Carlo Nonino

Temperature-Dependent Viscosity and Viscous Dissipation Effects in Microchannel Flows With Uniform Wall Heat Flux

A parametric investigation is carried out on the effects of temperature-dependent viscosity and viscous dissipation in simultaneously developing laminar flows of liquids in straight microchannels of constant cross sections. Reference is made to fluid heating conditions with a uniform heat flux imposed on the walls of the microchannels. Six different cross sectional geometries are considered, chosen among those usually adopted for microchannels (circular, flat, square, rectangular, trapezoidal, and hexagonal). Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite-element procedure is employed for the solution of the parabolized momentum and energy equations. Due to the high value of the ratio between the length and the hydraulic diameter in microchannels, such an approach is very advantageous with respect to the one based on the steady-state solution of the elliptic form of the governing equations in a three-dimensional domain corresponding to the whole microchannel. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented. Numerical results confirm that, in the laminar forced convection in the entrance region of straight microchannels, the effects of temperature-dependent viscosity and viscous dissipation cannot be neglected in a wide range of operative conditions.

NUMERICAL PREDICTION OF FLUID FLOW AND HEAT TRANSFER IN CROSS-FLOW MICRO HEAT EXCHANGERS

The results of CFD calculations can represent a useful complement to the experimental data on micro heat exchangers since they allow the designer to fetch details of the thermal fields inside these micro devices. On the other hand, obtaining the numerical solution for a complete heat transfer unit is very demanding in terms of required computational resources. This is particularly true for the case of crossflow micro heat exchangers since, due to the features of the flow patterns, the only symmetry planes that can be considered to simplify the computational domain are those parallel to both fluid streams. Therefore, as an alternative to massive CFD, a simplified FEM procedure was developed to allow the analysis of the fluid flow and heat transfer in cross-flow micro heat exchangers using ordinary workstations. A two-stage procedure is adopted on the assumption that all the thermophysical properties are constant within each microchannel and that all layers of microchannels are identical except for edge effects in the outer layers. First, an in-house FEM code for the solution of the parabolized Navier-Stokes equations is employed to compute the velocity field and the pressure drop in a single microchannel. Then, an appropriate mapping of the velocity field thus determined is used to obtain the velocity components in the fluid parts of a three-dimensional computational domain corresponding to a suitable portion of the micro heat exchanger. On this domain, the elliptic form of the equation energy is solved using another in-house FEM code. Since in a cross-flow micro heat exchanger the microchannels of one layer are perpendicular to those of the adjacent layers, it is impossible to discretize the computational domain with a structured grid consisting of hexahedral elements that are elongated in the flow direction. Thus, the possibility of independently meshing different parts of the domain using grids that do not match at the common interface (domain decomposition) has been implemented. To this purpose, an original method has been proposed, which requires neither iterations nor the evaluation of integrals on the interface (never easy when grids do not match). The original procedure has been subsequently extended to allow the modelling of the effects of flow maldistribution, which in cross-flow micro heat exchangers can originate from an inappropriate design of headers and manifolds and/or from the viscosity change associated with the temperature variation in the microchannels. An iterative scheme has been adopted so that the velocity field in each microchannel can be updated to account for a redistribution of the total mass flow rate on the basis of the constraint that the pressure drop must be the same for all the microchannels of each layer, even if microchannel velocities and average viscosities are different. The iterative procedure does not require new solutions of the parabolized Navier-Stokes equations. However, the mapping of the velocity field between grids with different nodal densities hinders the fulfilment of the discrete mass conservation constraint. This is restored by solving a Poisson equation for a velocity correction potential that allows the calculation of appropriate velocity corrections. Numerical results concern validation tests and sample applications.

Effects of flow maldistribution on the thermal performance of cross-flow micro heat exchangers

The combined effect of viscosity- and geometry-induced flow maldistribution on the thermal performance of cross-flow micro heat exchangers is investigated with reference to two microchannel cross-sectional geometries, three solid materials, three mass flow rates and three flow nonuniformity models. A FEM procedure, specifically developed for the analysis of the heat transfer between incompressible fluids in cross-flow micro heat exchangers, is used for the numerical simulations. The computed results indicate that flow maldistribution has limited effects on microchannel bulk temperatures, at least for the considered range of operating conditions.

