scholarly journals Temperature Distribution of High Temperature Protective Clothing Based on Partial Differential Equation

2018 ◽  
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
High Temperature ◽  
Temperature Distribution ◽  
Protective Clothing ◽  
Partial Differential

Boundary Control of Temperature Distribution in a Rectangular Functionally Graded Material Plate

2010 ◽  
Vol 133 (2) ◽  
Author(s):  
Hossein Rastgoftar ◽  
Mohammad Eghtesad ◽  
Alireza Khayatian
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Heat Flux ◽  
Steady State ◽  
Temperature Distribution ◽  
Functionally Graded ◽  
Order Partial Differential Equation ◽  
Partial Differential ◽  
Fg Plates ◽  
Graded Material

In this paper, an analytical method and a partial differential equation based solution to control temperature distribution for functionally graded (FG) plates is introduced. For the rectangular FG plate under consideration, it is assumed that the material properties such as thermal conductivity, density, and specific heat capacity vary in the width direction, and the governing heat conduction equation of the plate is a second-order partial differential equation. Using Lyapunov’s theorem, it is shown that by applying controlled heat flux through the boundary of the domain, the temperature distribution of the plate will approach a desired steady-state distribution. Numerical simulation is provided to verify the effectiveness of the proposed method such that by applying the boundary transient heat flux, in-domain distributed temperature converges to its desired steady-state temperature.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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