Laminar Mixed Convection Heat Transfer Research Articles

Numerical Predictions of Laminar Free and Mixed Convection Heat Transfer to Supercritical Water from a Non-Isothermal Vertical Plate

Numerical predictions of heat transfer have been made for laminar free and mixed convective heat transfer from non-isothermal vertical plane surface to supercritical water. Variation of all the thermo-physical properties of the supercritical fluid under investigation have been considered. The numerical scheme employed in the present investigation is first validated with respect to experimental data for isothermal wall conditions and good agreement is achieved with maximum deviation not exceeding 15 %. Linear and parabolic variation of wall temperatures are considered for the present investigation. Computations are made for two pressures of 225 Bar and 235 Bar, for wide range of temperature difference from 4K to 20K. The values of temperature difference are chosen. Based on the results obtained, correlations have been proposed to evaluate the Nusselt numbers for both free and mixed convection with pressure ratios of P/Pc = 1.02 (p = 225 bar) and P/Pc = 1.065 (p = 235 bar). The correlations cover a range of Rayleigh numbers, Rax from 106 to 109 for Free Convection and grashoff Number/Reynolds Number2 ranging from 0.4 to 8 for Mixed convection. The proposed correlations for local Nusselt numbers do not exceed maximum deviation of 15% from the predicted values. It has been found that the maximum deviation occurs for those cases for which the pseudo-critical temperature, T* is within the boundary layer. It is further observed that for these cases both the velocity and temperature profiles are distorted at locations where the temperature is close to the pseudo-critical temperature thereby affecting the gradients at the wall, which in turn influences the heat transfer coefficient.

Mixed convection Casson polymeric flow from a nonlinear stretching surface with radiative flux and non‐Fourier thermal relaxation effects: Computation with CSNIS

AbstractThermal non‐Newtonian polymer coating flows is growing as a major area in materials processing. Inspired by new developments in this field which require more sophisticated mathematical models, the current investigation examines the laminar viscoplastic boundary layer flow and mixed convective heat transfer over a power‐law nonlinear stretching surface. To simulate thermal relaxation effects the hyperbolic Cattaneo‐Christov heat flux model is deployed. The non‐Newtonian polymer characteristics are described by employing the Casson flow model. High temperature conditions invoke thermal radiation flux which is analyzed with an algebraic flux model. Via robust similarity transformations, the primitive partial differential conservation equations for momentum and energy equations are rendered into a system of coupled non‐linear ordinary differential equations with associated wall and free stream boundary conditions. The emerging boundary value problem is solved numerically with an efficient Chebyshev Spectral Newton Iterative scheme (CSNIS), in the MATLAB platform. The resulting solutions are discussed for different emerging parameters using graphs and tables. Validation is included with special cases from the literature. With increasing power law stretching index increases, the flow is decelerated, and temperatures are reduced. Increment in mixed convection parameter boosts the velocity but suppresses temperature and thermal boundary layer thickness. Increasing non‐Fourier Deborah number, temperatures are depleted whereas with increasing radiative flux parameter they are increased. With elevation in Casson non‐Newtonian parameter, velocity is decreased whereas temperature is enhanced and Nusselt number is suppressed.

Simulation of conductive fins effect on mixed convection heat transfer in a two-dimensional inclined channel using the lattice Boltzmann method

