Analysis of heat transfer in n-immiscible layers of a horizontal Jeffrey fluid film flow

Abstract

This paper deals with theoretical analysis of heat transfer in n-immiscible layers of a horizontal Jeffrey fluid film, driven by a heated plate and surface tension gradient. The formulation of the horizontal n-immiscible layers is based on mass, momentum, and energy conservation laws. The resulting systems of coupled linear ordinary differential equations are solved to obtain exact solutions for velocity, temperature, volume flow rate, shear stress, and rate of heat transfer. The effects of flow control parameters of interest, such as the inverse capillary number C, thermal conductivity of fluid χ, and Brinkmann number Br, on the velocity and temperature of the 5-immiscible layers, are investigated through graphical analysis. It is observed that increasing C leads to an increase in the velocity of all 5-immiscible layers. The temperature of all 5-immiscible layers also rises with increasing values of C, χ, and Br. The analysis of these 5-immiscible layers provides significant knowledge and understanding that may be applied to systems with a higher or lower number of immiscible layers utilizing the expressions derived for n-immiscible layers of a fluid film. Moreover, a comparison between immiscible layers of Newtonian fluid and Jeffrey fluid films is made in terms of velocity and temperature.

Keywords

• Heat transfer
• n-immiscible layers
• Thin film flow
• Jeffrey fluid
• Exact analytic solutions