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Articles 1 - 7 of 7
Full-Text Articles in Mechanical Engineering
An Exercise With The He’S Variation Iteration Method To A Fractional Bernoulli Equation Arising In A Transient Conduction With A Non-Linear Boundary Heat Flux, Jordan Hristov
Jordan Hristov
Surface temperature evolution of a body subjected to a nonlinear heat flux involving counteracting convection heating and radiation cooling has been solved by the variations iteration method (VIM) of He. The surface temperature equations comes as a combination of the time-fractional (half-time) subdiffusion model of the heat conduction and the boundary condition relating the temperature field gradient at the surface through the Riemann-Liouville fractional integral. The result of this equation is a Bernoulli-type ordinary fractional equation with a nonlinear term of 4th order. Two approaches in the identification of the general Lagrange multiplier and a consequent application of VIM have …
Integral-Balance Solution To The Stokes’ First Problem Of A Viscoelastic Generalized Second Grade Fluid, Jordan Hristov
Integral-Balance Solution To The Stokes’ First Problem Of A Viscoelastic Generalized Second Grade Fluid, Jordan Hristov
Jordan Hristov
Integral balance solution employing entire domain approximation and the penetration dept concept to the Stokes’ first problem of a viscoelastic generalized second grade fluid has been developed. The solution has been performed by a parabolic profile with an unspecified exponent allowing optimization through minimization of the norm over the domain of the penetration depth. The closed form solution explicitly defines two dimensionless similarity variables and , responsible for the viscous and the elastic responses of the fluid to the step jump at the boundary. The solution was developed with three forms of the governing equation through its two dimensional forms …
Thermal Impedance At The Interface Of Contacting Bodies: 1-D Example Solved By Semi-Derivatives, Jordan Hristov
Thermal Impedance At The Interface Of Contacting Bodies: 1-D Example Solved By Semi-Derivatives, Jordan Hristov
Jordan Hristov
Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances of two bodies with different initial temperatures contacting at the interface ( ) at . The approach is purely analytic and uses only semi-derivatives (half-time) and semi-integrals in the Riemann-Liouville sense. The example solved clearly reveals that the fractional calculus is more effective in calculation the thermal resistances than the entire domain solutions
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 …
A Short-Distance Integral-Balance Solution To A Strong Subdiffusion Equation: A Weak Power-Law Profile, Jordan Hristov
A Short-Distance Integral-Balance Solution To A Strong Subdiffusion Equation: A Weak Power-Law Profile, Jordan Hristov
Jordan Hristov
The work presents an integral solution of the time-fractional subdiffusion through a preliminary defined profile with unknown coefficients and the concept of penetration layer well known from the heat diffusion The profile satisfies the boundary conditions imposed at the boundary of the boundary layer in a weak form 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 subdiffusion equation in rectilinear 1-D conditions.
Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov
Heat-Balance Integral To Fractional (Half-Time) Heat Diffusion Sub-Model, Jordan Hristov
Jordan Hristov
The fractional (half-time) sub-model of the heat diffusion equation, known as Dirac-like evolution diffusion equation has been solved by the heat-balance integral method and a parabolic pro file with unspecified exponent. The fractional heat-balance integral method has been tested with two classic examples: fixed temperature and fixed flux at the boundary. The heat-balance technique allows easily the convolution integral of the fractional half-time derivative to be solved as a convolution of the time-independent approximating function. The fractional sub-model provides an artificial boundary condition at the boundary that closes the set of the equations required to express all parameters of the …