An analytical approach of heat transfer modelling with thermal stresses in circular plate by means of Gaussian heat source and stress function

In the proposed research work we have used the Gaussian circular heat source. This heat source is applied with the heat flux boundary condition along the thickness of a circular plate with a nite radius. The research work also deals with the formulation of unsteady-state heat conduction problems along with homogeneous initial and non-homogeneous boundary condition around the temperature distribution in the circular plate. The mathematical model of thermoelasticity with the determination of thermal stresses and displacement has been studied in the present work. The new analytical method, Reduced Differential Transform has been used to obtain the solution. The numerical results are shown graphically with the help of mathematical software SCILAB and results are carried out for the material copper.

Heat Transfer Analysis of Laminar Pulsating Flow in a Rectangular Channel Using Infrared Thermography

While numerous applied studies have successfully demonstrated the feasibility of unsteady cooling solutions, a consensus has yet to be reached on the local instantaneous conditions that result in heat transfer enhancement. The current work aims to experimentally validate a recent analytical solution (on a local time-dependent basis) for the common flow condition of a fully-developed incompressible pulsating flow in a uniformly-heated vessel. The experimental setup is found to approximate the ideal constant heat flux boundary condition well, especially for the decoupled unsteady scenario where the amplitude of the most significant secondary contributions (capacitance and lateral conduction) amounts to 1.2% and 0.2% of the generated heat flux, respectively. Overall, the experimental measurements for temperature and heat flux oscillations are found to coincide well with a recent analytical solution to the energy equation by the authors. Furthermore, local time-dependent heat flux enhancements and degradations are observed to be qualitatively similar to those of wall shear stress from a previous study, suggesting that the thermal performance is indeed influenced by hydrodynamic behaviour.

The model reduction of the Vlasov-Poisson-Fokker-Planck system to the Poisson-Nernst-Planck system via the Deep Neural Network Approach

The model reduction of a mesoscopic kinetic dynamics to a macroscopic continuum dynamics has been one of the fundamental questions in mathematical physics since Hilbert's time. In this paper, we consider a diagram of the diffusion limit from the Vlasov-Poisson-Fokker-Planck (VPFP) system on a bounded interval with the specular reflection boundary condition to the Poisson-Nernst–Planck (PNP) system with the no-flux boundary condition. We provide a Deep Learning algorithm to simulate the VPFP system and the PNP system by computing the time-asymptotic behaviors of the solution and the physical quantities. We analyze the convergence of the neural network solution of the VPFP system to that of the PNP system via the Asymptotic-Preserving (AP) scheme. Also, we provide several theoretical evidence that the Deep Neural Network (DNN) solutions to the VPFP and the PNP systems converge to the a priori classical solutions of each system if the total loss function vanishes.

MHD Powell–Eyring dusty nanofluid flow due to stretching surface with heat flux boundary condition

A steady MHD boundary layer flow of Powell–Eyring dusty nanofluid over a stretching surface with heat flux condition is studied numerically. It is assumed that the fluid is incompressible and the impacts of thermophoresis and Brownian motion are taken into regard. In addition, the Powell–Eyring terms are considered in the momentum boundary layer and thermal boundary layer. The dust particles are seen as to be having the same size and conform to the nanoparticles in a spherical shape. We obtain a system of ordinary differential equations that are suitable for analyzed numerically using the fourth-order Runge–Kutta method via software algebraic MATLAB by applying appropriate transformations to the system of the governing partial differential equations in our problem. There is perfect compatibility between the bygone and current results when comparing our numerical solutions with the available data for values of the selected parameters. This confirms the validity of the method used here and thus the validity of the results. The influence of some parameters on the boundary layer profiles (the velocity and temperature for the particle phase and fluid phase, and nanoparticle concentration) is discussed. The results of this study display that the profiles of the velocity for particle and fluid phases increase with increasing Powell–Eyring fluid parameter, but reduce with height in magnetic field values. Mass concentration of the dust particles decreases the temperature of both the particle and fluid phases. The results also indicate the concentration of nanoparticle contraction as Schmidt number increases.

Effects of Jet Impingement on Convective Heat Transfer in Effusion Holes

A common design for cooling the combustor liner of gas turbines is a double wall composed of impingement jets that feed effusion cooling holes. An important cooling mechanism associated with the effusion hole is the convective cooling provided to the liner wall, which is in contact with the hot main gas flowing through the combustor. While the combination of impingement jets and effusion holes has been studied earlier, mostly in terms of cooling effectiveness, investigators have not fully evaluated the effect the impingement jet has on the local internal convection within the effusion hole. This study evaluates the detailed effects of the impingement geometry on the local convective heat transfer coefficients within the effusion hole, which provides insights as to the design decisions for cooling combustor liners. Using a scaled-up, 3D-printed effusion hole with a constant heat flux boundary condition, local convective heat transfer coefficients were measured for a range of impingement geometries and positions relative to the effusion holes. Results showed a strong influence on the convective heat transfer resulting from the placement of the impingement hole relative to the effusion hole. In particular, the results showed a strong sensitivity to the circumferential and radial placement of the impingement jet with little sensitivity to the jet-to-effusion distance.

