Energy equations and shock equations

Keyword(s):  
2020 ◽  
Vol 22 (4) ◽  
pp. 1439-1452
Author(s):  
Mohamed L. Benlekkam ◽  
Driss Nehari ◽  
Habib Y. Madani

AbstractThe temperature rise of photovoltaic’s cells deteriorates its conversion efficiency. The use of a phase change material (PCM) layer linked to a curved photovoltaic PV panel so-called PV-mirror to control its temperature elevation has been numerically studied. This numerical study was carried out to explore the effect of inner fins length on the thermal and electrical improvement of curved PV panel. So a numerical model of heat transfer with solid-liquid phase change has been developed to solve the Navier–Stokes and energy equations. The predicted results are validated with an available experimental and numerical data. Results shows that the use of fins improve the thermal load distribution presented on the upper front of PV/PCM system and maintained it under 42°C compared with another without fins and enhance the PV cells efficiency by more than 2%.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Muhammad Bilal ◽  
Hamna Arshad ◽  
Muhammad Ramzan ◽  
Zahir Shah ◽  
Poom Kumam

AbstractThe key objective of the present research is to examine the hybrid magnetohydrodynamics (MHD) nanofluid (Carbon-nanotubes and ferrous oxide–water) CNT–Fe3O4/H2 flow into a horizontal parallel channel with thermal radiation through squeezing and dilating porous walls. The parting motion is triggered by the porous walls of the channel. The fluid flow is time-dependent and laminar. The channel is asymmetric and the upper and lower walls are distinct in temperature and are porous. With the combination of nanoparticles of Fe3O4 and single and multi-wall carbon nanotubes, the hybrid nanofluid principle is exploited. By using the similarity transformation, the set of partial differential equations (PDEs) of this mathematical model, governed by momentum and energy equations, is reduced to corresponding ordinary differential equations (ODEs). A very simple numerical approach called the Runge–Kutta system of order four along with the shooting technique is used to achieve the solutions for regulating ODEs. MATLAB computing software is used to create temperature and velocity profile graphs for various emerging parameters. At the end of the manuscript, the main conclusions are summarized. Through different graphs, it is observed that hybrid-nanofluid has more prominent thermal enhancement than simple nanofluid. Further, the single-wall nanotubes have dominated impact on temperature than the multi-wall carbon nanotubes. From the calculations, it is also noted that Fe2O3–MWCNT–water has an average of 4.84% more rate of heat transfer than the Fe2O3–SWCNT–water. On the other hand, 8.27% more heat flow observed in Fe2O3–SWCNT–water than the simple nanofluid. Such study is very important in coolant circulation, inter-body fluid transportation, aerospace engineering, and industrial cleaning procedures, etc.


1954 ◽  
Vol 5 (1) ◽  
pp. 25-38 ◽  
Author(s):  
K. E. G. Wieghardt

SummaryA simple one parametric method, due to A. Walz and based on the momentum and energy equations, for calculating approximately laminar boundary layers is extended to cover axi-symmetric flow as well as plane flow. The necessary computing work is reduced a little.Another known method which requires still less computing work is also extended for axi-symmetric flow and, with the amendment of a numerical constant, proves adequate for practical purposes.


1993 ◽  
Vol 50 (1) ◽  
pp. 51-70 ◽  
Author(s):  
D. Zoler ◽  
S. Cuperman ◽  
J. Ashkenazy ◽  
M. Caner ◽  
Z. Kaplan

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.


2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Masao Furukawa

The state of the art of thermally self-excited oscillatory heat pipe technology is briefly mentioned to emphasize that there exists no oscillating/pulsating heat pipe (OHP/PHP) suited to long-distance heat transport. Responding to such conditions, this study actively proposes a newly devised conceptually novel type of OHP/PHP. In that heat pipe, the adiabatic section works as it were the dream pipe invented by Kurzweg. This striking quality of the proposed new-style OHP/PHP produces high possibilities of long-distance heat transport. To support such optimistic views, an originally planned mathematical model is introduced for feasibility studies. Hydraulic considerations have first been done to understand what conditions are required for sustaining bubble-train flows in a capillary tube of interest. Theoretical analysis has then been made to solve the momentum and energy equations governing the flow velocity and temperature fields in the adiabatic section. The obtained analytical solutions are arranged to give algebraic expressions of the effective thermal diffusivity, the performance index combined with the tidal displacement, and the required electric power. Computed results of those three are displayed in the figures to demonstrate the realizability of that novel OHP.


