Understanding Macroscopic Heat/Mass Transfer Using Meso- and Macro-Scale Simulations

Abstract

Summary. Scalar (heat or mass) transfer in the macroscale is the result of microscale diffusion and convection effects. Our fundamental hypothesis is that heat or mass transfer behavior can be synthesized from the behavior of a single, instantaneous, point source of heat or mass, and that understanding this behavior leads to an improved understanding of transport. Based on this concept, a simulation technique has been developed that involves the tracking of trajectories of heat or mass markers in a flow field, and then applying simple statistical methods to extract information about the macroscopic temperature or concentration field. The motion of these scalar markers is decomposed into a convection part, which is calculated using macroscopic flow simulations, and a diffusion part, which is simulated using a mesoscopic Monte-Carlo approach. Three different cases where this simulation methodology can been applied are presented, each one with different physics and with distinct applications. The first case is about heat transfer without convection (applied to the determination of the effective thermal conductivity of a nanocomposite material), the second case is the case of heat transfer in laminar flow (with applications in microfluidics), and the third case is the case of heat transfer with strong convective effects (applied to turbulent heat transport). The combination of a macroscopic and a mesoscopic simulation applied here allows the simulation of heat or mass transfer in cases that other conventional approaches are not feasible, and it allows the investigation of the physics of heat or mas transport in a more natural way.

Distribution and history of extensional stresses on vWF surrogate molecules in turbulent flow

“…This random jump took values from a normal probability density function that had a zero mean and a standard deviation that depends on the fluid properties and the molecular diffusivity of the particles. The equation of motion for each marker in each space direction x is given by 71 where is the displacement of the marker relative to its source at time t + 1, is the velocity of the fluid in the x direction at position , is the time step, and Z is a random number following a standard normal distribution.…”

Efficient Lagrangian scalar tracking method for reactive local mass transport simulation through porous media

“…In order to take into account the time the solute particles take to reach the wall as they travel through the flow field, the LST results can be expressed in terms of effective first-order reaction kinetics by fitting LST results to Equations (9) and (10), where the concentration is assumed to be proportional to the number of walkers into the domain (see also [26,27,29] for obtaining the concentration field in other configurations). The effective half-lives and effective first-order reaction rate constants are plotted in Figures 11 and 12, respectively, for several saltleached scaffolds typically used in bone tissue engineering (porosity between 80 and 95%, and an average pore size between 180 and 450 microns).…”

“…Macroscopic solute transport is modeled using the Lagrangian scalar tracking (LST) method [6,7] in conjunction with the LBM algorithm. Similar techniques have been applied in our laboratory for heat transfer in microfluidics [8,9] and by others for the simulation of the motion of nanoparticles in low Reynolds number flows [10]. The fundamental hypothesis is that solute transport behavior of passive markers is the combination of convection (obtained using the velocity field from the LBM simulations) and diffusion (obtained from a mesoscopic Monte-Carlo approach that simulates Brownian motion).…”