【摘要】 基于里兹不稳定温度场泛函,应用变分法求泛函极值,首次获得了中厚板轧后冷却正规阶段温度场的变分解,该解为抛物线型分布.该解与分离变量法获得的解析解及有限差分解比较表明,该解对分离变量法获得的解析解及有限差分解具有较高的逼近程度,误差均不超过6℃.同时推导出了平均温度,平均冷却速率,平均温度出现位置,心表温差以及冷却到容许误差所需要时间的解析式.最后通过实例证明了所获变分解的可靠性.更多还原

【Abstract】 Based on Ritz transient temperature field functional, the variational solution of temperature field for the plate after rolling during fully developed regime was first obtained by variational method.Its distribution was a parabola.The comparison between the variational results and those analytical results by the separation variable method as well as the numerical results by finite difference method showed that the results obtained by variational method have higher forecast precision with the analytical and numerical results,and the maximum error among them is less than 6 ℃.Besides,the expressions of the average temperature,average cooling rate,occurrence location of the average temperature,the temperature difference between plate surface and centre along thick direction,and the time required for cooling to a certain margin of error are also given.A test proves the reliability of variational function.更多还原