Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid

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 (the main solution and example 1) and the dimensionless version showing various sides of the flow field and how the dimensionless groups control it: mainly the effect of the Deborah number. Numerical simulations demonstrating the effect of the various operating parameter and fluid properties on the developed flow filed have been performed.Comment: 19 pages, 6 figures; in press Thermal Science, volume 16, 2012, issue

Practical Data Correlation of Flashpoints of Binary Mixtures by a Reciprocal Function: The Concept and Numerical Examples

Simple data correlation of flashpoint data of binary mixture has been developed on a basic of rational reciprocal function. The new approximation requires has only two coefficients and needs the flashpoint temperature of the pure flammable component to be known. The approximation has been tested by literature data concerning aqueous-alcohol solution and compared to calculations performed by several thermodynamic models predicting flashpoint temperatures. The suggested approximation provides accuracy comparable and to some extent better than that of the thermodynamic methods.Comment: 6 pages and 5 tables IN PRESS; Thermal Science vol. 15, issue 3, 201

The heat-balance integral method by a parabolic profile with unspecified exponent: Analysis and Benchmark Exercises

The heat-balance integral method of Goodman has been thoroughly analyzed in the case of a parabolic profile with unspecified exponent depending on the boundary condition imposed. That the classical Good man's boundary conditions defining the time-dependent coefficients of the prescribed temperature profile do not work efficiently at the front of the thermal layers if the specific parabolic profile at issue is employed. Additional constraints based on physical assumption enhance the heat-balance integral method and form a robust algorithm defining the parabola exponent . The method has been compared by results provided by the Veinik's method that is by far different from the Good man's idea but also assume forma tion of thermal layer penetrating the heat body. The method has been demonstrated through detailed solutions of 4 1-D heat-conduction problems in Cartesian co-ordinates including a spherical problem (through change of vari ables) and over-specified boundary condition at the face of the thermal layer.Comment: 22 page

Thermal impedance estimations by semi-derivatives and semi-integrals: 1-D semi-infinite cases

Simple 1-D semi-infinite heat conduction problems enable to demonstrate the potential of the fractional calculus in determination of transient thermal impedances under various boundary conditions imposed at the interface (x=0). The approach is purely analytic and very effective because it uses only simple semi-derivatives (half-time) and semi-integrals and avoids development of entire domain solutions. 0x