Majid Bahrami

Pressure Drop of Fully Developed, Laminar Flow in Rough Microtubes

The characteristics of fully-developed, laminar, pressure-driven, incompressible flow in rough circular microchannels are studied. A novel analytical model is developed that predicts the increase in pressure drop due to wall roughness in microtubes. The wall roughness is assumed to posses a Gaussian isotropic distribution. The present model is compared with experimental data, collected by other researchers and good agreement is observed.

Modeling thermal contact resistance: A scale analysis approach

A compact analytical model is developed for predicting thermal contact resistance (TCR) of nonconforming rough contacts of bare solids in a vacuum. Instead of using probability relationships to model the size and number of microcontacts of Gaussian surfaces, a novel approach is taken by employing the scale analysis method. It is demonstrated that the geometry of heat sources on a half-space for microcontacts is justifiable for an applicable range of contact pressure

Thermal conductivity and contact resistance of metal foams

Accurate information on heat transfer and temperature distribution in metal foams is necessary for design and modelling of thermal-hydraulic systems incorporating metal foams. The analysis of heat transfer requires determination of the effective thermal conductivity as well as the thermal contact resistance (TCR) associated with the interface between the metal foam and the adjacent surfaces/layers. In this study, a test bed that allows the separation of effective thermal conductivity and TCR in metal foams is described. Measurements are performed in a vacuum under varying compressive loads using ERG Duocel aluminium foam samples with different porosities and pore densities. Also, a graphical method associated with a computer code is developed to demonstrate the distribution of contact spots and estimate the real contact area at the interface. Our results show that the porosity and the effective thermal conductivity remain unchanged with the variation of compression in the range 0‐2MPa; but TCR decreases significantly with pressure due to an increase in the real contact area at the interface. Moreover, the ratio of real to nominal contact area varies between 0 and 0.013, depending upon the compressive force, porosity, pore density and surface characteristics. (Some figures in this article are in colour only in the electronic version)

Pressure Drop in Rectangular Microchannels as Compared With Theory Based on Arbitrary Cross Section

Pressure driven liquid flow through rectangular cross-section microchannels is investigated experimentally. Polydimethylsiloxane microchannels are fabricated using soft lithography. Pressure drop data are used to characterize the friction factor over a range of aspect ratios from 0.13 to 0.76 and Reynolds number from 1 to 35 with distilled water as working fluid. Results are compared with the general model developed to predict the fully developed pressure drop in arbitrary cross-section microchannels. Using available theories, effects of different losses, such as developing region, minor flow contraction and expansion, and streaming potential on the measured pressure drop, are investigated. Experimental results compare well with the theory based on the presure drop in channels of arbitrary cross section.

Thermal Contact Resistance of Nonconforming Rough Surfaces, Part 2: Thermal Model

A new analytical model is developed for thermal contact resistance (TCR) of nonconforming rough surfaces. TCR is considered as the superposition of macro- and microthermal resistances. The effects of roughness, load, and radius of curvature on TCR are investigated. It is shown that there is a value of surface roughness that minimizes the TCR for a fixed load and geometry. Simple correlations for determining TCR, using relationships introduced in Part 1 of this study, are derived that cover the entire range of TCR from conforming rough to smooth spherical contacts. With introduction of an approximate model, it is shown that the effective microthermal resistance is not a function of surface curvature and contact pressure profile. The comparison of the present model with 600 experimental data points shows good agreement in the entire range of TCR. A criterion for conforming contacts is proposed that gives a range for the ratio of out-of-flatness to surface roughness.

Assessment of relevant physical phenomena controlling thermal performance of nanofluids

This paper provides an overview of the important physical phenomena necessary for the determination of effective thermal conductivity of nanofluids. Through an investigation, a large degree of randomness and scatter has been observed in the experimental data published in the open literature. Given the inconsistency in these data, it is impossible to develop a comprehensive physical-based model that can predict all the trends. This also points out the need for a systematic approach in both experimental and theoretical studies. Upper and lower bounds are developed for steady-state conduction in stationary nanofluids. Comparisons between these bounds and the experimental data indicate that all the data (except for carbon nanotube data) lie between the lower and upper bounds.

