Similarity solutions for a moving-flat plate thermal boundary layer

In this paper, the thermal boundary-layer problem of a semi-infinite flat plate moving in a constant velocity free stream is studied. The similarity equations with viscous dissipation for the thermal boundary-layer are derived and solved by numerical techniques. Under some specific conditions, the thermal boundary-layer similarity equation can be integrated analytically. The results are analyzed for very small Eckert number case and large Eckert number case. It is found that, for the two cases, wall heat fluxes will increase with the increase of the velocity ratio . With increasing Eckert number, the viscous dissipation heating will become dominant. However, for the Prandtl number when the Eckert number is small, it is found that wall heat fluxes will increase with increasing Prandtl number only for a certain range of velocity ratio . For the other range, the wall heat fluxes will have a maximum at a certain Prandtl number, and, when the Prandtl number is larger than the critical value, wall heat fluxes will decrease with increasing Prandtl number. Some examples of the lower solution branch are also presented to compare with the upper solution branch. It is found that the lower solution branch will result in lower heat fluxes at the wall.