procedure.

Three‐dimensional numerical simulation of the hydrothermal system within TAG‐Like sulfide mounds

A 3‐D finite element algorithm, with incorporated explicit pipe‐like elements, is developed to solve the coupled time‐dependent heat transport and fluid flow differential equations and yield the internal temperature and fluid velocity fields for TAG‐like mounds. A range of models with permeable and impermeable upper boundaries and different thermal conductivities are investigated. The solutions have three common features: a central high‐temperature zone which coincides with a non‐magnetic zone inferred from magnetic data; fluid upflow along the vertical high‐permeability column, surrounding a central pipe; and a maximum fluid velocity of the order of the observed maximum value at the central black smokers. Thermal conductivity variations strongly influence the temperature distribution but not the fluid velocity pattern.

Fracture‐induced hydrothermal convection in the oceanic crust and the interpretation of heat‐flow data

Small‐scale seafloor heat‐flow variations with a characteristic wavelength of about 1200 m have been observed on a profile over a sediment‐sealed ridge flank. Two theories have been advanced to explain them‐low aspect ratio hydrothermal convection in a highly permeable basement layer 600 m thick or high aspect ratio convection in an anisotropic permeable layer 200 m thick, induced by 20 m topographic variations with a 1000 m half wavelength. Neither theory is totally satisfactory. The first requires a very thick highly permeable zone while the absence of any resolvable basement relief on a complementary seismic survey limits the credibility of the second.We hypothesize that sub‐critical hydrothermal convection in normal upper oceanic crust, driven by discrete fractures, can cause the observed heat flow anomalies. We test the hypothesis by using a finite‐element code to solve the coupled time‐dependent heat transport and fluid flow differential equations. Discrete fractures are incorporated explicitly. We show that the inclusion of fractures in layers 2A and 2B promotes convection. Fluid flow through fractures causes horizontal thermal gradients, and initiates and maintains sub‐critical convection within the upper basalts. The predicted heat flow variations are comparable with the observed data.

Pressure drop and transient heat transport in forced flow single phase helium II at high Reynoldsnumbers

Pressure drop and transient heat transport measurements had been performed in the superfluid helium test loop at CEA/CEN-Grenoble, France. Single phase helium II was circulated through a 28 mm I.D. tube, over a length of 200 m for mass flow rates between 0.02 and 0.1 kg/s. Steady-state pressure drop measurements allow us to estimate the friction factor for Reynolds numbers in the 10 6 range. Rectangular heat pulses were applied at mid-length, and the fluid temperature was measured at several locations along the flow, upstream and downstream. A code has been developed which uses the two-fluid model to simulate time-dependent heat transport helium 11 flow. Simulation results are in good agreement with experimental measurements.

Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states

We present optical shadowgraph flow visualization and heat transport measurements of Rayleigh–Bénard convection with rotation about a vertical axis. The fluid, water with Prandtl number 6.4, is confined in a cylindrical convection cell with radius-to-height ratio Γ = 1. For dimensionless rotation rates 150 < Ω < 8800, the onset of convection occurs at critical Rayleigh numbers Rc(Ω) much less than those predicted by linear stability analysis for a laterally infinite system and qualitatively consistent with finite-aspect-ratio, linear-stability calculations of Buell & Catton (1983). As in the calculations, the forward bifurcation at onset is to states of localized flow near the lateral walls with azimuthal periodicity of 3 < m < 8. These states precess in the rotating frame, contrary to the assumptions of Buell & Catton (1983) but in quantitative agreement with recent calculations of Goldstein et al. (1992), with a frequency that is finite at onset but goes to zero as Ω goes to zero. At Ω = 2145 we find primary and secondary stability boundaries for states with m = 4, 5, 6, and 7. Further, we show that at higher Rayleigh number, there is a transition to a vortex state where the vortices form with the symmetry of the existing azimuthal periodicity of the sidewall state. Aperiodic, time-dependent heat transport begins for Rayleigh numbers at or slightly above the first appearance of vortices. Visualization of the formation and interactions of thermal vortices is presented, and the behaviour of the Nusselt number at high Rayleigh numbers is discussed.

Asymmetric modes and the transition to vortex structures in rotating Rayleigh-Bénard convection.

We report heat transport measurements and optical shadowgraph visualization of rotating Rayleigh-B\'enard convection. For dimensionless rotation rates 1404300, the initial transition to convection, occurring at a Rayleigh number R much less than the linear-stability value for roll or vortex states, is a forward Hopf bifurcation to an azimuthally asymmetric state with mode number n. States with n=3, 4, 5, 6, and 7 exist at low to moderate R and precess with frequencies that depend on R and \ensuremath{\Omega}. At higher R there is a continuous transition to a state with noisy, time-dependent heat transport, a distinct array of vortices in the central region, and a modulation of the precession speed of the outer structures.

The TINTE Modular Code System for Computational Simulation of Transient Processes in the Primary Circuit of a Pebble-Bed High-Temperature Gas-Cooled Reactor

The TINTE code deals with the nuclear and thermal transient behavior of a high-temperature reactor, taking into consideration the mutual feedback effects in two-dimensional r-z geometry, including the following: 1. time-dependent neutron flux calculation2. time-dependent heat source distribution (local and nonlocal fractions)3. time-dependent heat transport from the fuel to the fuel element surface4. time-dependent global temperature distribution5. gas flow distribution for a given mass flow or given pressure difference or even under natural circulation conditions6. convection and its feedback to the circulation. The TINTE code has been tested against transient experiments performed at the Arbeitsgemein-schaft Versuchsreaktor. It has also been used successfully for other reactor investigations and thermofluid problems including design studies for a small heating reactor of the peu à peu loading type.

Time dependent heat transport in subcooled superfluid helium

The authors present an extensive study on the behaviour of time dependent heat transport in subcooled He II under conditions which are closely related to the cooling problem of superconducting magnets. Experimental results on the delay for onset of burnout and on the transient recovery from burnout are discussed. A theoretical model is derived from the assumption that heat diffusion characterized by the Gorter-Mellink equation is the dominant mode of heat transport and that thermal waves play no direct role in this connection. The comparison of experimental and calculated results shows a very satisfactory agreement which fully validates the model.

Temperature in heat generating solids with memory

The present paper is concerned with time dependent heat transport by wave propagation in an homogeneous isotropic elastic solid with memory. The energy generated in the material for electrical heating or chemical or nuclear reactions is propagated with a finite speed.

Transient heat transport in He II

Experimental and theoretical investigations of time dependent heat transport in He II have identified several new phenomena not previously reported. For heat fluxes greater than the steady state peak value, there is an observed time delay between the initiation of heating and the onset of film boiling. The time delay is seen to be nearly equal to the enthalpy rise in the helium divided by the applied heat flux. A well defined relationship is shown to exist between the time delay and the applied heat flux. Simple theoretical analysis of heat conductivity in He II is shown to predict the functional dependence and give approximately the correct proportionality factor. Experimental results are reported over a range of temperatures, 1.6 K to 2.1 K and for two external pressures, near saturated vapour pressure and at 0.125 MPa.