Thermoelectric Viscoelastic Fluid with Fractional Integral and Derivative Heat Transfer

2015 ◽  
Vol 7 (4) ◽  
pp. 528-548 ◽  
Author(s):  
Magdy A. Ezzat ◽  
A. S. Sabbah ◽  
A. A. El-Bary ◽  
S. M. Ezzat
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Fluid Flow ◽  
Heat Conduction ◽  
General Solution ◽  
Viscoelastic Fluid ◽  
Fractional Integral ◽  
Heat Sources ◽  
One Dimensional ◽  
Time Fractional Derivative

AbstractA new mathematical model of magnetohydrodynamic (MHD) theory has been constructed in the context of a new consideration of heat conduction with a time-fractional derivative of order 0 < α ≤ 1 and a time-fractional integral of order 0 < γ ≤ 2. This model is applied to one-dimensional problems for a thermoelectric viscoelastic fluid flow in the absence or presence of heat sources. Laplace transforms and state-space techniques will be used to obtain the general solution for any set of boundary conditions. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameters on all the studied fields.

scholarly journals Mathematical simulation of forest fire front influence on wood-based building using one-dimensional model of heat transfer

2020 ◽  
Vol 200 ◽  
pp. 03007
Author(s):  
Nikolay V Baranovskiy ◽  
Aleksey Malinin
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Heat Conduction ◽  
Mathematical Simulation ◽  
Forest Fire ◽  
Dimensional Model ◽  
One Dimensional ◽  
Building Enclosures ◽  
Fire Front ◽  
Fire Impact

The purpose of the present paper is to mathematical simulation of heat transfer in enclosures of wood-based building when exposed to thermal radiation from forest fire front. One-dimensional mathematical model is used. Mathematically, heat transfer in building enclosures is described by system of non-stationary equations of heat conduction with corresponding initial and boundary conditions. It is suggested to use several scenarios of forest fire impact. Temperature distribution on wall depth is obtained for different scenarios of forest fire impact on building enclosures.

Natural Convection From Protruding Heat Sources in a Channel

2003 ◽  
Author(s):  
Tunc Icoz ◽  
Qinghua Wang ◽  
Yogesh Jaluria
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Natural Convection ◽  
Rayleigh Scattering ◽  
Convection Heat Transfer ◽  
Separation Distance ◽  
Natural Convection Heat Transfer ◽  
Temperature Profiles ◽  
Heat Sources ◽  
Convection Heat

Natural convection has important implications in many applications like cooling of electronic equipment due to its low cost and easy maintenance. In the present study, two-dimensional natural convection heat transfer to air from multiple identical protruding heat sources, which simulate electronic components, located in a horizontal channel has been studied numerically. The fluid flow and temperature profiles, above the heating elements placed between an adiabatic lower plate and an isothermal upper plate, are obtained using numerical simulation. The effects of source temperatures, channel dimensions, openings, boundary conditions, and source locations on the heat transfer from and flow above the protruding sources are investigated. Different configurations of channel dimensions and separation distances of heat sources are considered and their effects on natural convection heat transfer characteristics are studied. The results show that the channel dimensions have a significant effect on fluid flow. However, their effects on heat transfer are found to be small. The separation distance is found to be an important parameter affecting the heat transfer rate. The numerical results of temperature profiles are compared with the experimental measurements performed using Filtered Rayleigh Scattering (FRS) technique in an earlier study, indicating good agreement. It is observed that adiabatic upper plate assumption leads to better temperature predictions than isothermal plate assumption.

Microprocessor Silicon Die Temperature Prediction by Simplified Boundary Conditions

2015 ◽  
Author(s):  
Koji Nishi ◽  
Tomoyuki Hatakeyama ◽  
Shinji Nakagawa ◽  
Masaru Ishizuka
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Boundary Conditions ◽  
Thermal Resistance ◽  
Hot Spot ◽  
Three Dimensional ◽  
Thermal Design ◽  
Target Temperature ◽  
One Dimensional ◽  
Thermal Network

The thermal network method has a long history with thermal design of electronic equipment. In particular, a one-dimensional thermal network is useful to know the temperature and heat transfer rate along each heat transfer path. It also saves computation time and/or computation resources to obtain target temperature. However, unlike three-dimensional thermal simulation with fine pitch grids and a three-dimensional thermal network with sufficient numbers of nodes, a traditional one-dimensional thermal network cannot predict the temperature of a microprocessor silicon die hot spot with sufficient accuracy in a three-dimensional domain analysis. Therefore, this paper introduces a one-dimensional thermal network with average temperature nodes. Thermal resistance values need to be obtained to calculate target temperature in a thermal network. For this purpose, thermal resistance calculation methodology with simplified boundary conditions, which calculates thermal resistance values from an analytical solution, is also introduced in this paper. The effectiveness of the methodology is explored with a simple model of the microprocessor system. The calculated result by the methodology is compared to a three-dimensional heat conduction simulation result. It is found that the introduced technique matches the three-dimensional heat conduction simulation result well.

scholarly journals A Useful Equation for Gas Turbine Design

2018 ◽  
Vol 140 (03) ◽  
pp. S52-S53
Author(s):  
Lee S. Langston
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Gas Turbine ◽  
Rankine Cycle ◽  
Combined Cycle ◽  
Brayton Cycle ◽  
Nonlinear Superposition ◽  
Transient Conditions ◽  
One Dimensional ◽  
Turbine Design

This article presents three different gas turbine phenomena and design cases. The sketch in the article shows a schematic of a combined cycle powerplant consisting of a Brayton cycle (gas turbine) whose exhaust provides energy to a Rankine cycle (steam turbine). Frequently, one can use simple but exact one-dimensional (1D) heat conduction solutions to estimate the heat loss or gain of gas turbine components under transient conditions. These easy-to-use solutions are found in most undergraduate heat transfer texts. The article suggests that those three widely different gas turbine phenomena and design cases all have the simple, nonlinear superposition form.

Sign in / Sign up

Export Citation Format

Share Document