1986 ◽  
Vol 163 ◽  
pp. 27-58 ◽  
Author(s):  
Laurence Armi

This is a theoretical and experimental study of the basic hydraulics of two flowing layers. Unlike single-layer flows, two-layer flows respond quite differently to bottom depth as opposed to width variations. Bottom-depth changes affect the lower layer directly and the upper layer only indirectly. Changes in width can affect both layers. In fact for flows through a contraction control two distinct flow configurations are possible; which one actually occurs depends on the requirements of matching a downstream flow. Two-layer flows can pass through internally critical conditions at other than the narrowest section. When the two layers are flowing in the same direction, the result is a strong coupling between the two layers in the neighbourhood of the control. For contractions a particularly simple flow then exists upstream in which there is no longer any significant interfacial dynamics; downstream in the divergent section the flow remains internally supercritical, causing one of the layers to be rapidly accelerated with a resulting instability at the interface. A brief discussion of internal hydraulic jumps based upon the energy equations as opposed to the more traditional momentum equations is included. Previous uniqueness problems are thereby avoided.


Author(s):  
Abhijit Mukherjee ◽  
Satish G. Kandlikar

Flow boiling through microchannels is characterized by nucleation of vapor bubbles on the channel walls and their rapid growth as they fill the entire channel cross-section. In parallel microchannels connected through a common header, formation of vapor bubbles often results in flow maldistribution that leads to reversed flow in certain channels. The reversed flow is detrimental to the heat transfer and leads to early CHF condition. One way of eliminating the reversed flow is to incorporate flow restrictions at the channel inlet. In the present numerical study, a nucleating vapor bubble placed near the restricted end of a microchannel is numerically simulated. The complete Navier-Stokes equations along with continuity and energy equations are solved using the SIMPLER method. The liquid-vapor interface is captured using the level set technique. The results show that with no restriction the bubble moves towards the nearest channel outlet, whereas in the presence of a restriction, the bubble moves towards the distant but unrestricted end. It is proposed that channels with increasing cross-sectional area may be used to promote unidirectional growth of the vapor plugs and prevent reversed flow.


Author(s):  
A. Agrawal ◽  
G. Biswas ◽  
S. W. J. Welch ◽  
F. Durst

The bubble formation and heat transfer on a horizontal surface have been numerically analyzed using a volume of fluid (VOF) based interface tracking method incorporated into a complete solution of the Navier-Stokes and the thermal energy equations. The numerical method took into account the effects of surface tension, the interface mass transfer and the corresponding latent heat. The computations demonstrated capability of the algorithm in generating quantitative information on unsteady periodic bubble release patterns and on the spatially and temporally varying film thickness. The computations also predict the transport coefficients on the horizontal surface.


2009 ◽  
Vol 76 (3-4) ◽  
pp. 305-315 ◽  
Author(s):  
DASTGEER SHAIKH

AbstractWe develop a two dimensional, self-consistent, compressible fluid model to study evolution of Alfvenic modes in partially ionized astrophysical and space plasmas. The partially ionized plasma consists mainly of electrons, ions and significant neutral atoms. The nonlinear interactions amongst these species take place predominantly through direct collision or charge exchange processes. Our model uniquely describe the interaction processes between two distinctly evolving fluids. In our model, the electrons and ions are described by a single-fluid compressible magnetohydrodynamic (MHD) model and are coupled self-consistently to the neutral fluid via compressible hydrodynamic equations. Both plasma and neutral fluids are treated with different energy equations that adequately enable us to monitor non-adiabatic and thermal energy exchange processes between these two distinct fluids. Based on our self-consistent model, we find that the propagation speed of Alfvenic modes in space and astrophysical plasma is slowed down because these waves are damped predominantly due to direct collisions with the neutral atoms. Consequently, energy transfer takes place between plasma and neutral fluids. We describe the mode coupling processes that lead to the energy transfer between the plasma and neutral and corresponding spectral features.


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