Two new analytical temperature solutions are reported on the viscous dissipation effect in a microchannel flow driven by an oscillating lower plate, an extension of Stokes's second problem. The methodology is solving the momentum and energy equations analytically, assuming Newtonian, one-dimensional, incompressible, laminar with constant properties. Although the velocity solution had long been obtained, only a time-averaged temperature solution had been available, until recently; when two full time-dependent temperature solutions were reported, for two symmetric temperature boundary conditions. The present work extends further with two more full solutions on asymmetric thermal conditions, namely, insulated on one oscillatory plate and isothermal on the other stationary plate, and vice-versa. Comparisons are also made with the previous two cases, and all four solutions are validated with numerical solutions. This fundamental study may have application to such a situation as the synovial flow in artificial hip-joints.

两个新的分析温度解决方案报告了由振荡下板驱动的微通道流动中的粘性耗散效应，这是斯托克斯第二个问题的扩展。该方法通过分析求解动量和能量方程，假设牛顿、一维、不可压缩、具有恒定特性的层流。虽然速度解早已得到，但直到最近才获得时间平均温度解。当报告两个完全时间相关的温度解时，对于两个对称的温度边界条件。目前的工作进一步扩展了关于不对称热条件的两个更完整的解决方案，即在一个振荡板上绝缘，在另一个固定板上等温，反之亦然。还与前两种情况进行了比较，所有四种解决方案都通过数值解决方案进行了验证。这项基础研究可能适用于人工髋关节滑液流等情况。