The simulation of the laminar mixed convection heat transfer inside a 2-D inclined channel was investigated here by employing the lattice Boltzmann method (LBM). The channel was equipped with conductive fins. The effects of inclination angle (φ), geometrical parameters (e and A), and a wide range of the Richardson numbers (Ri = 0.1-10) at fixed Reynolds number (Re = 100) on the heat transfer and flow structure were studied. The numerical model was validated by the published benchmark problems. Results were analyzed in terms of isotherms, streamlines, average Nusselt number, and average temperature. It found that the Nu increases with a decrease in the number, height, and width of fins. Results showed that when the channel equipped with 16 fins the reduction in Nu value reaches 62% compared to the empty channel. In addition, at Ri = 1 and N = 8, the Nusselt number decreased by about 52-77% for different fin widths compared to the channel without fins. However, the Richardson number and inclination angle enhanced the heat transfer rate in terms of the average Nusselt number. It revealed that a higher heat transfer rate belongs to the Ri = 10 and φ = 60°. The finding of this work showed the capability of LBM in simulating the mixed convection heat transfer in an inclined channel equipped with fins. A numerical analysis of the results produced a comprehensive set of results that could be utilized to reduce heat transfer. This paper can provide a novel framework for the design of air solar collectors and heat exchange systems.

Study of mixed convection in a horizontal cylindrical pipe partially filled with a porous medium saturated with a single fluid

The three-dimensional numerical simulation of laminar mixed convection heat transfer with and without porous medium in a cylindrical duct was carried out in this study. The cylinder is divided into three parts. The first and the third parts are adiabatic, while the central part is subjected to a constant heat flux. The effects of Darcy number, porosity, permeability and Nusselt number on heat transfer were considered. This problem is modeled by the Navier-stokes equations in the fluid region and by the Darcy-Brinkman-Forchheimer equation in the porous region, and for the thermal field the energy equation is used. The resolution of these equations was performed by the computational fluid dynamics code Ansys15.2 software using finite volume approach. The obtained results showed an accumulation of the hot fluid with stratification in the upper part of the pipe while the lower region of the pipe remained at practically constant temperature. The effect of the porous matrix is very noticeable on the velocity profile. The insertion of a porous high permeability medium significantly improves heat transfer.

Hydrothermal and energy analysis of flat plate solar collector using copper oxide nanomaterials with different morphologies: Economic performance

Flat plate solar collectors (FPSCs) have gotten a lot of attention in the last decade because of their ease of installation and design. The current study focused on numerical aspects of a three-dimensional (3D) inclined tube-on-absorbing sheet solar collector. The numerical model was considered to work under a conjugated laminar mixed convection heat transfer mechanism in the range of 100 ≤ Re ≤ 1300. CuO/H2O nanofluids were used as the working fluids. The impact of different parameters on the thermal efficiency of the current FPSC, including inlet temperature, nanoparticle size, volume concentration, and various copper oxide morphologies, on the heat transfer, thermodynamics, thermal, and economic performance, was studied. According to simulation results, the solar collector using distilled water (DW) under 293 K performed better in terms of heat transfer and energy efficiency than those using 303 K and 313 K. In comparison to other sizes and volume concentrations, nanosphere nanofluids with 20 nm and 4% showed higher hydrothermal performance characteristics. Nanoplatelets-shaped CuO nanofluids illustrated the higher values for pressure drop, heat transfer, energy gain, energy efficiency, and lower values for surface plate temperature and outlet temperature, followed by nanocylinders, nanoblades, nanobricks, and nanospheres, respectively. The economic performance indicators recommended that nanobricks CuO nanofluids with 1% volume fraction were the best fluid replacement for water in solar collector applications.

Experimental and numerical study of mixed convection with surface radiation heat transfer in an air-filled ventilated cavity

The present study deals with the experimental and numerical investigation of steady combined laminar mixed convection and surface radiation heat transfer in the air-filled enclosure subjected to a constant heat flux supplied to the vent side of the cavity. Experimental results are presented for heat inputs, Q = 3.19 W–16.71 W, Reynolds number, Re = 4814–166385, and Richardson number, Ri = 0.1–25. In the present study, the numerical simulation is also performed in the two–dimensional vented cavity to enrich the experimental work for aspect ratio, A = 1–5, and surface emissivity, ε = 0.05–0.85. The momentum and energy equations under Boussinesq approximations are solved using a well-known finite-volume method, and numerical code is developed in Fortan 90 for getting all numerical results. Based on the experimental data, correlations are developed for the Nusselt number and maximum temperature of the heated surface.

