Mathematical modelling for solving nonlinear heat diffusion problems of pavement spherical roads in Makkah

References

• Abd-El-Malek , M.B. and Helal , M.M. 2006 . Semi-analytical method for solving nonlinear heat diffusion problems in spherical medium . Journal of Computational and Applied Mathematics , 193 ( 1 ) : 10 – 21 .
   Web of Science ®Google Scholar
• Abdel-Hamid , B. and Frankel , J.I. An accurate approximation of heat diffusion problems in composite media . Al-Azhar Engineering Second International Conference . pp. 36 – 48 .
   Google Scholar
• Al-Abdulwahhab , H.I. and Ramadhan , R. 1995 . “ Manifestation of temperature variation of flexible and rigid pavements in Dhahran, Saudi Arabia ” . In The Fourth Saudi Engineering Conference Vol. 2 , King Abdul-Aziz University, Jeddah, Saudi Arabia
   Google Scholar
• Al-Abdulwahhab , H.I. , Fatani , M. , Dubabe , I. , Bubshait , A. and Noureldin , A.S. 1995 . “ Design and maintenance criteria for local asphalt concrete mixes ” . In The Fourth Saudi Engineering Conference Vol. 2 , King Abdul-Aziz University, Jeddah, Saudi Arabia
   Google Scholar
• Alawi, M.H., 2000. Design and performance of rut resistant asphaltic concrete mixtures, PhD Thesis, Leeds, Leeds University, UK
   Google Scholar
• Cotta , R.M. 1994 . “ The integral transform method in computational heat and fluid flow. Special Keynote Lecture ” . In Proceedings of the 10th International Heat Transfer Conference Vol. 1 , 43 – 60 . Brighton, UK, SK-3
   Google Scholar
• Cotta , R.M. and Mikhailov , M.D. 1993 . Integral transform method . Applied Mathematical Modelling , 17 ( 3 ) : 156 – 161 .
   Web of Science ®Google Scholar
• Davies , T.W. 1988 . Transient conduction in a sphere with counteracting radiative and convective heat transfer at the surface . Applied Mathematical Modeling , 12 : 429 – 433 .
   Web of Science ®Google Scholar
• Frankel , J.I. , Vick , B. and Ozisik , M.N. 1987 . General formulation and analysis of hyperbolic heat conduction in composite media . International Journal of Heat Mass Transfer , 30 ( 7 ) : 1293 – 1305 .
   Web of Science ®Google Scholar
• Harik , I.E. , Jianping , P. , Southgate , H. and Allen , D. 1994 . Temperature effect on rigid pavements . Journal of Transportation Engineering , 120 ( 1 ) : 127 – 143 .
   Web of Science ®Google Scholar
• Hofstra , A. and Klomp , A.J.G. 1972 . “ Permanent deformation of flexible pavements under simulated road traffic conditions ” . In Third International Conference on the Structural Design of Asphalt Pavement London
   Google Scholar
• Metrological & Environmental Protection Administration, Scientific Information & Documentation Centre, 2008. Surface Annual Climatological Report. Kingdom of Saudi Arabia
   Google Scholar
• Monteiro , E.R. , Macêdo , E.N. , Quaresma , N.N. and Cotta , R.M. 2009 . Integral transform solution for hyperbolic heat conduction in a finite slab . International Communications in Heat and Mass Transfer , 36 ( 4 ) : 297 – 303 .
   Web of Science ®Google Scholar
• Mulhholland , G.P. and Cobble , M.H. 1972 . Diffusion through composite media . International Journal of Heat Transfer , 15 : 147 – 160 .
   Web of Science ®Google Scholar
• Naveira , C.P. , Lachi , M. , Cotta , R.M. and Padet , J. 2007 . Integral transform solution of transient forced convection in external flow . International Communications in Heat and Mass Transfer , 34 ( 6 ) : 703 – 712 .
   Web of Science ®Google Scholar
• Salt , H. 1983 . Transient conduction in a two-dimensional composite slab-I. Theoretical development of temperature modes . Internationsl Journal of Heat Mass Transfer , 26 ( 11 ) : 1611 – 1616 .
   Web of Science ®Google Scholar
• Serfaty , R. and Cotta , R.M. 1990 . Integral transform solutions of diffusion problems with nonlinear equation coefficients . International Communications in Heat and Mass Transfer , 17 ( 6 ) : 851 – 864 .
   Web of Science ®Google Scholar
• Yoder , E.J. and Witzak , M.W. 1975 . Principles of pavement design , New York : John Wiley and Sons Inc .
   Google Scholar