In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}...In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.展开更多
One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger net...One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object,while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional.展开更多
文摘In this paper, we study the nonexistence of solutions of the following time fractional nonlinear Schr?dinger equations with nonlinear memory where 0, ιλ denotes the principal value of ιλ, p>1, T>0, λ∈C/{0}, u(t,x) is a complex-value function, denotes left Riemann-Liouville fractional integrals of order 1-λ and is the Caputo fractional derivative of order . We obtain that the problem admits no global weak solution when and under different conditions for initial data.
基金supported by the Scientific and Technological Research Program of Chongqing Municipal Education Commission(Grant No.KJ1710251)
文摘One-stream heat exchangers and one-stream heat exchanger networks are widely used in engineering. In this paper, the heat transfer performance evaluation of one-stream heat exchangers and one-stream heat exchanger networks is analyzed with the concepts of entropy generation rate, entropy generation number, revised entropy generation number, entropy resistance, entransy dissipation rate, entransy dissipation number and generalized thermal resistance. For the analyzed one-stream heat exchangers, our numerical results show that the extremum value of the entransy dissipation rate and the minimum values of the entropy resistance and the generalized thermal resistance always lead to the largest heat transfer rate or the lowest temperature of the cooled object,while the minimum values of the other parameters do not always. For the analyzed one-stream heat exchanger networks, the minimizations of entransy dissipation rate, entransy dissipation number and generalized thermal resistance always correspond to the lowest average temperature of the cooled objects, while the minimizations of the other parameters do not. Therefore, only the extremum entransy dissipation principle and the minimum generalized thermal resistance principle are always applicable for the heat transfer performance evaluation of the systems in this paper, while the applicability of the other parameters is conditional.
