Viscoelastic materials are a kind of representative passive vibration control materials with many applications in civil engineering for earthquake mitigation in building structures, and these materials often serve in a thermo-elastic coupling environment. In this work, a one-dimensional magneto-thermoviscoelastic problem of a single-layer viscoelastic plate is investigated with memory-dependent derivative and nonlocal effect in the context of generalized thermo-elasticity. The plate is placed in a magnetic field, and the upper surface is subjected to a thermal shock. The governing equations for the single-layer plate are formulated considering the time delay and the kernel function of the memory-dependent derivative, nonlocal effect, temperature-dependent properties, and magnetic field. The Laplace transform and its numerical inversion are employed to solve this problem. The nondimensional temperature, displacement, and stress are calculated and presented graphically. Based on the numerical results, the influence of time delay and kernel function of the memory-dependent derivative, nonlocal effect parameters, temperature-dependent properties, and magnetic field parameters on the distributions of the nondimensional temperature, displacement, and stress are discussed.

Saturation of the water vapor is essential to form frost inside a permeable membrane. The main goal of this paper is to develop a numerical model that can predict temperature and humidity inside a membrane in order to show the location and time of saturation. This numerical model for heat and mass transfer is developed to show that frost formation may be prevented or delayed by controlling the moisture transfer through the membrane, which is the new approach in this paper. The idea is to simultaneously dry and cool air to avoid saturation conditions and thereby eliminate condensation and frosting in the membrane. Results show that saturation usually occurs on side of the membrane with the highest temperature and humidity. The numerical model is verified with experimental data and used to show that moisture transfer through the membrane can delay or prevent frost formation.

The demands for increasingly smaller, more capable, and higher power density technologies have heightened the need for new methods to manage and characterize extreme heat fluxes. This work presents the use of an anisotropic version of the time-domain thermoreflectance (TDTR) technique to characterize the local heat transfer coefficient (HTC) of a water-cooled rectangular microchannel in a combined hot-spot heating and subcooled channel-flow configuration. Studies focused on room temperature, single-phase, degassed water flowing at an average velocity of ≈3.5 m/s in a ≈480 μ m hydraulic diameter microchannel (e.g., Re ≈ 1850), where the TDTR pump heating laser induces a local heat flux of ≈900 W/cm 2 in the center of the microchannel with a hot-spot area of ≈250 μ m 2 . By using a differential TDTR measurement approach, we show that thermal effusivity distribution of the water coolant over the hot-spot is correlated to the single-phase convective heat transfer coefficient, where both the stagnant fluid (i.e., conduction and natural convection) and flowing fluid (i.e., forced convection) contributions are decoupled from each other. Our measurements of the local enhancement in the HTC over the hot-spot are in good agreement with established Nusselt number correlations. For example, our flow cooling results using a Ti metal wall support a maximum HTC enhancement via forced convection of ≈1060 ± 190 kW/m 2 K, where the Nusselt number correlations predict ≈900 ± 150 kW/m 2 K.

A surface plasmon resonance (SPR) imaging microscopy coupled to a high-speed camera is used to visualize the frost propagation inside a subcooled liquid droplet. The SPR experimental setup consists of a 50 nm thick gold-coated cover glass placed on a BK7 dove prism and optically matched using index matching liquid. Collimated monochromatic light of 600 nm wavelength is incident on the gold-glass interface at 71.8°, which corresponds to the SPR minima angle for ice (RI 1.309). Images are captured using Photron APS-RS camera at 1000 fps with a shutter speed of 1 ms. The prism and the gold film are cooled using a thermo-electric cooler (TEC). A water droplet is placed on the gold film and the temperature of the droplet is decreased from room temperature (23.0 ± 1 °C) to below 0 °C. Adjacent to the water droplet, the vapor condensates to form tiny droplets. The tiny condensate droplets would freeze first and the frost propagates through the condensate region. During this period the central droplet is in a subcooled state. The speed of frost propagation through the condensates is slow and takes tens of seconds to cover the gold film with ice. Within a single condensate droplet, however, the frost propagation velocity is expected to be considerably higher. Eventually the frost line reaches the central droplet. There is a delay of few seconds between the frost line reaching the droplet and frost propagation inside the droplet. The point at which frost touches the subcooled droplet acts as a nucleation site for the droplet and the frost propagates in the droplet at high speed. The average velocities of frost propagations in the subcooled liquid droplet were calculated to be 5.2 ± 0.3 cm/s and 7.4 ± 0.5 cm/s, when the gold film temperature was -5.0 ± 1 °C and -7.8 ± 1 °C respectively.

