Seeking proper and reasonable constitutive relations to study the characteristics of flow and heat transfer of viscoelastic fluid is a hot topic in recent years. In this work, a new distributed order time fractional constitution model is put forward to analyse the unsteady natural convection boundary layer flow and heat transfer, in which the magnetic field effect is considered. The mid-point quadrature method is applied to approach the distributed order integrals and the L1-formula is employed to discrete the time fractional derivatives. The influences of different involved parameters on the velocity and temperature distributions and the comparisons of the distributions with different constitution models are presented by graphical illustrations and discussed in detail.

寻求合适，合理的本构关系来研究粘弹性流体的流动和传热特性是近年来的热门话题。提出了一种新的分布阶次时间分数构成模型，对非自然对流边界层的流动和传热进行了分析，并考虑了磁场的影响。采用中点正交方法逼近分布阶积分，并采用L1公式离散时间分数导数。通过图示说明并详细讨论了涉及的不同参数对速度和温度分布的影响，以及不同构造模型的分布比较。