Secondary flow in non-isothermal viscoelastic parallel-plate flow

The non-isothermal, parallel-plate flow of a viscoelastic fluid is investigated. Using the singular perturbation method the problem for the stream function X is reduced to a non-homogeneous boundary-value problem for the biharmonic operator in an infinite strip. An exact solution is then obtained using Fourier integral transforms. Our analysis shows the existence of thermally induced recirculating eddies, even when inertia is neglected.