Mixed convection heat transfer of a nanofluid in a closed elbow-shaped cavity (CESC)

The current survey’s primary purpose is to conduct the computational modeling of laminar mixed convection heat transfer of nanofluids inside a CESC using a finite volume method. Water/Cu nanofluid at 0–6% volume fractions was selected as a working fluid. The investigation was done at Grashof numbers of 10,000 < Gr < 100,000 and Richardson numbers of 0.1, 1, and 10. All parameters of the hydrodynamic flow and mixed convection heat transfer are presented as Nusselt number, the coefficient of friction, dimensionless velocity in different sections of the cavity, and entropy generation and temperature contours. Results indicated that nanofluid with higher volume fraction causes heat transfer enhancement. Using nanofluid, applying the gravity domain and the existence of lid driven in studied geometry affect flow behavior. Solid nanoparticles’ existence causes better temperature distribution and better stimulation of buoyancy force, which can be considered another factor for improving buoyancy force. By increasing Grashof number, the circulation mechanism’s improvement is the most significant factor in reducing entropy generation in studied geometry. At the beginning of fluid collision with the surface, the highest temperature variation between the surface and the fluid occurred by considering the fluid temperature. Hence, at the bottom areas of the hot surface, entropy generation is always the least.

Experimental Enhancement of Mixed Convection Heat transfer in Hot Base Rectangular Channel

This paper presents an experimental study to enhance the flow and heat transfer enhancement over horizontal and orientation channel with hot base by laminar mixed convection heat transfer. The hot base is fitted with the longitudinal rectangular fin arrays as a finned wall. The study covered the following range: modified Grashof number varied (3× 101 - 8× 108), Reynolds number in range 1800-2300, and Pyrantel number 0.71. The bottom finned wall of the channel was supplied with constant heat flux, while the other sides are insulated. The experiment part includes a suitable test rig that was built to get accurate decisions. A good mechanism was created to get the orientation angles at (90°,120°, 150 °and 180°) then to analysis this effect on heat transfer for laminar flow force convection. Three different cases are investigated: the effect of modified Grashof number and orientation angles on fluid particles flow and heat removal will be an enhancement. The experiment results show that the average heat transfer coefficient increased with Reynolds number and an increase of the Grashof number for all orientation angles due to increases buoyancy forces, thus causes a detach with the secondary layer flow. The average heat transfer coefficient and fins effectiveness are enhanced to 25% at highest longitudinal orientation angles.

OVERLAPPING MULTI-DOMAIN SPECTRAL METHOD FOR NON-DARCIAN MIXED CONVECTION CHEMICALLY REACTING FLOW OF MICROPOLAR FLUID OVER A FLAT PLATE IN A POROUS MEDIA

An efficient overlapping multi-domain spectral method is presented and used in the analysis of a two-dimensional steady laminar MHD mixed convection flow, heat and mass transfer over a vertical flat plate embedded in a porous medium. The effect of chemical reaction, thermal radiation, heat source/sink and other parameters influencing the flow has been analyzed by imposing magnetic force transverse to the plate in a non-Darcy porous medium with constant wall temperature and concentration conditions. The flow equations are expressed in dimensionless form and solved using overlapping multidomain bivariate spectral local linearization method (OMD-BSLLM). An analysis of the convergence and accuracy of the OMD-BSLLM is given using error norms and residual errors. Comparisons with previously published work for special cases of the problem are performed and excellent concurrence is found; hence reliable results are being presented. The influence of certain parameters on the fluid properties and flow characteristics is analyzed. The skin friction, heat and mass transfer coefficients are presented for the concentrated flow and the turbulent boundary layer flow. The flow characteristics are found to be smaller for turbulent boundary layer flows than concentrated particle flows. This type of flow has an application in catalytic and chromatographic reactions, packed absorption and distillation towers.

