Effects of viscous disspation and fluid axial heat conduction on entrance-region heat transfer in parallel plates : Part I : The thermal boundary condition of the first kind

Consideration is given to the effects of viscous dissipation and fluid axial heat conduction on the heat transfer in the thermal entrance region of a laminar plane Couette-Poiseuille flow. The temperature distribution of the fluid for -∞<z<∞ is determined by solving the energy equation including the viscous dissipation term and the fluid axial heat conduction term subject to the constant wall temperature boundary condition. The results indicate that viscous heating has a strong effect where velocity gradient is large and, because of the heat conducted upstream, transverse variation in fluid temperature exists in the region z≤0 and the temperature profile at z=0 is greatly affected by fluid axial heat conduction. The effects of relative velocity, Brinkman number and Peclet number on developing temperature distribution and Nusselt number at the walls are discussed