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Purpose - The purpose of this paper is to present an approach capable of solving Burgers' equation. Diagonal Padé approximation with a factorization scheme is applied to find numerical solutions of the one-dimensional Burgers' equation by presenting explicit factoring the polynomials of the approximation. The numerical results obtained by this approach, for various values of viscosity, have been compared with the exact solution and are found to be in good agreement with each other. Design/methodology/approach - In this paper, factorized diagonal Padé approach is applied to solve Burgers' equation. In this method, Burgers' equation is reduced to a system of ordinary differential equations and is solved piecewise analytically to obtain the solution of the problem. Findings - The results of proposed approach show that when the obtained results are compared to similar methods, this approach gives better accuracy. Also, the graphs with small ? values satisfy the physical properties of the problem; therefore, the approach is promising for nonlinear problems. Research limitations/implications - The authors' experiments show that the applied method worked fine with Burgers' equation and they hope to extend it to some other nonlinear problems. Practical implications - The proposed method is easy to implement and the given algorithm is easy to use, even for non experts. The approach is flexible to use high order Padé approximants. Originality/value - In the approach described in the paper, Padé approximation is calculated in a different manner than the classical approach. [ABSTRACT FROM AUTHOR]

Purpose - The purpose of this paper is to show how, with a view to the shortcomings of traditional optimization methods, a multi-objective optimization concerning the structure sizes of micro-channel heat sink is performed by adaptive genetic algorithm. The optimized micro-channel heat sink is simulated by computational fluid dynamics (CFD) method, and the total thermal resistance is calculated to compare with that of thermal resistance network model. Design/methodology/approach - Taking the thermal resistance and the pressure drop as goal functions, a multi-objective optimization model was proposed for the micro-channel cooling heat sink based on the thermal resistance network model. The coupled solution of the flow and heat transfer is considered in the optimization process, and the aim of the procedure is to find the geometry most favorable to simultaneously maximize heat transfer while obtaining a minimum pressure drop. The optimized micro-channel heat sink was numerically simulated by CFD software. Findings - The results of optimization show that the base convection thermal resistance contributes to maximum the total thermal resistance, and base conduction thermal resistance contributes to least. The width of optimized micro-channel and fin are 197 and 50?µm, respectively, and the corresponding total thermal resistance of the whole micro-channel heat sink is 0.838?K/W, which agrees well with the analysis result of thermal resistance network model. Research limitations/implications - The convection heat transfer coefficient is calculated approximately here for convenience, and that may induce some errors. Originality/value - The maximum difference in temperature of the optimized micro-channel cooling heat sink is 84.706?K, which may satisfy the requirement for removal of high heat flux in new-generation chips. The numerical simulation results are also presented, and the results of numerical simulation show that the optimized micro-channel heat sink can enhance thermal transfer performance. [ABSTRACT FROM AUTHOR]