In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The ev...In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10–10.展开更多
Periodic whole cross-section computation models are established for segmental baffle heat exchanger, shutter baffle heat exchanger, and trapezoid-like tilted baffle heat exchanger. The reliability of models is verifie...Periodic whole cross-section computation models are established for segmental baffle heat exchanger, shutter baffle heat exchanger, and trapezoid-like tilted baffle heat exchanger. The reliability of models is verified by comparing the simulated results to the results obtained from the Bell-Delaware method. Due to the orthogonal assembly of the baffles, the shell side fluid shows the twisty flow of trapezoid-like tilted baffle heat exchanger. The essential mechanism on disturbing flow and heat transfer enhancement is revealed by defining the non-dimensional factor η of the shell side fluid flow direction of heat exchanger and the field synergy principle. The results show that at the same Reynolds number, the shell side fluid convection heat transfer coefficient of trapezoid-like tilted baffle heat exchanger is 12.43%-24.33% and 6.71%-11.51% higher than those of segmental baffle heat exchanger and shutter baffle heat exchanger, respectively. The shell side fluid flow velocity field and the pressure gradient field of trapezoid-like tilted baffle heat exchanger and shutter baffle heat exchanger decreases compared with that of segmental baffle heat exchanger, so the shell side fluid flow resistance and pressure drop is increased; the shell side comprehensive performance of trapezoid-like tilted baffle heat exchanger is 5.85%-9.06% higher than that of segmental baffle heat exchanger, and 15.27%-23.28% higher than that of shutter baffle heat exchanger. In this study, a baffle structure with higher efficiency of the energy utilization for the heat exchanger is provided.展开更多
文摘In this paper the Black Scholes differential equation is transformed into a parabolic heat equation by appropriate change in variables. The transformed equation is semi-discretized by the Method of Lines (MOL). The evolving system of ordinary differential equations (ODEs) is integrated numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10–10.
基金financially supported by the National Natural Science Foundation of China (Grant No. 21776263, No. 51006092, No. 51776190, No. 51476147)the Henan Province Science and Technology Breakthrough Plan of China (Grant No. 182102310022)the Applied Research Plan of Key Scientific Research Projects of Henan Province Higher Education of China (Grant No. 18A470001, No. 17A530006)
文摘Periodic whole cross-section computation models are established for segmental baffle heat exchanger, shutter baffle heat exchanger, and trapezoid-like tilted baffle heat exchanger. The reliability of models is verified by comparing the simulated results to the results obtained from the Bell-Delaware method. Due to the orthogonal assembly of the baffles, the shell side fluid shows the twisty flow of trapezoid-like tilted baffle heat exchanger. The essential mechanism on disturbing flow and heat transfer enhancement is revealed by defining the non-dimensional factor η of the shell side fluid flow direction of heat exchanger and the field synergy principle. The results show that at the same Reynolds number, the shell side fluid convection heat transfer coefficient of trapezoid-like tilted baffle heat exchanger is 12.43%-24.33% and 6.71%-11.51% higher than those of segmental baffle heat exchanger and shutter baffle heat exchanger, respectively. The shell side fluid flow velocity field and the pressure gradient field of trapezoid-like tilted baffle heat exchanger and shutter baffle heat exchanger decreases compared with that of segmental baffle heat exchanger, so the shell side fluid flow resistance and pressure drop is increased; the shell side comprehensive performance of trapezoid-like tilted baffle heat exchanger is 5.85%-9.06% higher than that of segmental baffle heat exchanger, and 15.27%-23.28% higher than that of shutter baffle heat exchanger. In this study, a baffle structure with higher efficiency of the energy utilization for the heat exchanger is provided.
