THERMAL SCIENCE
International Scientific Journal
FROM THE GUEST EDITOR OF PART ONE: FRACTIONAL CALCULUS TO HEAT, MOMENTUM, AND MASS TRANSFER PROBLEMS
ABSTRACT
Fractional Calculus is a hot topic encompassing a broad list of problems such new analytical and, numerical technique, efficient solution of complex problems in modelling of transient heat and flow problems. In contrast to the well-known integer counterparts, the fractional derivatives and integrals are not local [1-3] widely encountered in applications to transient rheology [4, 5], heat [6, 7] and mass transfer [8, 9], non-linear diffusion in porous and granular media [10], Stefan problem [11-13] manifest this technique as a power tool for efficient engineering solutions of complex problems.
THERMAL SCIENCE YEAR
2012, VOLUME
16, ISSUE
Issue 2, PAGES [7 - 9]
- Oldham , K. B. , Spanier, J., The Fractional Calculus , Academic Press, New York, USA, 1974
- Babenko, Yu. I., Heat-Mass Transfer, Methods for Calculation of Thermal and Diffusional Fluxes (in Russian), Khimia Publ., Moscow, 1984
- Debnath, L., Nonlinear Partial Differential Equations for Scientist and Engineers, Birkhouser, Boston, USA, 1997
- Siddique, I., Vieru, D., Stokes Flows of a Newtonian Fluid with Fractional Derivatives and Slip at the Wall, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 822- 826
- Qi, H., Xu, M., Some Unsteady Unidirectional Flows of a Generalized Oldroyd-B Fluid with Fractional Derivative, Appl. Math. Model., 33 (2009), 11, pp. 4184-4191
- Agrawal, O. P., Application of Fractional Derivatives in Thermal Analysis of Disk Brakes, Nonlinear Dynamics , 38 (2004), 1-4, pp. 191-206
- Kulish , V. V., Lage, J. L. , Fractional-Diffusion Solutions for Transient Local Temperature and Heat Flux, J. Heat Transfer, 122 (2000), 2, pp. 372-376
- dos Santos, M. C, et al., Development of Heavy Metal Sorption Isotherm Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 814-817
- Hristov J., Starting Radial Subdiffusion from a Central Point through a Diverging Medium (a Sphere): Heat-Balance Integral Method, Thermal Science, 15 (2011), Suppl. 1, pp. S5-S20
- Pfaffenzeller, R. A., Lenzi, M. K., Lenzi, E. K., Modeling of Granular Material Mixing Using Fractional Calculus, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 818-821
- Meilanov, R. P., Shabanova, M. R. , Akhmedov, E. N., A Research Note on a Solution of Stefan Problem with Fractional Time and Space Derivatives, Int. Rev. Chem. Eng., 3 (2011), 6, pp. 810-813
- Voller, V. R. , An Exact Solution of a Limit Case Stefan Problem Governed by a Fractional Diffusion Equation, Int. J. Heat Mass Transfer, 53 (2010), 23-24, pp. 5622-5625
- Liu, J., Xu, M., Some Exact Solutions to Stefan Problems with Fractional Differential Equations, J. Math. Anal. Appl., 351 (2010), 2, pp. 536-542
- He, J.-H, Li, Z. B., Converting Fractional Differential Equations into Partial Differential Equations, Thermal Science, 16 (2012), 2, pp. 331-334
- Li, Z.-B.,He, J.-H, Zhu, W.-H., Exact Solutions of Time-Fractional Heat Conduction Equation by the Fractional Complex Transform, Thermal Science, 16 (2012), 2, pp. 335-338
- Wang, Q.-L., He, J.-H, Li, Z.-B., Fractional Model for Heat Conduction in Polar Bear Hairs, Thermal Science, 16 (2012), 2, pp. 339-342
- Siddique, I., Vieru, D., Exact Solutions for Rotational Flow of a Fractional Maxwell Fluid in a Circular Cylinder, Thermal Science, 16 (2012), 2, pp. 345-355
- Mahmood, A., On Analytical Study of Factional Oldroyd-B Flow in Annular Region of Two Torsionally Oscillating Cylinders, Thermal Science, 16 (2012), 2, pp. 411-421
- Hristov, J., Integral-Balance Solution to the Stokes' First Problem of a Viscoelastic Generalized Second Grade Fluid, Thermal Science, 16 (2012), 2, pp. 395-410
- Proti},M. Z., et al., Application of Fractional Calculus in Ground Heat Flux Estimation, Thermal Science, 16 (2012), 2, pp. 373-384 From the Guest Editor of Part One THERMAL SCIENCE: Year 2012, Vol. 16, No. 2, pp. VII-IX IX
- Hristov, J., Thermal Impedance at the Interface of Contacting Bodies: 1-D Examples Solved by Semi-Derivatives, Thermal Science, 16 (2012), 2, pp. 623-627
- Beibalaev, V. D., Meilanov, R. P., The Dirihlet Problem for the Fractional Poisson's Equation with Caputo Derivatives: A Finite Difference Approximation and a Numerical Solution, Thermal Science, 16 (2012), 2, pp. 385-394
- Guo, P., Li, C., Zeng, F., Numerical Simulation of the Fractional Langevin Equation, Thermal Science, 16 (2012), 2, pp. 357-363
- Chen, A., Guo, P., Li, C., Numerical Algorithm Based on Fast Convolution for Fractional Calculus, Thermal Science, 16 (2012), 2, pp. 365-371
- Wu, L.-Y. He. J.-H., Explosion-Proof Textile with Hierarchical Steiner Tree Structure, Thermal Science, 16 (2012), 2, pp. 343-344
- Lorenzo, C. F., Hartley, T. T., Generalized Functions for the Fractional Calculus, NASA/TP- 1999-209424/Revl, 1999