Mathematical Modeling of Heat-Transfer for a Moving Sheet in a Moving Fluid


1 Department of Mathematics, Faculty of Science and Humanity Studies, Salman Bin AbdulAziz University, P. O. Box 83, Alkharj11942, KSA.

2 Department of Basic Engineering Science, College of Engineering, Menoufia University, Shebin El-Kom, Egypt.


A mathematical model was developed for determining the heat transfer between a moving sheet that passes through a moving fluid environment to simulate the fabrication process of sheet and fiber-like materials. Similarity transformations were introduced to reduce the governing equations to two nonlinear ordinary differential equations. For high values Prandtl number, the energy equation became much stiffer or singularly perturbed and the standard numerical methods failed to handle it. An innovative procedure combining shooting and singular perturbation technique was developed. The results show that the heat transfer depends on the relative velocity between the moving fluid and the moving sheet to a certain value after that value the relative velocity has no effect. If blowing effect is found the thermal layer becomes thinner and temperature profiles are backed together.