Bilinearization Approach for Diffusion Problems Involving the Calculation of Dissipative Fields

REFERENCES

• D. A. Nield and A. Bejan , Convection in Porous Media, , 3rd ed. , Springer-Verlag, New York , 2006 .
   Google Scholar
• D. K. Cheng , Field and Wave Electromagnetics , Addison-Wesley , Reading , MA , 1989 .
   Google Scholar
• J. S. Gulliver , Introduction to Chemical Transport in the Environment , Cambridge University Press, New York , 2007 .
   Google Scholar
• M. D. Greenberg , Advanced Engineering Mathematics, , 2nd ed., Prentice Hall, Upper Saddle River, NJ , 1998.
   Google Scholar
• C.-H. Huang and C.-Y. Yeh , An Optimal Control Algorithm for Entrance Concurrent Flow Problems , Int. J. Heat Mass Transfer , vol. 46 , pp. 1013 – 1027 , 2003 .
   Web of Science ®Google Scholar
• C.-H. Huang , A Nonlinear Optimal Control Problem in Determining the Strength of the Optimal Boundary Heat Fluxes , Numer. Heat Transfer B , vol. 40 , pp. 411 – 429 , 2001 .
   Web of Science ®Google Scholar
• L. Dedè , Optimal Flow Control for Navier–Stokes Equations: Drag Minimization , Int. J. Numer. Meth. Fluids , vol. 55 , pp. 347 – 366 , 2007 .
   Web of Science ®Google Scholar
• A. Kunoth , Adaptive Wavelet Schemes for an Elliptic Control Problem with Dirichlet Boundary Control , Numer. Algorithms , vol. 39 , pp. 199 – 220 , 2005 .
   Web of Science ®Google Scholar
• H.-C. Lee , Analysis and Computational Methods of Dirichlet Boundary Optimal Control Problems for 2D Boussinesq Equations , Adv. Comput. Math. , vol. 19 , pp. 255 – 275 , 2003 .
   Web of Science ®Google Scholar
• G. Bärwolfe , Boundary Control of a Boussinesq Equation for a Crystal Growth Problem: Aspects of Numerical Solution , Int. J. Comput. Math. , vol. 85 , pp. 329 – 343 , 2008 .
   Web of Science ®Google Scholar
• N. Zabaras , Y. Ruan , and O. Richmond , Design of Two-Dimensional Stefan Processes with Desired Freezing Front Motions , Numer. Heat Transfer B , vol. 21 , pp. 307 – 325 , 1992 .
   Web of Science ®Google Scholar
• M. N. Ozisik and H. R. B. Orlande , Inverse Heat Transfer , Taylor & Francis, New York , 2000 .
   Google Scholar
• E. Katamine , H. Azegami , T. Tsubata , and S. Itoh , Solution to Shape Optimization Problems of Viscous Flow Fields , Int. J. Comput. Fluid Dynam. , vol. 19 , pp. 45 – 51 , 2005 .
   Web of Science ®Google Scholar
• E. B. Ratts and A. G. Raut , Entropy Generation Minimization of Fully Developed Internal Flow with Constant Heat Flux , ASME J. Heat Transfer , vol. 126 , pp. 656 – 659 , 2004 .
   Web of Science ®Google Scholar
• E. Magyari , I. Pop , and B. Keller , Effect of Viscous Dissipation on the Darcy Forced-Convection Flow Past a Plane Surface , J. Porous Media , vol. 6 , pp. 111 – 122 , 2003 .
   Web of Science ®Google Scholar
• T. Moulton and G. K. Ananthasuresh , Micromechanical Devices with Embedded Electro-Thermal-Compliant Actuation , Sensors and Actuators A , vol. 90 , pp. 38 – 48 , 2001 .
   Web of Science ®Google Scholar
• A. Bejan , Entropy Generation Minimization , CRC Press, Boca Raton, FL , 1996 .
   Google Scholar
• F. Strub , J. Castaing-Lasvignottes , M. Strub , M. Pons , and F. Monchoux , Second Law Analysis of Periodic Heat Conduction Through a Wall , Int. J. Thermal Sci. , vol. 44 , pp. 1154 – 1160 , 2005 .
   Web of Science ®Google Scholar
• O. Bautista , F. Méndez , and J. L. Martinez-Meyer , (Bejan's) Early vs. Late Regimes Method Applied to Entropy Generation in One-Dimensional Conduction , Int. J. Thermal Sci. , vol. 44 , pp. 570 – 576 , 2005 .
   Web of Science ®Google Scholar
• Z. Kolenda , J. Donizak , and J. Hubert , On the Minimum Entropy Production in Steady State Heat Conduction Processes , Energy , vol. 29 , pp. 2441 – 2460 , 2004 .
   Web of Science ®Google Scholar
• A. Bejan , Advanced Engineering Thermodynamics, , 3rd ed. , Wiley , New York , 2006 .
   Google Scholar
• S. V. Patankar , Numerical Heat Transfer and Fluid Flow , Taylor & Francis, Washington, DC , 1980 .
   Google Scholar
• J. Strikwerda , Finite Difference Schemes and Partial Differential Equations , Society for Industrial and Applied Mathematics , Philadelphia , 2004 .
   Google Scholar
• J. N. Reddy , An Introduction to the Finite Element Method, , 3rd ed. , McGraw-Hill , New York , 2006 .
   Google Scholar
• O. T. O'Meara , Introduction to Quadratic Forms , Springer-Verlag, New York , 1971 .
   Google Scholar
• M. Tye-Gingras and L. Gosselin , Thermal Resistance Minimization for a Fin-and-Porous Medium Heat Sink with Evolutionary Algorithms , Num. Heat Transfer A , vol. 54 , pp. 349 – 366 , 2008 .
   Web of Science ®Google Scholar
• K. Kalli , H. L. Dobb , D. Webb , K. Caroll , C. Themistos , M. Komodromos , G.-D. Peng , Q. Fang , and I. W. Boyd , Development of an Electrically Tuneable Bragg Grating Filter in Polymer Optical Fibre Operating at 1.55 µm, Measurement Sci. Technol. , vol. 18, pp. 3155–3164, 2007.
   Web of Science ®Google Scholar
• I. Wyzkiewicz , I. Grabowska , M. Chudy , Z. Brzozka , M. Jakubowska , T. M. Wisniewski , T. Wisniewski , and A. Dybko , Self-regulating Heater for Microfluidic Reactors , Sensors and Actuators B , vol. 114 , pp. 893 – 896 , 2006 .
   Web of Science ®Google Scholar
• Matlab Optimization Toolbox User's Guide , Version 3 , The MathWorks Inc. , Natick , MA , 2004 .
   Google Scholar
• F. Mathieu-Potvin and L. Gosselin , Méthodes numériques évolutionnaire pour l'optimisation topologique en transfert thermique (in French) , Proc. 8ième Colloque Interuniversitaire Franco-Québécois , Montréal , Québec , Canada , 2007 , pp. 415 – 420 .
   Google Scholar
• M. N. Ozoik , Heat Conduction, , 2nd ed. , Wiley , New York , 1993 .
   Google Scholar