Two Approaches to the Study of Temperature Effect on the Dissipative Properties of Materials

In order to study the effect of temperature changes on the dissipative properties of materials, two approaches are used. The first approach implies introducing some temperature function under the sign of the integral in the heredity theory equation and simultaneously taking into account the dependence of the elastic modulus on temperature. As a result, based on experimental data on the thermal creep of soils, the expression for determining the hysteresis energy losses under the periodic voltage changes was obtained depending on temperature changes.According to the second approach, the expression for determining the hysteresis energy losses under isothermal conditions at different temperatures was obtained by introducing into the heredity theory equation an approximation of the experimental dependences of instantaneous deformation and temperature creep parameters for steel Kh18 N10T.

Diurnal Extrema Timing—A New Climatological Parameter?

We address the following question: Are turning points of daily air temperature function a piece of relevant climatological information worth recording and analyzing? Diurnal Extrema Timing (DET) are daily occurrence times of air temperature minimum and maximum. Although unrecognized and unrecorded as a meteorological variable, the exact timing of daily temperature extrema plays a crucial role in the characterization of air temperature variability. In this study, we introduce the DET concept and assess the plausibility of this potential parameter in detecting temperature extrema timing changes. Conceptualization of the DET parameter has, for a primary goal, the supplementation of vital spatial information to the daily measurements of air temperature extrema. The elementary analysis of annual trends of daily DET examines the significance of this parameter in describing changes in the time domain of air temperature variability. The introduction of the new Climate Parameter Sensitivity Index (CPSI) for evaluating the susceptibility of climate parameters to climate change directs attention to the importance of the systematic acquisition of the timing of daily extrema in climate observations. The results of this study reveal the timing of daily air temperature maximum as the most vulnerable to climate change among temperature and timing extrema indices.

Interaction between Screw Dislocation and Interfacial Crack in Fine-Grained Piezoelectric Coatings under Steady-State Thermal Loading

The mechanical behavior of fine-grained piezoelectric/substrate structure with screw dislocation and interface edge crack under the coupling action of heat, force and electricity are studied. Using the mapping function method, firstly, the finite area plane is transformed into the right semi-infinite plane, then the expression of the temperature field is given with the help of the complex function, and then the temperature field of the problem is achieved. By constructing the general solution of the governing equation with temperature function, the analytical expression of the image force is derived. Finally, the effects of material parameters, temperature gradient, coating thickness and crack size on image force are analyzed by numerical examples. The results show that the temperature gradient has a very significant effect on the image force, and thicker coating is conducive to the stability of dislocation and interface crack.

Comparison of analytical methods and numerical methods in modeling the physical phenomenon of heat conduction with free radiation

The development of mathematical setting for modeling heat conduction phenomena in the presence of radioactive effects is well known. The importance in the study of heat conduction in relation to radioactive effects is relevant in several engineering applications such as combustion, materials science, fluid mechanics and other areas. This research is based on the mathematical model of the heat equation to study the physical phenomenon of heat transfer along a metal bar with slightly insulated sides with the effect of free radiation. To calculate the temperature function that allows modeling the heat transfer process along the bar, the Fourier series solution is constructed step by step, in addition an alternative method of calculating the temperature by using the explicit numerical method is given. The calculation of the temperature along the bar is compared by analytical and numerical method by computing the percentage error and different temperature profiles are plotted to verify the fit of the two approaches. The methods developed throughout the research can be extended to other types of physical phenomena that are useful in related research and in education in engineering subjects such as fluid mechanics and heat transfer.

Modeling of heat transport phenomena using the equations of mathematical physics

The study of physical phenomena that include conservative principles is part of the research field of the equations of mathematical physics. To deepen in methods to solve the equations of mathematical physics is a contribution in understanding the modeling of applications in different areas. This research studies the physical phenomenon of heat transport with convection from the viewpoint of modeling with differential equations. The advantage of working with equations is to apply the techniques of mathematical analysis and numerical methods to obtain the temperature function. In the research, the solution of the heat transport model is computed according to the analytical method of separable variables in order to represent the temperature function as a trigonometric series. With the help of a simple numerical method, it is possible to derive a scheme of calculation of the temperature function. By performing a case study, the methods are compared, and their fit is verified by simulation.

