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A computational analysis based upon the kinetic, mesoscopic numerical tool is adapted for elucidating the buoyancy-driven convection in the square shaped open cavity having the partially active wall under the influence of the uniform magnetic field (B). A heater (size-half of the height of the cavity) is positioned along the vertical, no-slip wall of the cavity (while another vertical end is open to the atmosphere). Other regions of no-slip partially heated vertical wall, as well as top and bottom walls, are thermally insulated. The significance of heater location (bottom, middle and top), the angle of magnetic field (0°, 45° and 90°), Hartmann number (0–100) and Rayleigh number (103–105) on natural convection have been illustrated. The interpretation of results have been carried out by studying the streamlines, isotherms, centreline variation of temperature; velocity component profiles and Nusselt number (local, average). The dependence of the Nusselt number with the magneto-convective parameter is presented and discussed. Heat transfer rate increases with the angle of the magnetic field. © Springer Nature India Private Limited 2019.

Department of Chemical Engineering

International Journal of Applied and Computational Mathematics

MHD free convection in a partially heated open-ended square cavity: Effect of angle of magnetic field and heater location

In this work, we have presented the numerical results for 2D, steady, laminar and incompressible flow in a square, two-sided, lid-driven cavity with a decentered heated triangular block (maintained at the isothermal thermal condition, TH) for non- Newtonian power-law fluids. The range of flow governing parameters considered for the numerical experimentations are Reynolds number (100 ≤ Re ≤ 1000), Richardson Number (Ri = 0.01, 1, 10) power law index; (0.2 ≤ n ≤ 1.8), blockage (10% and 30% of the height of cavity) and Prandtl number of Pr = 1. The upper and lower walls of the square cavity are kept moving in the opposite directions along –x axis (u−ux) and are thermally insulated. The left and right stationary walls are exposed to ambient condition (Tc). The governing flow equations are solved by using the finite volume approach and SIMPLE algorithm. Heat transfer characteristics and flow kinematics are revealed by systematic variation of streamlines and temperature contours. The effect of mixed convection parameter, i.e., Ri, found to have a negligible impact on fluid and thermal structure inside the cavity for fluids with n = 0.2.Heat transfer rate found to be lower for Ri = 0.01 for both blockages. © 2018 Elsevier Ltd

World University root node

International Journal of Mechanical Sciences

Mixed convection in a two-sided lid-driven cavity containing heated triangular block for non-Newtonian power-law fluids

The present research numerically explores the hydrodynamic and thermal characteristics due to mixed convection in the rectangular enclosure with one of the vertical wall moving and containing centrally placed heated elliptical block for steady state condition. In particular, the influence of different flow pertaining parameters, such as, the direction of moving vertical wall (either in positive –y or negative –y coordinate directions), aspect ratio of an elliptical cylinder (Er = 0.5, 1 and 2) are studied for the broad range of dimensionless parameters (Reynolds number: 1 ≤ Re ≤ 5000; Prandtl number: 1 ≤ Pr ≤ 100 and Grashof number: 0 ≤ Gr ≤ 105) by using finite volume method (FVM) and SIMPLE numerical approach. The analysis of physical insights of an enclosure is accomplished by systematic evaluation of the streamlines as well as isotherms profiles. In order to compare mean heat transfer from an elliptical cylinder with that of circular shape, normalized Nusselt number (NuN) is estimated. Heat transfer characteristics are more predominantly affected due to the direction of moving lid than the aspect ratio of the elliptical cylinder. Also, the enclosure with moving wall along positive –y direction tends to enhance heat transfer rate. Rather than a pure circular shape, the enclosure with heated elliptical block (Er≠1) shows a higher rate of convective heat transfer. © 2018 Elsevier Masson SAS

International Journal of Thermal Sciences

Mixed convection characteristics in rectangular enclosure containing heated elliptical block: Effect of direction of moving wall

