Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

竖直恒温面自然对流边界层不稳定性研究

在无扰动、随机式扰动以及正弦式扰动下,通过对竖直恒温面处状态Ra为1.328×10^9、Pr为6.24的自然对流进行模拟,探索了热边界层的不稳定性和共振强化自然对流换热。结果表明:(1)竖直自然对流边界层上游位置的随机式扰动对热边界层的影响主要体现在稳定阶段;(2)该状态下的竖直自然对流边界层的特征频率为15 067,且相比于无扰动状态,频率为15 067的正弦式扰动能在竖直恒温面处提高5.15%的换热量;(3)在竖直自然对流边界层上游位置加入特征频率的正弦式扰动,竖直恒温面处的局部努塞尔数Nu均出现明显波动,且波动随着边界层高度的增加而增大。     

Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

Free convection boundary layers on a vertical surface in a heat-generating porous medium

The natural convection boundary-layer flow on a solid verticalsurface with heat generated within the boundary layer at a rateproportional to (T – T)^p (p 1) is considered. The surfaceis held at the ambient temperature T except near the leadingedge where it is held at a temperature above ambient. The behaviourof the flow as it develops from the leading edge is examinedand is seen to become independent of the initial heat input;however, it does depend strongly on the exponent p. For 1 p 2, the local heating eventually dominates at large distancesand there is a convective flow driven by this mechanism. Forp 4, the local heating does not have a significant effect,the fluid temperature remains relatively small throughout andthe heat transfer dies out through a wall jet flow. For 2 <p < 4, the local heating has a significant effect at relativelysmall distances, with a thermal runaway developing at a finitedistance along the surface.     

Heat capacity of superfine oxides of iron under applied magnetic fields

Heat capacity is one of the most characteristic and important properties when the peculiarities of magnetic nanosystems are studied. In these systems the magnetic ordering becomes obvious due to the thermal effects such as heat capacity anomalies. It was considered earlier that heat capacity change under magnetic fields applied is slight and it cannot be taken into account in thermodynamic calculations. However the experimental heat capacity data for ferrofluids under magnetic fields applied show that field and temperature heat capacity dependences have a complicated behavior and in magnetic fields an essential heat capacity change takes place. On the other hand in the literature the contradictory data about heat capacity of nanoparticles appear. According to some papers nanoparticles heat capacity can exceed heat capacity of a bulk material a few times.     

Is there a relationship between protein thermal stability and the denaturation heat capacity change?

It is shown the non-occurrence of a correlation between the values of the denaturation temperature and those of the denaturation heat capacity change for a set of 13 proteins possessing the ‘SH3-type’ fold from both mesophilic and thermophilic microorganisms. This seems to be a rather general result, because, fixed the size and the folding pattern, the denaturation heat capacity change is a nearly constant quantity, within the uncertainty limits of experimental determinations, regardless of the thermal stability of the protein. A precise definition of the thermodynamics of the hydrophobic effect is presented to clarify that the above finding does not imply that the hydrophobic effect does not play a role in the extra-thermal stability of thermophilic and hyperthermophilic proteins.     

Industrial need for accurate thermophysical data and for reliable prediction methods

Intelligent design of chemical-process equipment requires accurate thermophysical property values for pure components and mixtures including solutions. Databases used by practicing engineers should include the best numbers available and estimated uncertainties of these numbers. Many important property values have not been measured and must be estimated. Care should be exercised in selecting the estimation method. Property values that are a function of temperature, pressure, and/or composition can be correlated using appropriate equations. Such equations and the number of adjustable parameters in these equations should be selected with care. Examples of determining uncertainties, estimation techniques used, and correlating equations are given.     

Specific thermal and thermodynamic properties of the tellurites Fe2(TeO3)3, Fe2TeO5 and Fe2Te4O11

The temperature dependence of the molar heat capacities of the tellurites Fe₂(TeO₃)₃, Fe₂TeO₅ and Fe₂Te₄O₁₁ were determined. By statistical manipulation of the values obtained, the parameters in the equations for the corresponding compounds showing this dependence were determined using the least-squares method. These equations together with the standard molar entropies were used to determine the thermodynamic functions Δ₀^T S _m⁰, Δ_T^T,H _m⁰ and (Φ_m⁰ + Δ₀^T’ H _m⁰ / T) for T’=298.15 K.     

A fully automated adiabatic calorimeter for heat capacity measurement between 80 and 400 K

A fully automated adiabatic calorimeter controlled on line by a computer used for heat capacity measurements in the temperature range from 80 to 400 K was constructed. The hardware of the calorimetric system consisted of a Data Acquisition/Switch Unit, 34970A Agilent, a 7 1/2 Digit Nano Volt /Micro Ohm Meter, 34420A Agilent, and a P4 computer. The software was developed according to modern controlling theory. The adiabatic calorimeter consisted mainly of a sample cell equipped with a miniature platinum resistance thermometer and an electric heater, two (inner and outer) adiabatic shields, two sets of six junction differential thermocouple piles and a high vacuum can. A Lake Shore 340 Temperature Controller and the two sets of differential thermocouples were used to control the adiabatic conditions between the cell and its surroundings. The reliability of the calorimeter was verified by measuring the heat capacities of synthetic sapphire (α-Al₂O₃), Standard Reference Material 720. The deviation of the data obtained by this calorimeter from those published by NIST was within ±0.1% in the temperature range from 80 to 400 K.