The following information was submitted:
Transactions: WSEAS TRANSACTIONS ON HEAT AND MASS TRANSFER
Transactions ID Number: 42-294
Full Name: Kal Sharma
Position: Other
Age: ON
Sex: Male
Address: Prairie View A & M University, Prairie View, TX 77446
Country: UNITED STATES
Tel: (936) 261 9413
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E-mail address: jyoti_kalpika@yahoo.com
Other E-mails: krsharma@pvamu.edu
Title of the Paper: MANIFESTATION OF ACCELERATION DURING TRANSIENT DIFFUSION AND SIMULTANEOUS AUTOCATALYTIC NUCLEAR REACTIONS
Authors as they appear in the Paper: Kal
Email addresses of all the authors:
Number of paper pages: 27
Abstract: For a system of a given shape, there exists a critical size for which the rate of production of neutrons from fission reactions just equals the rate of removal of neutrons. For a long cylindrical rod, using parabolic transient Fick¡¦s laws of diffusion and simultaneous autocatalytic reaction, a critical radius for the system can be calculated as: Where ƒÑ1 is the first zero of the zero-order Bessel function J0, k1¡¨¡¦ is the autocatalytic first order reaction rate and DAB binary neutron diffusivity. This limit is referred to as the shape limit of nuclear fuel rod. Above this size, autocatalytic runaway can be expected. The transient concentration profile in a long cylindrical rod during simultaneous diffusion and autocatalytic reaction using the generalized Fick¡¦s laws of molecular diffusion and relaxation was derived. A lower limit on the radius of the fuel rod is obtained in order to avoid cycling of concentration ni the time domain during transience. !
The lower limit on the radius of the long cylindrical rod subject to simultaneous autocatalytic reaction and diffusion exist and found to be . Closed form analytical solution for transient concentration profile for simulataneous autocatalytic reaction and finite speed diffusion is derived using the method of separation of variables and by the method of Laplace transforms. The solution is bifurcated. At large relaxation times, the time portion of the solution is cosinous albeit damped by the decaying exponential. Both the cycling limit and shape limits have to be considered during design of nuclear fuel rod systems. The shape limit was derived from steady state considerations. The lower cycling limit was derived from transient finite speed diffusion considerations.
Keywords: Damped Wave Diffusion and Relaxation; Stokes Einstein Diffusion Coefficients; Nuclear Fission Reactions; Autocatalytic Reactions; Shape Limits; Method of Separation of Variables; Newton-Cotes Integration
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