The present work examines the influence of location of the heated triangular block along the vertical centerline of cavity on mixed convection characteristics. The flow is assumed to be 2D, steady, laminar and for incompressible and Newtonian. The physical domain of study is top lid-driven square cavity. The top and bottom walls of cavity are thermally insulated; while the both vertical walls are exposed to ambient (Tc). The cavity contains equilateral triangular block (size of edge, b), maintained at isothermal temperature condition (TH(&gt;Tc)) along its geometric horizontal centerline. The change in the position of block is permitted along the vertical centerline (x=0.5,y) of cavity. Flow pertaining equations are solved by using finite volume method (FVM) and SIMPLE algorithm. The dependence of various relevant dimensionless parameter, such as, Reynolds number (Re=1—1000), Richardson number (Ri=0.01,1,10), blockage (B‾=0.1,0.2,0.3) and location (Ly=0.25,0.5,0.75) of triangular block on convection characteristics have been elucidated. Flow and thermal patterns in the cavity are analyzed by systematic evaluation of streamline and temperature contours. Followed by heat transfer characteristics are presented by studying variation of local as well as average Nusselt number. Average Nu values are presented in the form of tables for different values of Ri. Higher heat transfer rates can be achieved for centered block position (Ly=0.5) than remaining two (Ly=0.25,0.75). © 2018 Elsevier Ltd

International Journal of Heat and Mass Transfer

Mixed convection characteristic in a lid-driven cavity containing heated triangular block: Effect of location and size of block

This work presents thermal lattice Boltzmann method simulation of magneto-hydrodynamic, buoyancy-driven convection in a partially differentially heated cavity (aspect ratio = 1) subjected to a magnetic field along the vertical direction, i.e. at 90°. Lattice Boltzmann method simulations are performed for three different cooler lengths (Lc = H/4, H/2, H) placed along the middle of one vertical wall for a wide range of Rayleigh and Hartmann numbers (103≤ Ra ≤ 105; Ha = 0, 60, 120) at fixed Prandtl number (Pr = 0.71, air). A partial heater is placed at the center of other vertical walls and its size is kept as half of the characteristic length (H/2). The physical insights of the systems are delineated by systematic analysis of stream function and temperature contours. Heat transfer characteristics of the cavity are elucidated by using averaged values of the Nusselt number. It is noted that average Nusselt number has a proportional dependence with cooler length and Rayleigh number, while it varied inversely with Hartmann number. Further, the functional dependence of average Nusselt number with cooler size, Rayleigh number, and Hartmann number is established for possible use in engineering design purpose. © 2018, © IMechE 2018.

Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

Computational analysis of magneto-hydrodynamic natural convection in partially differentially heated cavity: Effect of cooler size

The present numerical work explores the mixed convective flow and heat transfer analysis in top lid driven square cavity containing heated triangular block with constant heat flux (CHF) thermal condition. The fluid flow in the cavity is driven by top moving wall in +x direction, while all other walls are stationary. Governing equations are solved by using finite volume method (FVM) and SIMPLE scheme for range of pertaining parameters such as, Reynolds number (Re = 1, 10, 50, 100, 500 and 1000), Prandtl number (Pr = 1, 50, 100), and Grashof number (Gr = 0, 102, 103, 104 and 105). The influence of size of blockage (b = 10%, 20% and 30%) on momentum and heat transfer characteristics has also been explored. The physical insights of systems are delineated by analyzing variation of streamlines and isotherm contours; while the heat transfer characteristics are explored by using dimensionless heat transfer coefficient or Nusselt number (local as well as averaged values). It is observed that increase in Reynolds number enhances the heat transfer rate (Nusselt number) only up to Re = 180–220, later, deterioration of heat transfer rate is observed. The critical (Recr) as well as stagnant (Restag) Reynolds number of heat transfer for present case are identified. © 2016 Elsevier Ltd

Computational analysis of mixed convection heat transfer characteristics in lid-driven cavity containing triangular block with constant heat flux: Effect of Prandtl and Grashof numbers

