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Full-Text Articles in Mechanical Engineering
Starting Radial Subdiffusion From A Central Point Through A Diverging Medium (A Sphere): Heat-Balance Integral Method, Jordan Hristov
Starting Radial Subdiffusion From A Central Point Through A Diverging Medium (A Sphere): Heat-Balance Integral Method, Jordan Hristov
Jordan Hristov
The work presents an integral solution of the time-fractional subdiffusion equation as alternative approach to those employing hypergeometric functions. The integral solution suggests a preliminary defined profile with unknown coefficients and the concept of penetration (boundary layer) well known from the heat diffusion and hydrodynamics. The profile satisfies the boundary conditions imposed at the boundary of the boundary layer that allows its coefficients to be expressed through the boundary layer depth as unique parameter describing the profile. The technique is demonstrated by a solution of a time fractional radial equation concerning anomalous diffusion from a central point source in a …
Transient Flow Of A Generalized Second Grade Fluid Due To A Constant Surface Shear Stress: An Approximate Integral-Balance Solution, Jordan Hristov
Transient Flow Of A Generalized Second Grade Fluid Due To A Constant Surface Shear Stress: An Approximate Integral-Balance Solution, Jordan Hristov
Jordan Hristov
Integral balance solution to start-up problem of a second grade viscoelastic fluid caused by a constant surface stress at the surface has been developed by an entire-domain parabolic profile with an unspecified exponent. The closed form solution explicitly defines two dimensionless similarity variables ξ = y ν t and 2 D0 p t= χ = ν β , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed, as well comparison with the existing …