This paper presents a joint state and input estimation algorithm for the one-dimensional heat-conduction problem. A computationally efficient method is proposed in this work to solve the inverse heat-conduction problem (IHCP) using orthogonal collocation method (OCM). A Kalman filter (KF) algorithm is used in conjunction with a recursive-weighted least-square (RWLS)-based method to simultaneously estimate the input boundary condition and the temperature field over the heat-conducting element. A comparison study of the algorithm is shown with explicit finite-difference method (FDM) of approximation and analytical solution of the forward problem, which clearly reveals the high accuracy with lower-dimensional modeling. The estimation results show that the performance of the estimator is robust to noise sensitivity up to a certain level, which is practically acceptable.

The lagging behavior is first exemplified by a rapidly stretched spring and a one-dimensional fin to illustrate the phase-lag concept via the thermal and mechanical properties that most engineers are familiar with. The second-order lagging model is then introduced to correlate with drug delivery in tumors and bioheat transfer that involve multiple carriers in heat/mass transport. Analytical expressions for the phase lags are derived, aiming toward revealing different physical origins for delays in different systems. For drug delivery in tumors involving nonequilibrium mass transport, the lagging behavior results from the finite time required for the rupture of liposome in releasing the antitumor drug and the finite time required for tumor cells to absorb drugs. For bioheat transfer involving nonequilibrium heat transport, on the other hand, the lagging behavior results from the finite time required for exchanging heat between tissue and blood. Pharmacodynamical and biological properties affecting the phase lags, as well as the dominating parameters over the lagging response are identified through the nondimensional analysis. Involvement of the thermal Mach number, which measures the speed of blood flow relative to the conventional thermal wave speed, is a new feature in this extension of the lagging model. The second-order effects in lagging are well correlated with the number of carriers involved in nonequilibrium heat and mass transport.

The study of thermal transport based on the dual-phase lagging model involves not only the well known thermal properties but also two additional time parameters. Those parameters permit to take into account the thermal inertia and the microstructural interactions of the media in such a way that they establish the nonsimultaneity between temperature changes and heat flux. In the dual-phase lagging model, heat transport phenomena are extremely sensitive not only to the size of each time parameter but also to the relative size of them. In order to obtain useful and reliable results, it is important to develop methodologies for the determination of those time parameters. Additionally it is necessary to count with tools that allow evaluating easily the sensitivity of the temperature and heat to the changes in those time parameters. In this work, a system formed by a semi-infinite layer in thermal contact with a finite one, which is excited by a modulated heat flux, is studied. When the thermal effusivities of the layers are quite different, it is shown that a frequency range can be found in which the normalized amplitude and phase of the spatial component of the oscillatory surface temperature show strong oscillations. This behavior is used to obtain explicit formulas for determining simultaneously the time parameters as well as additional thermal properties of the finite layer, under the framework of the dual-phase lagging model of heat conduction. The limits of the corresponding equations for single-phase lagging models of heat conduction are also discussed.

If a thermal disturbance such as a step change in temperature is applied at each surface of a homogeneous slab of thickness 2L, the effect of cooling at x = +L at first has no effect at x = −L but is clearly evident after a time described by a Fourier number F 0 = λt/ρc p L 2 of around 0.2. To establish the time of a perceptible change the minimum value of φ i − (φ 1 + (φ 2 ) is sought, where φ 1 is the flux into a semi-infinite solid and φ 1 and φ 2 are the first and second eigenfunction contributions to the solution for a slab of finite thickness. Cooling throughout the slab is determined virtually by the first eigenfunction alone after F 0 = 0.22. For a fluid-cooled slab these values are larger.

