An improved analytical solution on viscous dissipation effect in extended Stokes' second problem in microchannel with isothermal boundaries.

In this analytical study, the fluid motion within a microchannel is induced by the oscillation of one surface parallel to the other stationary surface, termed the extended Stokes' problem. The novelty and research gap are acquiring the thermal effect of such motion due to the viscous dissipation or fluid friction, subject to symmetric isothermal boundary conditions. The study may shed light on the role of viscous dissipation in temperature rise in the synovial fluid of an artificial hip joint, or in the fluid layer of a mechanical bearing. The full exact analytical temperature field, until now, has been unsolved, as it involves unsteady flow with manipulation of a complicated velocity field. The assumptions in the model are one-dimensional, incompressible, laminar, Newtonian flow with constant properties in a microchannel. Through the methodology of partial differential equation analysis, the temperature field is obtained in terms of Brinkman number, Prandtl number and a dimensionless angular frequency, and results are verified with a reported numerical solution, for specified range of the variables. Results complement recent approximate solutions which are valid only for the limited condition of the dimensionless angular frequency being less than or equal to unity, whereby suggesting a new Stokes number.