This work illustrates the steady state, two dimensional natural convective flow and heat transfer features in square enclosure containing heated hexagonal block maintained either at constant wall temperature (CWT) or uniform heat flux (UHF) thermal conditions. Governing equations (mass, momentum and energy) are solved by using finite volume method (FVM) with 3rd order accurate QUICK discretization scheme and SIMPLE algorithm for range of field pertinent parameters such as, Grashof number (103 ≤ Gr ≤ 106), Prandtl number (1 ≤ Pr ≤ 100) and power law index (0.5 ≤ n ≤ 1.5). The analysis of momentum and heat transfer characteristics are delineated by evolution of streamlines, isotherms, variation of average Nusselt number value and Colburn factor for natural convection (jnH). A remarkable change is observed on fluid flow and thermal distribution pattern in cavity for both thermal conditions. Nusselt number shows linear variation with Grashof and Prandtl numbers; while rate of heat transfer by convection decreases for power law index value. Higher heat transfer rate can be achieved by using uniform heat flux condition. A Nusselt number correlation is developed for possible utilization in engineering/scientific design purpose. © 2016 Elsevier B.V.

Chinese Journal of Chemical Engineering

Laminar natural convection characteristics in an enclosure with heated hexagonal block for non-Newtonian power law fluids

This research work numerically analyzes 2D, steady state, mixed convective heat transfer for Newtonian fluids in lid driven square enclosure with centered triangular block (blockage — 10% or 30%) maintained either at the constant wall temperature or constant heat flux thermal conditions. The fluid flow in the enclosure is initiated by top moving wall in + x-direction, while all other walls are stationary. The top and bottom walls are thermally insulated. In particular, the governing field equations are solved for range of governing parameters such as, Reynolds number (1–1000), Prandtl number (1–100), and Grashof number (0–105). It is observed that the increase in inertial force enhances the heat transfer rate up to certain Reynolds number range (80–200), later deterioration of heat transfer rate is observed. Such behavior is found to be true for lower blockage (10%). Finally, functional dependence of average Nusselt number values with flow governing dimensionless parameters is developed and presented for its possible utilization in engineering and design purpose. © 2017 Elsevier B.V.

Mixed convection characteristics in lid-driven cavity containing heated triangular block

In this work, 2D, steady, natural convection in a partially active/heated open ended square cavity subjugated to the magnetic field for incompressible, Newtonian fluid is studied and presented. A simplified double distribution function (DDF)-thermal lattice Boltzmann method (TLBM) based on single relaxation time (SRT) is utilized for solving field controlling equations. One of the vertical walls of open cavity is exposed to the heat source (i.e., heater) partially; while another vertical wall is open to ambient. In particular, the influence of various geometric as well as parametric conditions, such as heater size (LH = 0.25, 0.5, 0.75), angle of magnetic field (θM = 0° 45° and 90°), Hartmann number (0 ≤ Ha ≤ 100) and Rayleigh number (103 ≤ Ra ≤ 105) on local and global convection features have been investigated. The dependence of average Nusselt number with magneto-convective parameter (λ = Ha2/Ra) has also been illustrated. It is observed that cavity with the applied magnetic field at θM = 45° offers highest heat transfer restriction than other considered cases. Effect of heater size remains effective only at higher Ra (≥105). © 2017 Institution of Chemical Engineers

Chemical Engineering Research and Design

Effect of angle of applied magnetic field on natural convection in an open ended cavity with partially active walls

Natural convection heat transfer in an square enclosure, consisting of a partially heated west wall with east end open to ambient, is investigated numerically by using an in-house computational fluid dynamics solver based on thermal lattice Boltzmann method. In particular, the influences of Rayleigh number (103-106), heating location (bottom, middle, and top) on west wall, and dimensionless heating length (0.25-0.75) on momentum and heat transfer characteristics of air are presented and discussed. The streamline patterns show bifurcation at the lowest Rayleigh number for bottom and middle heating, whereas at the highest Rayleigh number, all heating positions yield bifurcation and elongation of flow patterns with a secondary vortex near the lower side of open end. The middle and bottom heating locations show a linear increase in Nusselt number with heater size, whereas inverse dependence is seen for top heating. The maximum heat transfer is observed in the case of middle heating. As expected, average Nusselt number increased with increasing Rayleigh number. Finally, the functional dependence of the average Nusselt number on flow governing parameters (Rayleigh number and heating length) for different heating locations is presented as a simple predictive empirical relationship. © 2016 Taylor and Francis Group, LLC.

