A new analysis is made on the viscous dissipation within a microchannel parallel plate gap induced by an oscillating lower plate and a stationary upper plate, assuming a one-dimensional, incompressible, laminar, Newtonian flow with constant properties. Firstly, a new form of velocity solution is obtained, which consists of a main sinusoidal term and a block of time-dependent summation terms. This is shown to describe the same motion as the existing complex solutions, but has the advantage of, in the case of microchannel flow, describing the flow well by using the main term alone. This simplification enables a new analytical solution to be found for the temperature field in the microchannel flow, which has time-dependent characteristics, and is a function of the Prandtl number and the dimensionless parameter beta, which signifies the ratio of viscous diffusion to oscillation timescales. The existing classical solution has limitations, as it has only a time-averaged temperature solution, and also does not exhibit dependence on the Prandtl number. The existing solution lies within our solution domain only at the Prandtl number around unity, when graphical comparisons are made.

假设一个具有恒定特性的一维不可压缩层流牛顿流，对由振荡的下板和静止的上板引起的微通道平行板间隙内的粘性耗散进行了新的分析。首先，获得了一种新的速度解形式，它由一个主要的正弦项和一组与时间有关的求和项组成。它显示了与现有复杂解决方案相同的运动，但是在微通道流动的情况下，具有的优点是，仅使用主项就可以很好地描述流动。这种简化使得能够为微通道流中的温度场找到新的分析解决方案，该解决方案具有随时间变化的特征，并且是Prandtl数和无量纲参数beta的函数，它表示粘性扩散与振荡时标的比率。现有的经典解决方案具有局限性，因为它仅具有时间平均温度解决方案，并且也没有表现出对Prandtl数的依赖性。当进行图形比较时，现有解决方案仅在我们的解决方案域内的周围为Prandtl数。