Abstract

In the current study, using both linear and exponential forms of the Simplified Phan-Thien--Tanner constitutive equation (SPTT) for simulation of the polymeric stress tensor, exact analytical solutions for flow, temperature distributions and heat transfer of viscoelastic fluids passing through micro-scale channels, i.e. incorporating the effect of slip, are derived. The problem is solved with a constant heat flux at the. To analyze the effects of velocity slip in the vicinity of the wall region, a slip coefficient parameter is used to illustrate the important roles of slip phenomena on the enhancement of flow rate and consequently heat transfer of viscoelastic fluids in micro-scale geometries. In order to analyze the effect of mechanical energy in heating and cooling scenarios, results for both positive and negative values of the dimensionless Brinkman Number cases are obtained and investigated in detail. To study separately the contributions from entropy and the (internal) energy elasticity of mechanical energy in the heat transfer analysis of viscoelastic fluids a dimensionless parameter is employed. It is shown that this parameter can significantly influence the heat transfer modeling and neglect these parts of the energy equation can cause a considerable deviation.

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