Impacts of Thermal Conductivity and Variable Viscosity on the Dissipative Heat and Species Transport of MHD Flow in Porous Media

The investigation of dissipative heat and species diffusion of a conducting liquid under the combined influence of buoyancy forces in a moving plate is examined in the existence of magnetic field. The flowing liquid heat conductivity and viscosity are taken to be linearly varied as a temperature function. The governing derivative equations of the problem are changed to anon-linear coupled ordinary derivative equations by applying similarity quantities. The dimensionless model is solved using shooting technique along with the Runge-Kutta method. The outcomes for the flow wall friction, heat gradient and species wall gradient are offered in table and qualitatively explained. The study revealed that the Newtonian fluid viscosity can be enhanced by increasing the fluid flow medium porosity and the magnetic field strength. Hence, the study will improve the industrial usage of Newtonian working fluid.

Modeling of the physical phenomenon of heat generation by using partial differential equations

The equations of mathematical physics are a natural environment for modeling physical phenomena, an example of the above is evidenced by the heat equation in relation to its use in a variety of applications; directly related to the equations of mathematical physics are the solution methods that are used to construct the predictive models. This paper describes step by step the analytical method of separation of variables to perform a complete description of the heat conduction phenomenon in the presence of a heat generation source. The investigation by using mathematical arguments allowed to calculate the temperature function as the addition of a Fourier series and a function which represents the steady state; by performing a computational simulation, it was possible to demonstrate the accuracy of the results achieved.

Analysing the Contact Conduction Influence on the Heat Transfer Intensity in the Rectangular Steel Bars Bundle

Bundles of steel bars, besides metal foams, are an example of cellular solids. Such bundles constitute a charge during the heat treatment of bars. The paper presents a mathematical model of transient heat transfer in a bundle of rectangular steel bars based on the energy balance method. The key element of this model is the procedure of determining the effective thermal conductivity using the electrical analogy. Different mechanisms of heat transfer occurring within the analysed medium (conduction in steel and contact conduction) are assigned corresponding thermal resistances. The discussed procedure involves expressing these resistances with the use of arithmetic relationships describing their changes in the temperature function. Thermal contact resistance has been described with the use of the relationships determined experimentally. As a result of the performed calculations, the influence of contact conduction between the adjacent bars and bundle arrangement on its heating time was established. The results of the calculations show that the heating time of bundles can be lowered by 5–40% as a result of a decrease in the thermal contact resistance. This effect depends on the bar size and bundle arrangement. From the practical point of view, the analysed problem is connected with the optimization of the heat treatment processes of steel bars.

Jacobi Spectral Collocation Technique for Time-Fractional Inverse Heat Equations

In this paper, we introduce a numerical solution for the time-fractional inverse heat equations. We focus on obtaining the unknown source term along with the unknown temperature function based on an additional condition given in an integral form. The proposed scheme is based on a spectral collocation approach to obtain the two independent variables. Our approach is accurate, efficient, and feasible for the model problem under consideration. The proposed Jacobi spectral collocation method yields an exponential rate of convergence with a relatively small number of degrees of freedom. Finally, a series of numerical examples are provided to demonstrate the efficiency and flexibility of the numerical scheme.

3D MATHEMATICAL MODEL CHARACTERIZING THE DYNAMICS OF THE TEMPERATURE FIELD OF A WALL STRUCTURE WITH A DOUBLE-SIDED FACING FROM A SAPROPEL-HEMP COMPOSITE MATERIAL

In this paper, a 3D mathematical model is proposed to determine the dynamics of the temperature field in a three-layer composite sapropel-hemp slab. The proposed model consists of a system of three initial-boundary value problems with respect to the temperature function for each layer, respectively, and one initial-boundary value problem with respect to the unknown velocity of heat propagation along the thickness dimension of the composite sapropel-hemp slab.