This work develops a new measurement technique that determines the thermal diffusivity of thin films in both parallel and perpendicular directions, and presents experimental results on the thermal diffusivity of GaAs/AlGaAs-based thin-film structures. In the experiment, a modulated laser source heats up the sample and a fast-response temperature sensor patterned directly on the sample picks up the thermal response. From the phase delay between the heating source and the temperature sensor, the thermal diffusivity in either the parallel or perpendicular direction is obtained depending on the experimental configuration. The experiment is performed on a molecular-beam-epitaxy grown vertical-cavity surface-emitting laser (VCSEL) structure. The substrates of the samples are etched away to eliminate the effects of the interface between the film and the substrate. The results show that the thermal diffusivity of the VCSEL structure is 5–7 times smaller than that of its corresponding bulk media. The experiments also provide evidence on the anisotropy of thermal diffusivity caused solely by the effects of interfaces and boundaries of thin films.

The objective of the present work is to analyze rigorously the transient heat transfer of an irradiated particle by treating the radiant absorption on a local basis. A new conduction-to-radiation parameter is introduced to characterize the relative importance of heat transfer by conduction as compared with that by radiation. The study on the transient temperature field as a function of conduction-to-radiation parameter establishes a criterion identifying the circumstances where heat transfer by radiation is so predominant that conduction is negligible. The current effort is also directed at developing a convenient method for predicting the transient local maximum temperature and explosion time delay of an intensely irradiated liquid droplet.

The stability of a Boussinesq fluid-saturated horizontal porous layer heated from below is examined when the applied temperature gradient is the sum of a steady component and a time-dependent sinusoidal component. The Brinkman model is employed and only infinitesimal disturbances are considered. A perturbation solution as a function of the applied field is obtained. The critical Rayleigh number is obtained for several cases depending on the frequency of oscillations and it is found that it is possible to advance or delay the onset of convection by thermal modulation of the wall temperature. The Darcy limit and viscous flow limit are obtained as degenerate cases.

The reflooding of a tubular test section under oscillatory inlet flow conditions has been investigated experimentally for initial wall temperatures from 316° C to 760°C, oscillation periods from 2 to 6 s, and test section liquid level amplitudes up to 0.76 m. Compared to constant-injection reflooding, the oscillations always increase the liquid carryover rate in the early stages of reflooding. As reflooding progresses, the enhancement diminishes and becomes negative. The crossover point roughly coincides with saturation of the liquid at the quench front. The higher initial liquid carryover increases downstream heat transfer and speeds up quench front propagation, but it also reduces the test section mass accumulation rate, and for this reason delays quench front propagation at later stages. These effects are accentuated at higher oscillation amplitude and frequency. Large oscillations change the reflooding behavior substantially. Quantitative comparisons of quench front velocities and heat transfer immediately downstream of the quench front, obtained through the use of empirical local-condition correlations representing the steady-reflooding rate data, are presented.

Wind tunnel experiments were performed to determine heat transfer coefficients and fluid flow patterns for two contacting spheres. The experiments were carried out at three different angles of attack and for Reynolds numbers in the range from 4000 to 26,000. Three heat transfer conditions were considered: (a) both spheres thermally active, (b) forwardmost sphere thermally active and rearmost sphere adiabatic, and (c) forwardmost sphere adiabatic and rearmost sphere thermally active. Complementary experiments for a single sphere, encompassing the same parameter ranges, yielded baseline information for comparison with the two-sphere results. It was found that the largest effects of the sphere-to-sphere interaction on the heat transfer occurred when the two spheres were in line. At this orientation and for higher Reynolds numbers in the investigated range, there was substantial enhancement of the heat transfer with respect to that for the single sphere. At the other angles of attack, there was lesser enhancement. The visualization studies revealed such key fluid flow features as the reattachment of the separated flow from the first sphere on the second, the presence of strong recirculations, and the delay of separation due to pressure-driven transverse flows.

