Thermal radiation effects on heat and mass transfer over an unsteady stretching surface.(Research Article)(Report)

1. Introduction

The continuous surface heat and mass transfer problem has many practical applications in industrial manufacturing processes. The knowledge of flow and heat and mass transfer within a thin liquid film is crucial in understanding the coating process and design of heat exchangers and chemical processing equipments. This phenomenon is also applied in wire and fibre coatings, food stuff processing reactor fluidization, and transpiration cooling. The prime aim in almost every extrusion is to maintain the surface quality of the extrudate. The problem of extrusion of thin surface layers needs special attention to gain some knowledge for controlling the coating efficiently. In the pioneering work of Crane [1], the flow of Newtonian fluid over a linearly stretching surface was studied. Subsequently, the pioneering works of Crane are extended by many authors to explore various aspects of the flow and heat transfer occurring in an infinite domain of the fluid surrounding the stretching sheet (see [2-8]). However, these studies dealt with a steady flow only. In some cases the flow field and heat transfer can be unsteady due to a sudden stretching of the flat sheet or by a steep change of the temperature of the sheet.

Hossain et al. [9] determined the effect of radiation on natural convection flow of an optically thick viscous incompressible flow past a heated vertical porous plate with a uniform surface temperature and a uniform rate of suction where radiation is included by assuming the Rosseland discussion approximation.

Andersson et al. [10] investigated using a similarity transformation the flow of a thin liquid film of a power-law fluid by unsteady stretching of a surface. Later on, Andersson et al. [11] analyzed the momentum and heat transfer in a laminar liquid film on a horizontal stretching sheet governed by time-dependent boundary layer equations. Dandapat et al. [ 12] explored how the hydrodynamics and heat transfer in a liquid film on unsteady stretching surface are affected by thermo-capillarity. Tsai et al. [13] studied the non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity.

Liu and Andersson [14] generalized the analysis by Andersson et al. [11] of the thermal characteristics of a liquid film driven by an unsteady stretching surface. Here, they considered a more general form of the prescribed temperature variation of the stretching sheet than that considered in Andersson et al. [ 11] .

Elbashbeshy and Bazid [15] presented similarity solutions of the boundary layer equations, which describe the unsteady flow and heat transfer over an unsteady stretching sheet. However, as was to be later discovered by Abd El-Aziz [16], some physically unrealistic phenomena are encountered for specific values of the unsteadiness parameter. To that end, Abd El-Aziz [16] was concerned with correcting the similarity transformation introduced by Elbashbeshy and Bazid [15] and extended their analysis to include the effect of thermal radiation. Thermal radiation plays a very significant role in controlling heat transfer in polymer processing industry. The quality of the final product depends to a great extend on the heat controlling factors, and the knowledge of radiative heat transfer in the system can perhaps lead to a desired product with sought qualities.

In this paper, we extend the work of Abd El-Aziz [16] to include mass transfer. This problem arises in a number of industrial manufacturing processes such as polymer extrusion, wire drawing, metal and plastic extrusion, continuous casting, glass fibre production, crystal growing and paper production. The physical and thermal characteristics of such unsteady process are investigated in the boundary layer approximation, assuming variation of the surface temperature and concentration with the horizontal coordinate x and time, t. The main …