Theory of Rolling Contact Heat Transfer

1989 ◽  
Vol 111 (2) ◽  
pp. 257-263 ◽  
Author(s):  
A. Bejan
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Elastic Deformation ◽  
Contact Area ◽  
Peclet Number ◽  
Transfer Rate ◽  
Rolling Contact ◽  
Square Root ◽  
Péclet Number ◽  
Two Bodies

This paper addresses the fundamentals of the phenomenon of steady heat transfer by rolling contact between two bodies at different temperatures. The contact region is modeled according to the classical Hertz theory, by which the bodies undergo elastic deformation and the contact area has the shape of an ellipse. In the first part of the study it is shown that when the two bodies make contact continuously over the elliptical area, the overall heat transfer rate is proportional to the square root of the Peclet number based on the ellipse semiaxis parallel to the tangential (rolling) velocity. In the same case the heat transfer rate increases as the square root of the normal force (F) between the two bodies. The second part of the study treats the case when the rolling contact is made through a large number of asperities (contact sites) distributed over the elliptical contact area. The heat transfer rate is again proportional to the square root of the Peclet number. When the asperities are distributed randomly, the heat transfer rate increases as F5/6. In the case of regularly distributed asperities that undergo elastic deformation, the heat transfer rate is proportional to F13/18. The high Peclet number domain covered by this study is discussed in the closing section of the paper.

Effect of Microscopic Vortices Caused by Flow Interaction With Solid Obstacles on Heat Transfer in Turbulent Porous Media Flows

2019 ◽  
Author(s):  
Ching-Wei Huang ◽  
Vishal Srikanth ◽  
Haodong Li ◽  
Andrey V. Kuznetsov
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Porous Medium ◽  
Porous Media ◽  
Heat Transfer Rate ◽  
Contact Area ◽  
Transfer Rate ◽  
Porous Media Flow ◽  
Pore Scale ◽  
Solid Obstacles

Abstract Turbulent flow in a homogeneous porous medium was investigated through the use of numerical methods by employing the Reynolds Averaged Navier-Stokes (RANS) modeling technique. The focus of our research was to study how microscopic vortices in porous media flow influence the heat transfer from the solid obstacles comprising the porous medium to the fluid. A Representative Elementary Volume (REV) with 4 × 4 cylindrical obstacles and periodic boundary conditions was used to represent the infinite porous medium structure. Our hypothesis is that the rate of heat transfer between the obstacle surface and the fluid (qavg) is strongly influenced by the size of the contact area between the vortices and the solid obstacles in the porous medium (Avc). This is because vortices are regions with low velocity that form an insulating layer on the surface of the obstacles. Factors such as the porosity (φ), Pore Scale Reynolds number (Rep), and obstacle shape of the porous medium were investigated. All three of these factors have different influences on the contact area Avc, and, by extension, the overall heat transfer rate qavg. Under the same Pore Scale Reynolds number (Rep), our results suggest that a higher overall heat transfer rate is exhibited for smaller contact areas between the vortices and the obstacle surface. Although the size of the contact area, Avc, is affected by Rep, the direct influence of Rep on the overall heat transfer rate qavg is much stronger, and exceeds the effect of Avc on qavg. The Pore Scale Reynolds number, Rep, and the mean Nusselt number, Num, have a seemingly logarithmic relationship.

Ferro-nanofluid squeeze film lubrication with heat transfer

2021 ◽  
pp. 135065012110276
Author(s):  
Manimegalai Kavarthalai ◽  
Vimala Ponnuswamy
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Contact Time ◽  
Transfer Rate ◽  
Fluid Layer ◽  
Darcy Law ◽  
Squeeze Film ◽  
Mean Temperature ◽  
Special Cases ◽  
The Impact

A theoretical study of a squeezing ferro-nanofluid flow including thermal effects is carried out with application to bearings and articular cartilages. A representational geometry of the thin layer of a ferro-nanofluid squeezed between a flat rigid disk and a thin porous bed is considered. The flow behaviours and heat transfer in the fluid and porous regions are investigated. The mathematical problem is formulated based on the Neuringer–Rosensweig model for ferro-nanofluids in the fluid region including an external magnetic field, Darcy law for the porous region and Beavers–Joseph slip condition at the fluid–porous interface. The expressions for velocity, fluid film thickness, contact time, fluid flux, streamlines, pathlines, mean temperature and heat transfer rate in the fluid and porous regions are obtained by using a perturbation method. An asymptotic solution for the fluid layer thickness is also presented. The problem is also solved by a numerical method and the results by asymptotic analysis, perturbation and numerical methods are obtained assuming a constant force squeezing state and are compared. It is shown that the results obtained by all the methods agree well with each other. The effects of various parameters such as Darcy number, Beavers–Joseph constant and magnetization parameter on the flow behaviours, contact time, mean temperature and heat transfer rate are investigated. The novel results showing the impact of using ferro-nanofluids in the two applications under consideration are presented. The results under special cases are further compared with the existing results in the literature and are found to agree well.

scholarly journals Significance of Shape Factor in Heat Transfer Performance of Molybdenum-Disulfide Nanofluid in Multiple Flow Situations; A Comparative Fractional Study

Molecules ◽  
2021 ◽  
Vol 26 (12) ◽  
pp. 3711
Author(s):  
Asifa ◽  
Talha Anwar ◽  
Poom Kumam ◽  
Zahir Shah ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Heat Transfer ◽  
Skin Friction ◽  
Molybdenum Disulfide ◽  
Heat Transfer Rate ◽  
Shape Factor ◽  
Transfer Rate ◽  
Maximum Heat ◽  
Left Wall ◽  
Maximum Heat Transfer ◽  
Mos2 Nanoparticles

