THERMAL SCIENCE
International Scientific Journal
SEMI-DERIVATIVE INTEGRAL METHOD TO TRANSIENT HEAT CONDUCTION TIME-DEPENDENT HEAT FLUX BOUNDARY CONDITIONS
ABSTRACT
Transient heat conduction in semi-infinite medium with a time dependent heat flux as boundary condition has been solved by a semi-derivative integral-balance method. Two versions boundary fluxes have been considered: power-law and exponential.
KEYWORDS
PAPER SUBMITTED: 2021-05-20
PAPER REVISED: 2021-06-05
PAPER ACCEPTED: 2021-06-11
PUBLISHED ONLINE: 2021-12-18
- Goodman, T. R, The Heat Balance Integral and Its Application to Problems Involving a Change of Phase, Transactions of ASME, 80 (1958), 1-2, pp. 335-342
- Hristov, J., The Heat-Balance Integral Method by a Parabolic Profile with Unspecified Exponent: Analysis and Benchmark Exercises, Thermal Science, 13 (2009), 2, pp. 27-48
- Mitchel, S. L.,Myers, T. G., Improving the Accuracy of Heat Balance Integral Method Applied to thermal Problems with Time Dependent Boundary Conditions, Int. J. Heat Mass Transfer, 52 (2010), 17-18, pp. 3540-3551
- Hristov, J., An Alternative Integral-Balance Solution to Transient Diffusion of Heat (Mass) by time-Fractional Semiderivatives and Semiintegrals: Fixed boundary conditions, Thermal Science, 20 (2016), 6, pp. 1867-1878
- Hristov, J., Semi-derivative Integral Method (SDIM) to Transient Heat Conduction: Time-Dependent (Power-Law) Temperature Boundary Conditions, Thermal Science, 25 (2021), 5A, pp. 3557-3568
- Oldham, K. B., Spanier, J., The fractional Calculus, Academic Press, New York, USA, 1974
- Carslaw, H. S.,Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, London, UK, 1959
- Zubair, S. M., Chaudry, M. A., Heat Conduction in a Semi-Infinite Solid Subject to Time-Dependent Surface Heat Fluxes: An Analytical Study, Warme un Stoffubertragung, 28 (1993), 6, pp. 357-364
- Sahin, A., Analytical Solutions of Transient Heat Conduction in Semi-Infinite Solid with Time Varying Boundary Conditions by Means of Similarity Transformation, Int. Comm. Heat Mass Transfer, 22 (1995), 1, pp. 89-97
- Hristov, J., Double Integral-Balance Method to the Fractional Subdiffusion Equation: Approximate Solutions, Optimization Problems to be Resolved and Numerical Simulations, J. Vibration and Control, 23 (2017), 7, pp. 2795-2818