Heat Transfer Engineering

Effects of Heating Location and Size on Natural Convection in Partially Heated Open-Ended Enclosure by Using Lattice Boltzmann Method

A thermal lattice Boltzmann method is utilized for the numerical simulation of the natural convection heat transfer phenomena inside a differentially heated square cavity. Numerical simulations are performed to elucidate the combined effects of Prandtl number (0.71 ≤ Pr ≤ 100) and Rayleigh number (104 ≤ Ra ≤ 106) on heat transfer and fluid flow characteristics inside the cavity. Detailed insights are gained by the evaluation of isotherms, stream functions and vorticity profiles. For higher Prandtl and Rayleigh numbers, streamlines become more confined to hot wall with the loss of symmetry. Similarly, isotherms patterns become more stratified towards the hot wall. The centre-line velocity and temperature profiles are also analyzed. Further, the heat transfer rate is estimated in terms of average Nusselt number. It suggests a proportional increase in the average Nusselt number with the increasing values of Prandtl number for considered range of Rayleigh numbers. Finally, the numerical data for the average Nusselt number are presented in the form of a correlation for their best utilization in design and engineering practices. © 2015 Canadian Society for Chemical Engineering.

Canadian Journal of Chemical Engineering

Two-dimensional lattice Boltzmann simulation of natural convection in differentially heated square cavity: Effect of Prandtl and Rayleigh numbers

Natural convection characteristics of a partially heated open ended square cavity have been investigated numerically by using an in-house computational flow solver based on the passive scalar thermal lattice Boltzmann method (PS-TLBM) with D2Q9 (two-dimensional and nine-velocity link) lattice model. The partial part of left wall of the cavity is heated isothermally at either of the three different (bottom, middle and top) locations for the fixed heating length as half of characteristic length (H/2) while the right wall is open to the ambient conditions. The other parts of the cavity are thermally isolated. In particular, the influences of partial heating locations and Rayleigh number (103≤ Ra≤106) in the laminar zone on the local and global natural convection characteristics (such as streamline, vorticity and isotherm contours; centerline variations of velocity and temperature; and local and average Nusselt numbers) have been presented and discussed for the fixed value of the Prandtl number (Pr=0.71). The streamline patterns show qualitatively similar nature for all the three heating cases and Rayleigh numbers, except the change in the recirculation zone which is found to be largest for middle heating case. Isotherm patterns are shifted towards a partially heated wall on increasing Rayleigh number and/or shifting of heating location from bottom to top. Both the local and average Nusselt numbers, as anticipated, shown proportional increase with Rayleigh number. The cavity with middle heating location shown higher heat transfer rate than that for the top and bottom heating cases. Finally, the functional dependence of the average Nusselt number on flow governing parameters is also presented as a closure relationship for the best possible utilization in engineering practices and design. © 2015, Korean Institute of Chemical Engineers, Seoul, Korea.

Korean Journal of Chemical Engineering

Lattice Boltzmann analysis of effect of heating location and Rayleigh number on natural convection in partially heated open ended cavity

This work presents the lattice Boltzmann simulation of natural convection in an open ended square cavity subjected to partial heating. The size of heater is half of characteristic length and placed at middle location of one vertical wall. Numerical simulations are performed for three different fluids of industrial, scientific as well as domestic field, viz., air (. Pr = 0.71), dichloro-difluoro-methane (. Pr = 4.5) and water (. Pr = 7). The influence of the partial heater on heat and hydrodynamic characteristics of an open ended cavity have been elucidated. It is observed that isotherms become more confined toward the partially heated portion of wall with the increase in Prandtl number. The heat transfer rate shows linear increase with the Prandtl number, i.e., enclosure containing water shows higher heat transfer rate followed by R-12 refrigerant and air. The numerical results are summarized by the empirical correlation relating Nusselt number with Rayleigh and Prandtl numbers. © 2014 Taiwan Institute of Chemical Engineers.