A Compact Model for Spherical Rough Contacts

A new model is developed that considers the effect of roughness on the elastic contact of spherical bodies. A general pressure distribution is proposed that encompasses the contact of rough spheres and yields the Hertzian theory for ideally smooth surfaces. A new parameter, nondimensional maximum contact pressure, is introduced and it is shown that this is the key parameter that controls the contact. The results of the present study are presented in the form of compact relationships. These relationships are compared against the experimental data collected by others and good agreement is observed.

Comprehensive Modeling of Vehicle Air Conditioning Loads Using Heat Balance Method

The Heat Balance Method (HBM) is used for estimating the heating and cooling loads encountered in a vehicle cabin. A load estimation model is proposed as a comprehensive standalone model which uses the cabin geometry and material properties as the inputs. The model is implemented in a computer code applicable to arbitrary driving conditions. Using a lumped-body approach for the cabin, the present model is capable of estimating the thermal loads for the simulation period in real-time. Typical materials and a simplified geometry of a specific hybrid electric vehicle are considered for parametric studies. Two different driving and ambient conditions are simulated to find the contribution and importance of each of the thermal load categories. The Supplemental Federal Test Procedure (SFTP) standard driving cycle is implemented in the simulations for two North American cities and the results are compared. It is concluded that a predictive algorithm can be devised according to the driving conditions, vehicle speed, orientation, and geographical location. By using this model, the pattern of upcoming changes in the comfort level can be predicted in real-time in order to intelligently reduce the overall AC power consumption while maintaining driver thermal comfort.

Laminar Flow in Microchannels With Noncircular Cross Section

Analytical solutions are presented for laminar fully developed flow in micro-/ minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and hexagon. A point matching technique is used to calculate closed form solutions for the velocity distributions in the above-mentioned channel cross sections. The developed relationships for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including polygonal, rectangular, circular, elliptical, and rhombic cross sections. The present compact solutions provide a convenient and power tool for performing hydrodynamic analyses in a variety of fundamental and engineering applications such as in microfluidics, transport phenomena, and porous media.

Thermal Joint Resistances of Conforming Rough Surfaces with Gas-Filled Gaps

An approximate analytical model is developed for predicting the heat transfer of interstitial gases in the gap between conforming rough contacts. A simple relationship for the gap thermal resistance is derived by assuming that the contacting surfaces are of uniform temperature and that the gap heat transfer area and the apparent contact area are identical. The model covers the four regimes of gas heat conduction modes, that is, continuum, temperature jump or slip, transition, and free molecular. Effects of main input parameters on the gap and joint thermal resistances are investigated. The model is compared with other models and with more than 510 experimental data points in the open literature. Good agreement is shown over the entire range of the comparison. Nomenclature A = area, m 2 a = radius of contact, m bL = specimens radius, m c1 =V ickers microhardness coefficient, Pa c2 =V ickers microhardness coefficient d = distance between two parallel plates, m F =e xternal force, N Hmic = microhardness, Pa H � = c1(1.62σ � /m) c2 ,P a H ∗ = c1(σ � /m) c2 ,P a Kn = Knudsen number k = thermal conductivity, W/mK l = depth, m M =g as parameter, m Mg = molecular weight of gas, kg/kmol Ms = molecular weight of solid, kg/kmol m = mean absolute surface slope ns = number of microcontacts P = pressure, Pa Pr = Prandtl number Q = heat flow rate, W q = heat flux, W/m 2 R = thermal resistance, K/W r, z =c ylindrical coordinates T = temperature, K t = dummy variable Y = mean surface plane separation, m z = surface height, m αT = thermal accommodation coefficient γ = ratio of gas specific heats � = mean free path, m λ = nondimensional separation ≡ Y √ 2σ