JP Journal of Heat and Mass Transfer
Volume 20, Issue 2, Pages 169 - 178
(August 2020) http://dx.doi.org/10.17654/HM020020169 |
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NONISOTHERMAL DISSIPATIVE FLOW OF VISCOUS CHEMICALLY REACTING FLUID IN A POROUS CHANNEL
A. V. Baranov
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Abstract: Mathematical model of nonisothermal flow of viscous Newtonian fluid in a flat porous channel is presented. Many assumptions were made on the basis of the fact that the flow occurs at low values of the Reynolds number and at a high Peclet number. The Brinkman equation is used as a motion equation. The flow is accompanied by a chemical reaction that leads to a sharp increase in viscosity. The viscosity is considered to depend on the temperature and the degree of conversion. This, in turn, led to the inclusion of the kinetic equation of a chemical reaction in the mathematical model. It is believed that a chemical reaction takes place in one stage and can be described using a single parameter - the degree of conversion. When a certain critical degree of conversion is reached, the viscosity rushes to infinity and the fluid loses its fluidity. The heat output at a chemical reaction is not taken into account. The energy equation is denoted using a single-temperature model. Dissipative heat emissions are accounted. The problem is solved for temperature first-order boundary conditions. The solution was analyzed numerically by the finite difference method according to the iterative scheme. Calculations showed that the dependence of viscosity of some particular microvolume of the fluid upon the residence time in the channel has an extremal behavior. At first, there is a drop in the viscosity because of warming-up. Then the rate of chemical reaction increases with increasing temperature. This leads to an increase in viscosity primarily in near-wall layers. As a result, there is deceleration of velocity near the wall and the acceleration of the flow in the axial zone. The velocity profile becomes abruptly protruded. The significant influence of dissipation and variable viscosity on the Nusselt number and mass-average temperature is shown. |
Keywords and phrases: mathematical modeling, viscous fluid, nonisothermal flow, chemical reaction.
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