Inception conditions of density-wave oscillations were determined in two sodium heated once-through steam generator tubes, i.e., in a 44.43 m long helical coil of 0.018 i.d. and in a tube of 0.0131 m i.d., comprised of a 9.40 m long vertical- and an 11.05 m long, V-shaped horizontal tube. The operating conditions on the water/steam side for the experiments were: pressure: 6–19.1 MN/m 2 ; mass velocity 187–1020 kg/m 2 s; inlet subcooling: 3.2–168 K; outlet steam quality: 1.15–2.38. The 306 data obtained and the 74 data found in the literature from sodium and electrically heated once-through steam generator tubes were correlated within 7.5 percent accuracy for 98 percent of the time. The R.M.S. error for all the 380 data is 3.33 percent. The observed density-wave oscillations are time-delay oscillations and the length of the superheated steam region and the transit time in this region practically govern the mechanism of these oscillations. An empirical relation has also been established for this mechanism.

A study of the onset of transient natural convection from a suddenly heated, horizontal cylinder of finite diameter is presented. The termination of the initial conductive and “locally” conuectiue heat transfer regime which precedes the onset of global natural convection is treated as a thermal stability phenomenon. An analysis is presented wherein the effects of finite cylinder diameter, cylinder heat capacity, and cylinder thermal conductivity are included in calculations of the convective delay time. A simple experimental apparatus is described and data presented. The thermal stability analysis is confirmed experimentally and data is presented which indicates localized natural convection prior to global motion.

Experimental data are presented for the transient free convective heat transfer from a horizontal wire in air subjected to a step change in heat rate. An unbalanced Wheatstone bridge is described which allows simultaneous observation of wire temperature and heat rate, under transient as well as steady-state conditions. An “overshoot” of the steady-state is shown to occur in the transient decay of the Nusselt number, and the occurrence, magnitude, and duration of this phenomenon is shown to depend upon the Rayleigh number. Simple stability theory is shown to explain the delay in the convective process which is associated with the overshoot in heat transfer. Steady-state data are also presented and are shown to agree well with proposed low Rayleigh number correlations.

This paper presents results from a research program conducted a number of years ago on the problem of flashing flow of water in nozzles. In a previous paper [1] we presented results for the case of stagnation states in the low quality two-phase region. The present paper reports results for stagnation states in the subcooled region at pressures up to 9.05 × 10 3 kN/m 2 and subcooling from 0 to 60° C. Pressure profiles and flow rates are reported. The results are compared with limiting cases of Bernoulli flow (meta-stable liquid flow) and homogeneous equilibrium flow. As expected neither was able to predict the experimental results. A two-step model based upon nucleation delay, “discontinuous” transition to two-phase flow followed by frozen composition gave reasonable predictions of the flowrates and pressure profiles in the convergent section.

Experimental data for sodium boiling on horizontal surfaces containing artificial cavities at heat fluxes of 20,000 to 300,000 Btu/ft 2 hr and pressures between 40 to 106 mm Hg were obtained. Observations are made for stable boiling, unstable boiling and “bumping.” Some recorded temperature variations in the solid close to the nucleating cavity are presented. It is suggested that for liquid metals the time for bubble growth and departure is a very small fraction of the total bubble cycle, hence the delay time during which a thermal layer grows is the most significant part of the process. On this basis the transient conduction heat transfer is solved for a periodic process, and the period time is found to be a function of the degree of superheat, the heat flux and the liquid thermal properties. A simplified model for stability of nucleate pool boiling of liquid metals is postulated from which the minimum heat flux for stable boiling can be found as a function of liquid-solid properties, liquid pressure, the degree of superheat, and the cavity radius and depth. At relatively low heat fluxes, convection currents have significant effects on the period time of bubble formation. An empirical correlation is proposed, which takes into account the convection effects, to match the experimental results.