Simulating the Effects of Lower-Energy (<30 keV) Electrons on the Inner Magnetosphere Satellite Surface Charging Environment

&lt;p&gt;Satellite surface charging often occurs in the inner magnetosphere from the pre-midnight to the dawn sector when electron fluxes of&amp;#160; hundreds of eV to tens of keV are largely enhanced. Inner magnetosphere ring current models can be used to simulate/predict the satellite surface charging environment, with their flux outer boundary conditions specified either based on observations or provided by other models, such as MHD models. In the latter approach, the flux spectrum at the outer boundary is usually assumed to follow a Kappa or Maxwellian distribution, which however often departs greatly from, or underestimates, the realistic distribution below tens of keV, the energy range that is crucial in the spacecraft surface charging anomaly. This study aims to optimize the electron flux boundary condition of the inner magnetosphere ring current model to achieve a better representation of the surface charging environment. The MHD-parameterized flux spectrum is combined with an empirical electron flux model that specifies the &lt; 40 keV electron flux spectrum. New simulation results indicate that the surface charging environment, monitored by an integrated electron flux between 10&lt;E&lt;50 keV, is significantly enhanced by 1-2 orders of magnitude as opposed to the case in which Kappa/Maxwellian distribution is used at the outer boundary. The new results therefore show better agreement with Van Allen Probes measurements. The improved boundary condition also impacts the auroral precipitation, which may change the conductivity and circulated dynamics.&amp;#160;&lt;/p&gt;

A Model Analysis of the MAVEN/ROSE Electron Density Profiles at Mars

&lt;p&gt;The electron density (N&lt;sub&gt;e&lt;/sub&gt;) profiles&amp;#160;over the northern high-latitude region&amp;#160;measured&amp;#160;with Radio Occultation Science Experiments (ROSE) onboard the Mars Atmosphere and Volatile Evolution (MAVEN)&amp;#160;have indicated more complicated ionospheric structure of&amp;#160;Mars than previously thought.&amp;#160; Some of the profiles have shown wide and narrow shapes of the main N&lt;sub&gt;e&lt;/sub&gt;&amp;#160;peaks, while others&amp;#160;show anomalous characteristics of the topside plasma distribution.&amp;#160;&amp;#160;Large variations&amp;#160;in the topside N&lt;sub&gt;e&lt;/sub&gt;&amp;#160;scale heights are observed presumably in response to the outward&amp;#160;flow of ionospheric plasma&amp;#160;or changes in plasma temperatures.&amp;#160;&amp;#160;&amp;#160;We use our 1-D chemical diffusive model coupled with the Mars - Global Ionosphere Thermosphere Model (M-GITM) to interpret these N&lt;sub&gt;e&lt;/sub&gt; profiles.&amp;#160; Our model is a coupled finite difference primitive equation model which solves for plasma densities and vertical ion fluxes. &amp;#160;The photochemical equilibrium in the model for each ion is&amp;#160;assumed at the lower boundary,&amp;#160;while the flux boundary condition&amp;#160;is assumed&amp;#160;at the upper boundary to simulate plasma loss from the&amp;#160;Martian ionosphere.&amp;#160; The crustal magnetic field at the measured N&lt;sub&gt;e&lt;/sub&gt; locations is weak and mainly horizontal and does not allow plasma to move vertically. &amp;#160;&amp;#160;Thus, the primary plasma loss from the topside ionosphere at these locations is most likely caused by diverging horizontal fluxes of ions, indicating that the dynamics of the upper ionosphere of Mars is controlled by the solar wind.&amp;#160;&amp;#160;The primary source of ionization in the model is due to solar EUV radiation. &amp;#160;We find that the variation in the topside N&lt;sub&gt;e&lt;/sub&gt;&amp;#160;scale heights is sensitive to magnitudes of upward ion fluxes derived from ion velocities that we impose at the upper boundary to explain the topside ionospheric structure.&amp;#160; The model requires upward velocities ranging from 60 ms&lt;sup&gt;-1&lt;/sup&gt; to 80 ms&lt;sup&gt;-1&lt;/sup&gt; for all ions to ensure an agreement with the measured N&lt;sub&gt;e&lt;/sub&gt; profiles. The corresponding outward fluxes in the range 1.6 x 10&lt;sup&gt;6&amp;#160;&lt;/sup&gt;&amp;#8211; 3.8 x 10&lt;sup&gt;6&lt;/sup&gt;&amp;#160;cm&lt;sup&gt;-2&lt;/sup&gt;&amp;#160;s&lt;sup&gt;-1&amp;#160;&lt;/sup&gt;are calculated for O&lt;sub&gt;2&lt;/sub&gt;&lt;sup&gt;+&lt;/sup&gt;&amp;#160;compared to those for O&lt;sup&gt;+&lt;/sup&gt;&amp;#160;in the range 4 x 105 &amp;#8211; 6 x 105 cm&lt;sup&gt;-2&lt;/sup&gt; s&lt;sup&gt;-1&lt;/sup&gt;.&amp;#160; The model results for the northern N&lt;sub&gt;e&lt;/sub&gt; profiles will be presented in comparison with the measured N&lt;sub&gt;e&lt;/sub&gt; profiles. &amp;#160;This work is supported by Mohammed Bin Rashid Space Centre (MBRSC), Dubai, UAE, under Grant ID number 201604.MA.AUS.&lt;/p&gt;