Guided Air by Convection to Cool-Down Inclined Channel Supported by Two Heat Sources

This paper presents the numerical study of the laminar mixed-convection heat transfer of two identical protruding heat sources mounted in an inclined channel with obstacle. The control volume method and the SIMPLER algorithm are used to solve the dimensionless governing equations of mass, momentum, and energy for mixed convection. The effects of the obstacle, the channel inclination and the Reynolds number 5 ≤Re≤ 30 on streamlines and isotherms as well as on the heat transfer rate at the surface of each component are investigated for Pr=0.71 and Gr=105. The finding results show that for the channel inclination angle in the range 30° ≤φ≤60°, the obstacle has a large effect on the rate of transfer. In addition, by analyzing the effect of the obstacle size, it has been found out that the obstacle height has a strong effect on the cooling rate of the area between the two sources while the obstacle width effect is less noticeable.

A numerical study of mixed convection heat transfer in a lid-driven cavity using Al2O3-water nanofluid

This study aims a numerical investigation of steady, laminar mixed convection heat transfer in a two-dimensional cavity by employing a finite volume method with a fourth-order approximation of convective terms, when nanoparticles are present. With the aim of solving two-dimensional momentum and energy conservation equations, a finite volume method on a non-uniform staggered grid is utilized. Second-order central differences are utilized to approximate diffusion terms in momentum and energy equations, while the development of a non-uniform four-point fourth-order interpolation (FPFOI) scheme is performed for the convective terms. Continuity and momentum equations are solved using the SIMPLE (Semi-Implicit Method for Pressure-Linked Equation) algorithm. In order to evaluate heat transfer enhancement, various viscosity and thermal conductivity models were employed. Numerical solution results were obtained in different models in cases where Gr number is between 103 and 105, Re number is 10-100-1000 and nanoparticle volumetric fraction is 0-5%.

Laminar entry region mixed convection heat transfer from an inclined rectangular fin array

Purpose The paper aims to investigate the influence of the angle of inclination on mixed convection heat transfer from rectangular plated shrouded fin array computationally. This study has got applications in the various thermal field such as cooling, solar thermal and so on. Design/methodology/approach A computational study is made to evaluate the thermal performance in an inclined channel. Findings Increase in clearance from 0.01 to 0.25 results in an increase of local Nusselt number by is as high as 15% near the exit. At a higher value of Gr with an increase in C* from 0.10, Nu is found to increase by 5.5%. Increase in Gr by 1.37 times results in enhancement of Nu by a maximum of 25-30%. Around 10% increase in overall Nu value is observed with an increase in inclination (i.e. from 30° to 60°). Practical implications This study has got applications in the various thermal field such as cooling, solar thermal and so on. Originality/value Entry region mixed convection in a shrouded inclined finned channel is performed.

Numerical investigation of mixed convection heat transfer behavior of nanofluid in a cavity with different heat transfer areas

The main purpose of this research is the numerical modeling of laminar mixed convection heat transfer inside an open square cavity with different heat transfer areas. In the considered geometry, cold fluid enters the cavity. At the middle of the cavity, there is a hot isothermal circular heat source. For increasing the heat transfer, solid silver nanoparticles with volume fractions (φ) of 0, 2 and 4% are added to water. Studied Re numbers are 10, 50, 120 and 200. The location of the hot zone changes the temperature distribution in the fluid layers. If the heat transfer area is located in an appropriate location, temperature distribution becomes more uniform. Increasing Re leads to smaller temperature gradients in regions near the hot surface and higher temperature at fluid layers close to the surface. By increasing fluid velocity, backflows do not improve heat transfer but it is able to change the heat transfer mechanism. By decreasing the fluid velocity, the effects of velocity gradients and extension of the velocity boundary layer increase and friction coefficient attains the maximum value.