Entrance and temperature dependent property effects in the laminar forced convection in straight ducts with uniform wall temperature

The paper reports the results of a parametric investigation on the effects of temperature dependent viscosity and thermal conductivity on forced convection in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. Uniform temperature boundary conditions are specified at the duct walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries, namely circular and flat ducts, are considered. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number are presented for different values of the entrance Prandtl number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain an approximate value of the local Nusselt number by separately considering the effects of temperature dependent viscosity and those of temperature dependent thermal conductivity.

Nusselt number correlations for simultaneously developing laminar duct flows of liquids with temperature dependent properties

New correlations, suitable for engineering applications, for the mean Nusselt number in the entrance region of circular tubes and square ducts with uniform heat flux boundary conditions specified at the walls are proposed. These correlations are obtained on the basis of the results of a previous parametric investigation on the effects of temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight ducts of constant cross-sections. In these studies, a finite element procedure has been employed for the numerical solution of the parabolized momentum and energy equations. Viscosity and thermal conductivity are assumed to vary with temperature according to an exponential and to a linear relation, respectively, while the other fluid properties are held constant. Axial distributions of the mean Nusselt number, obtained by numerical integration from those of the local Nusselt number, are used as input data in the derivation of the proposed correlations. A superposition method is proved to be applicable in order to estimate the Nusselt number by considering separately the effects of temperature dependent viscosity and thermal conductivity. Therefore, for each of the considered cross-sectional geometries, two distinct correlations are proposed for flows of liquids with temperature dependent viscosity and with temperature dependent thermal conductivity, in addition to that obtained for constant property flows.

Temperature dependent viscosity and thermal conductivity effects on the laminar forced convection in straight microchannels

A parametric investigation is carried out on the effects of viscous dissipation and temperature dependent viscosity and thermal conductivity in simultaneously developing laminar flows of liquids in straight microchannels of constant cross-sections. Uniform heat flux boundary conditions are specified at the heated walls. Viscosity is assumed to vary with temperature according to an exponential relation, while a linear dependence of thermal conductivity on temperature is assumed. The other fluid properties are held constant. Two different cross-sectional geometries are considered, corresponding to both axisymmetric (circular) and three-dimensional (square) microchannel geometries. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Brinkman number and of the viscosity and thermal conductivity Pearson numbers. Moreover, a superposition method is proved to be applicable in order to obtain the correct value of the Nusselt number by considering separately the effects of temperature dependent viscosity and viscous dissipation and those of temperature dependent thermal conductivity. In fact, it is found that the influence of the temperature dependence of thermal conductivity on the value of the Nusselt number is independent of the value of the Brinkman number, i.e., it is the same no matter whether viscous dissipation is negligible or not. Finally, it is demonstrated that, in liquid flows, the main effects on pressure drop of temperature dependent fluid properties can be retained even if only viscosity is allowed to vary with temperature, the other properties being assumed constant.Copyright

Viscous dissipation and temperature dependent viscosity effects in simultaneously developing flows in flat microchannels with convective boundary conditions

The effects of viscous dissipation and temperature dependent viscosity in simultaneously developing laminar flows of liquids in straight microchannels of arbitrary but constant cross-section are studied with reference to convective thermal boundary conditions. Viscosity is assumed to vary linearly with temperature, in order to allow a parametric investigation, while the other fluid properties are held constant. A finite element procedure, based on a projection algorithm, is employed for the step-by-step solution of the parabolized momentum and energy equations. Axial distributions of the local overall Nusselt number and of the apparent Fanning friction factor in flat microchannels are presented with reference to both heating and cooling conditions for two different values of the Biot number. Examples of temperature profiles at different axial locations are also shown.