Transient Nonsimilarity Nonlinear Heat Diffusion Solutions

1983 ◽  
Vol 105 (2) ◽  
pp. 295-301 ◽  
Author(s):  
F. B. Cheung
Keyword(s):  
Temperature Field ◽  
Finite Difference ◽  
Differential Equations ◽  
Analytical Method ◽  
Previous History ◽  
Parabolic Type ◽  
Heat Diffusion ◽  
Diffusion Equations ◽  
History Of ◽  
Large Heat

An approximate analytical method for treating parabolic type nonlinear heat diffusion equations is descibed in this study. The method involves transformation of the partial differential equations along with their initial and boundary conditions in terms of several pseudo-similarity variables followed by numerical solution of a system of quasi-ordinary differential equations. One obvious advantage of the approach is that the solution at a particular time can be found independently of the previous history of the temperature field. The simplicity and directness of the method are illustrated by solving the problem of combined conduction and thermal radiation in a large, heat-generating, particulate bed in contact with a solid. Comparison of the present analytical results is made with available finite difference solutions and found to be good.

Certain problems with the application of stochastic diffusion processes for description of chemical engineering phenomena; Kolmogorov and classic diffusion equations

1988 ◽  
Vol 53 (6) ◽  
pp. 1181-1197
Author(s):  
Vladimír Kudrna
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Parabolic Type ◽  
Diffusion Equations ◽  
Stochastic Motion ◽  
Energy Component ◽  
Classic Form

The paper presents alternative forms of partial differential equations of the parabolic type used in chemical engineering for description of heat and mass transfer. It points at the substantial difference between the classic form of the equations, following from the differential balances of mass and enthalpy, and the form following from the concept of stochastic motion of particles of mass or energy component. Examples are presented of the processes that may be described by the latter method. The paper also reviews the cases when the two approaches become identical.

Digital simulation of photoacoustic impulse responses

1986 ◽  
Vol 64 (9) ◽  
pp. 1049-1052 ◽  
Author(s):  
Richard M. Miller
Keyword(s):  
Finite Difference ◽  
Impulse Response ◽  
Depth Distribution ◽  
Digital Simulation ◽  
Heat Diffusion ◽  
Finite Difference Approximation ◽  
Diffusion Equations ◽  
Difference Approximation ◽  
Impulse Responses ◽  
Solid Samples

Impulse-response photoacoustic spectroscopy provides information on the depth distribution of chromophores in solid samples. To gain an understanding of the way in which sample properties affect the impulse response, a digital model has been generated. This model is based on discretization of time and space coupled with a finite-difference approximation of the governing heat-diffusion equations. The simulations are compared with experimental results.

Similarity and Generalized Finite-Difference Solutions of Parabolic Partial Differential Equations

1972 ◽  
Vol 39 (2) ◽  
pp. 584-590
Author(s):  
A. M. Clausing
Keyword(s):  
Partial Differential Equations ◽  
Finite Difference ◽  
Differential Equations ◽  
Parabolic Equations ◽  
Finite Difference Methods ◽  
Parabolic Type ◽  
Computational Effort ◽  
Partial Differential ◽  
Considerable Saving ◽  
Boundary Layer Equations

Techniques are presented for obtaining generalized finite-difference solutions to partial differential equations of the parabolic type. It is shown that the advantages of similarity in the solution of similar problems are generally not lost if the solution to the original partial differential equations is effected in the physical plane by finite-difference methods. The analysis results in a considerable saving in computational effort in the solution of both similar and nonsimilar problems. Several examples, including both the heat-conduction equation and the boundary-layer equations, are given. The analysis also provides a practical means of estimating the accuracy of finite-difference solutions to parabolic equations.

scholarly journals THE EXACT FINITE-DIFFERENCE SCHEME FOR VECTOR BOUNDARY‐VALUE PROBLEMS WITH PIECE‐WISE CONSTANT COEFFICIENTS

1998 ◽  
Vol 3 (1) ◽  
pp. 114-123
Author(s):  
H. Kalis
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Boundary Value ◽  
Parabolic Type ◽  
Second Order ◽  
Mhd Equations ◽  
System Of Differential Equations ◽  
Constant Coefficients

We will consider the exact finite‐difference scheme for solving the system of differential equations of second order with piece‐wise constant coefficients. It is well‐known, that the presence of large parameters at first order derivatives or small parameters at second order derivatives in the system of hydrodynamics and magnetohydrodynamics (MHD) equations (large Reynolds, Hartmann and others numbers) causes additional difficulties for the applications of general classical numerical methods. Thus, important to work out special methods of solution, the so‐called uniform converging computational methods. This gives a basis for the development of special monotone finite vector‐difference schemes with perturbation coefficient of function‐matrix for solving the system of differential equations. Special finite‐difference approximations are constructed for a steady‐state boundary‐value problem, systems of parabolic type partial differential equations, a system of two MHD equations, 2‐D flows and MHD‐flows equations in curvilinear orthogonal coordinates.