Flow and Thermal Mechanisms in Receiver Tube of Parabolic Trough Collectors with Rings Axially Connected Together and Radially Connected to the Inner Tube Surface

Artificial obstructions on the underside of receiver tubes can increase the heat transfer coefficient between the receiver tubes (Heat Exchanger, HX) of Parabolic Trough Collectors (PTCs) and water as a working fluid. In this study, we numerically and experimentally tested the behavior of laminar mixed convective heat transfer in HX tube installed with baffles. These baffles are rings that are connected together axially and connected radially to the inner tube surface. Using ANSYS fluent Version 15.0, we performed computation fluid dynamics modeling to achieve heat transfer enhancement in HX tubes equipped with turbulator baffles under laminar flow conditions. Moreover, the effects of Pitch ratio (P/D) = 3, 6 and 10 and Reynolds number Re#480 were recorded. The novel application of the rings that are connected axially together and radially to the inner tube surface contributes to the long-term storage of thermal energy and promotes heat transfer via. conduction from the tube surface to the center line of the water flow within a short period. In the study, the baffles generated a vortex to increase the Nusselt number (Nu) inside the HX. To simulate heat flux, we calculated the constant wall heat flux of the receiver tube using an electric heater. Results indicated that using 20 rings as baffles instead of plain tubes improves heat transfer by up to 75%. As P/D decreased and re increased, the heat transfer rate, friction factor (f) and Thermal Enhancement Factor (TEF) increased.

Inexpensive Computations Using Computational Fluid Dynamics Combined With Asymptotics Applied to Laminar Mixed Convection in a Vertical Channel

Abstract In this work, a solution technique is proposed by synergistically combining asymptotics and computational fluid dynamics to ascertain a problem of laminar mixed convection heat transfer in a vertical channel. First, numerical simulation is carried out on a vertical channel that consists of an aluminum heater plate assembly at the center of the channel. The numerical model is treated as a conjugate heat transfer problem, and the concept of perturbation and blending is incorporated wherein the limiting solution of natural and forced convection is obtained in terms of average Nusselt number. These correlations are then blended to find a unified composite correlation that work very well for extreme limits of mixed convection. The Richardson number is chosen as an independent variable in the present analysis; as a result, the Nusselt number correlation is cogent for the mixed convection region. Upon performing the numerical simulations, the results of the mixed convection are then compared with experimental results available in the literature for the purpose of validation of the numerical solution. The results of the present work emphasize that, with minimum computational fluid dynamics (CFD) solutions, one can obtain a reasonably good composite correlation for the Nusselt number for mixed convection and also a substantial reduction of computations is possible ensuing an asymptotically flawless solution.

Numerical Study of Laminar Mixed Convection Heat and Mass Transfer with Phase Change in Vertical Channel

The present analysis is concerned with the effects of simultaneous heat and mass transfer phenomena on downward laminar flow of humid air in a vertical channel with isothermal wet walls using an elliptical formulation. The nonlinear partial differential equations describing the physical system was solved using the finite volume method implemented on a staggered mesh, the velocity-pressure coupling is processed by the SIMPLE algorithm. In this work, particular attention is paid to study the effect of the ambient conditions on evaporation rate of water. The major results show that the sensible heat is always transferred from the air to the walls; the latter must be heated when evaporation is important. In addition the evaporation rate increases noticeably with decrease of the Reynolds number and humidity of the inlet air.

Mixed convection in a lid-driven cavity containing triangular block with constant heat flux: Effect of location of block

The present work examines the two-dimensional, steady, laminar mixed convective fluid circulation and heat transfer in a square lid-driven cavity influenced by the change in the location of the triangular block with constant heat flux (CHF) thermal condition. The effect of the changes in the location of block along the vertical centerline (x=0.5,y) of the cavity has been explored. The dependence of various flow governing dimensionless parameters, 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 the streamline, temperature contours, Nusselt numbers, etc. has been illustrated. A normalized Nusselt number is also calculated for studying the difference in heat transfer rate with that of constant wall temperature condition. The results of the study indicates higher heat transfer rates for centered block position (Ly=0.5) than remaining two (Ly=0.25,0.75). For a given blockage, Nusselt number shows decline with increasing Ri. The summary of research is expressed by using two forms of empirical correlations (Nu¯=f(Ly,Re)),Nu¯=f(B,Re) for possible utilization in engineering design.