In this modern era, nanofluids are considered one of the advanced kinds of heat transferring fluids due to their enhanced thermal features. The present study is conducted to investigate that how the suspension of molybdenum-disulfide (MoS2) nanoparticles boosts the thermal performance of a Casson-type fluid. Sodium alginate (NaAlg) based nanofluid is contained inside a vertical channel of width d and it exhibits a flow due to the movement of the left wall. The walls are nested in a permeable medium, and a uniform magnetic field and radiation flux are also involved in determining flow patterns and thermal behavior of the nanofluid. Depending on velocity boundary conditions, the flow phenomenon is examined for three different situations. To evaluate the influence of shape factor, MoS2 nanoparticles of blade, cylinder, platelet, and brick shapes are considered. The mathematical modeling is performed in the form of non-integer order operators, and a double fractional analysis is carried out by separately solving Caputo-Fabrizio and Atangana-Baleanu operators based fractional models. The system of coupled PDEs is converted to ODEs by operating the Laplace transformation, and Zakian’s algorithm is applied to approximate the Laplace inversion numerically. The solutions of flow and energy equations are presented in terms of graphical illustrations and tables to discuss important physical aspects of the observed problem. Moreover, a detailed inspection on shear stress and Nusselt number is carried out to get a deep insight into skin friction and heat transfer mechanisms. It is analyzed that the suspension of MoS2 nanoparticles leads to ameliorating the heat transfer rate up to 9.5%. To serve the purpose of achieving maximum heat transfer rate and reduced skin friction, the Atangana-Baleanu operator based fractional model is more effective. Furthermore, it is perceived that velocity and energy functions of the nanofluid exhibit significant variations because of the different shapes of nanoparticles.

scholarly journals Assessment of TiO2 Nanoconcentration and Twin Impingement Jet of Heat Transfer Enhancement—A Statistical Approach Using Response Surface Methodology

Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 595
Author(s):  
Mahir Faris Abdullah ◽  
Rozli Zulkifli ◽  
Hazim Moria ◽  
Asmaa Soheil Najm ◽  
Zambri Harun ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Response Surface Methodology ◽  
Response Surface ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Tio2 Nanoparticle ◽  
Experimental Results ◽  
Improvement Rate ◽  
Design Expert ◽  
Impingement Jet

Impinging jets are considered to be a well-known technique that offers high local heat transfer rates. No correlation could be established in the literature between the significant parameters and the Nusselt number, and investigation of the interactions between the correlated factors has not been conducted before. An experimental analysis based on the twin impingement jet mechanism was achieved to study the heat transfer rate pertaining to the surface plate. In the current paper, four influential parameters were studied: the spacing between nozzles, velocity, concentration of Nano solution coating and nozzle-plate distance, which are considered to be effective parameters for the thermal conductivity and the heat transfer coefficient of TiO2 nanoparticle, an X-ray diffraction (XRD) and field emission scanning electron microscopy (FESEM) analysis were done, which highlighted the structure and showed that the nanosolution coated the surface homogenously. Moreover, a comparison was done for the experimental results with that of the predicted responses generated by the Design Expert software, Version 7 User’s Guide, USA. A response surface methodology (RSM) was employed to improve a mathematical model by accounting for a D-optimal design. In addition, the analysis of variance (ANOVA) was employed for testing the significance of the models. The maximum Nu of 91.47, where H = S = 1 cm; Reynolds number of 17,000, and TiO2 nanoparticle concentration of 0.5% M. The highest improvement rate in Nusselt was about 26%, achieved with TiO2 Nanoparticle, when S = 3 cm, H = 6 cm and TiO2 nanoparticle = 0.5 M. Furthermore, based on the statistical analysis, the expected values were found to be in satisfactory agreement with that of the empirical data, which was conducted by accounting for the proposed models’ excellent predictability. Multivariate approaches are very useful for researchers, as well as for applications in industrial processes, as they lead to increased efficiency and reduced costs, so the presented results of this work could encourage the overall uses of multivariate methods in these fields. Hypotheses: A comparison was done for the predicted responses generated by the Design Expert software with the experimental results and then studied to verify the following hypotheses: ► Preparation of three concentrations of TiO2 nanosolution was done and studied. ► The heat transfer rate could be increased by surface coating with TiO2 nanoparticle. ► The heat transfer could be improved by the impingement jet technique with suitable adjustments.

scholarly journals Heat Transmission Reinforcers Induced by MHD Hybrid Nanoparticles for Water/Water-EG Flowing over a Cylinder

Coatings ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 623
Author(s):  
Firas A. Alwawi ◽  
Mohammed Z. Swalmeh ◽  
Amjad S. Qazaq ◽  
Ruwaidiah Idris
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Liquid Velocity ◽  
Flow Characteristics ◽  
Hybrid Nanoparticles ◽  
Critical Parameters ◽  
Heat Transmission ◽  
Constant Wall Temperature

The assumptions that form our focus in this study are water or water-ethylene glycol flowing around a horizontal cylinder, containing hybrid nanoparticles, affected by a magnetic force, and under a constant wall temperature, in addition to considering free convection. The Tiwari–Das model is employed to highlight the influence of the nanoparticles volume fraction on the flow characteristics. A numerical approximate technique called the Keller box method is implemented to obtain a solution to the physical model. The effects of some critical parameters related to heat transmission are also graphically examined and analyzed. The increase in the nanoparticle volume fraction increases the heat transfer rate and liquid velocity; the strength of the magnetic field has an adverse effect on liquid velocity, heat transfer, and skin friction. We find that cobalt nanoparticles provide more efficient support for the heat transfer rate of aluminum oxide than aluminum nanoparticles.

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