405: Previous History of Bladder Cancer is an Independent Prognostic Factor for Upper Tract Transitional Cell Carcinoma

2007 ◽  
Vol 177 (4S) ◽  
pp. 135-135
Author(s):  
Eiji Kikuchi ◽  
Akira Miyajima ◽  
Ken Nakagawa ◽  
Mototsugu Oya ◽  
Takashi Ohigashi ◽  
...  
Keyword(s):  
Bladder Cancer ◽  
Prognostic Factor ◽  
Transitional Cell Carcinoma ◽  
Cell Carcinoma ◽  
Transitional Cell ◽  
Previous History ◽  
Independent Prognostic Factor ◽  
Upper Tract ◽  
History Of

Popliteal artery thrombosis secondary to a tibial osteochondroma

VASA ◽  
2011 ◽  
Vol 40 (3) ◽  
pp. 251-255 ◽  
Author(s):  
Gruber-Szydlo ◽  
Poreba ◽  
Belowska-Bien ◽  
Derkacz ◽  
Badowski ◽  
...  
Keyword(s):  
Case Report ◽  
Magnetic Resonance Angiography ◽  
Popliteal Artery ◽  
Doppler Ultrasonography ◽  
Histopathological Examination ◽  
Previous History ◽  
Plain Radiography ◽  
Artery Thrombosis ◽  
History Of ◽  
The Right

Popliteal artery thrombosis may present as a complication of an osteochondroma located in the vicinity of the knee joint. This is a case report of a 26-year-old man with symptoms of the right lower extremity ischaemia without a previous history of vascular disease or trauma. Plain radiography, magnetic resonance angiography and Doppler ultrasonography documented the presence of an osteochondrous structure of the proximal tibial metaphysis, which displaced and compressed the popliteal artery, causing its occlusion due to intraluminal thrombosis..The patient was operated and histopathological examination confirmed the diagnosis of osteochondroma.

Rhabdomyolysis in DOMS

1999 ◽  
Vol 38 (05) ◽  
pp. 164-168 ◽  
Author(s):  
Gloria Ruiz Hernandez ◽  
C. Sanchez Marchori ◽  
J. Munoz Moliner ◽  
C. Martinez Carsi
Keyword(s):  
Bone Scintigraphy ◽  
Previous History ◽  
Biochemical Studies ◽  
History Of ◽  
Increased Activity

SummaryA 26-year-old man with a previous history of external twin bursitis was remitted to our Department for a bone scintigraphy. Before the study, the patient performed an elevated number of intense sprints. Bone scintigraphy showed a bilaterally increased activity in both anterior rectum muscles suggesting rhabdomyolysis. Biochemical studies and MRT confirmed the diagnosis.

Coronary Artery Bypass Grafting in a Patient with Organophosphate Poisoning

2015 ◽  
Vol 18 (4) ◽  
pp. 167 ◽  
Author(s):  
Rajeeva R. Pieris ◽  
Ravindra Fernando
Keyword(s):  
Coronary Artery ◽  
Coronary Artery Bypass Grafting ◽  
Coronary Artery Bypass ◽  
Artery Bypass ◽  
Previous History ◽  
Organophosphate Poisoning ◽  
Bypass Grafting ◽  
Artery Bypass Grafting ◽  
Excellent Health ◽  
History Of

A 43-year-old male, with no previous history of mental illness, was diagnosed with coronary heart disease, after which he became acutely depressed and attempted suicide by ingesting an organophosphate pesticide. He was admitted to an intensive care unit and treated with pralidoxime, atropine, and oxygen. His coronary occlusion pattern required early coronary artery bypass grafting (CABG) surgery. His family, apprehensive of a repeat suicidal attempt, requested surgery be performed as soon as possible. He recovered well from the OP poisoning and was mentally fit to express informed consent 2 weeks after admission. Seventeen days after poisoning, he underwent coronary artery bypass grafting and recovered uneventfully. Six years later, he remains in excellent health. We report this case because to the best of our knowledge there is no literature regarding CABG performed soon after organophosphate poisoning.

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