Mixed convection heat transfer from a triangular cylinder subjected to upward cross flow

Unsteady laminar mixed (forced and free) convection heat transfer and fluid flow over long horizontal equilateral triangular cylinder subjected to upward cross flow are investigated numerically. The computation model is a two-dimensional unconfined rectangular domain with an aspect ratio of 1.4. A second order upwind scheme was used for differencing of the convection terms, and SIMPLE algorithm was adopted. The working fluids are air (Pr = 0.7) and water (Pr = 7). The equilateral isothermal triangular cylinder is placed in a uniform stream. The effect of buoyancy is incorporated into the Navier-Stokes (NS) equations using the Boussinesq approximation. This study is a case of “assisting flow” where the buoyancy-induced flow and fluid motions have the same upward direction. The basic dimensionless simulation variables, Reynolds and Richardson numbers, are varied in the range 10 ≤ Re ≤ 200 and 0 ≤ Ri ≤ 10. The flow characteristics such as the mean drag, mean rms lift coefficients and the Strouhal number are computed for each simulation. The flow patterns and isotherms are generated to interpret and understand the underlying physical mechanism. The cylinder surface mean Nusselt number was computed for mixed as well as for forced and free convection conditions. The computational data were used to develop the several Nusselt number correlations for forced, free and mixed convection flow.

Numerical Investigation of Mixed Convection Heat Transfer in Steady Flow Past a Row of Three Square Cylinders

In this paper, the numerical simulations of laminar mixed convection heat transfer from row of three isothermal square cylinders placed in side-by-side arrangement are carried out to understand the behavior of fluid flow around those cylinders under gradual effect of thermal buoyancy and its effect on the evacuation of heat energy. The numerical results are presented and discussed for the range of these conditions: Re = 10 to 40, Ri = 0 to 2 at fixed value of Prandtl number of Pr = 1 and at fixed geometrical configuration. In order to analyze the effect of thermal buoyancy on fluid flow and heat transfer characteristics the main results are illustrated in terms of streamline and isotherm contours. The total drag coefficient as well as average Nusselt number of each cylinder are also computed to determine exactly the effect of buoyancy strength on hydrodynamic force and heat transfer evacuation of each cylinder.

Numerical study of the effects of surface roughness on the mixed convection heat transfer of a laminar flow inside a horizontal curved dimpled tube

The effects of surface roughness on the hydro-thermal performance of laminar mixed convection heat transfer of water have been investigated numerically. The geometry was a semicircular curved horizontal dimples tube with a fixed dimensionless radius of curvature (2R/D = 6.62) and dimensionless roughness height of e/D = 0.1. Under low values of Re (100,200,400) and Gr numbers (20,000.100000,400,000), a constant heat flux was imposed on the tube walls. The three-dimensional governing equations were discretized, using a finite volume method. Dimensionless temperature, convective heat transfer coefficient, axial dimensionless velocity contours, secondary flow vectors, and surface friction coefficient are presented and discussed. The results showed that for identical conditions, the dimpled tube has better thermal performance compared to a smooth tube, especially in low Re values. So that in the low Re values, the dimpled tube has 58.2% higher heat transfer coefficient in comparison with the smooth ones. However, this predominance in thermal characteristics is mitigated by increasing Re number. Additionally, it has been shown that the skin friction coefficient of a curved dimpled tube is less than that of a smooth one in low Reynolds values. Using Colburn j factor and friction coefficient (f), and presenting j/f versus Re shows that the dimpled tube is more efficient at Re < 200.