Nonlinear rotating viscoelastic liquid convection with temperature modulation

In this study, heat transport in thermal convection of rotating viscoelastic liquids heated from below with temperature modulation is analyzed. The study is performed using Fourier series with a minimal representation. The constitutive relationship of the Oldroyd liquid B model is taken into consideration. The resulting Khayat–Lorenz model in the generalized form is solved using the numerical technique of Runge–Kutta–Fehlberg 45 with the adaptive grid method, and this solution is used to quantify the heat transport. The combined effect of the temperature modulation and Coriolis force on the thermal convection is investigated for various values of the amplitude of modulation and Taylor number. It is shown that the temperature modulation and Coriolis force lead to the enhancement of heat transport. As particular cases, the results of three liquids, namely Maxwell, Newtonian, and Rivlin–Ericksen, are obtained in the current study, which are found to have a good agreement with the available results.     

Turbulent heat transfer of natural convection between two vertical parallel plates

We measure heat transfer coefficients of natural convection between two vertical smooth parallel plates heated uniformly in the laminar, transition, and turbulent regions. The heat transfer characteristics are experimentally investigated with changing width, δ, between the vertical parallel plates, wall heat flux, q_w, overall watercourse length, L,of the vertical parallel plate and heating conditions. For natural convection between the vertical parallel plates, in the turbulent region of , the heat transfer is strongly suppressed owing to the effect of combined convection. On the contrary, the heat transfer in the laminar region is enhanced due to the tunnel effect. These tendencies become pronounced with decreasing δ and increasing L.The location of the heat transfer reduction shifts downstream with increasing q_w under a fixed δ. Furthermore, under smaller δ, we cannot clearly distinguish the transition process in accordance with both the heat transfer enhancement in the laminar region and the heat transfer reduction in the turbulent region. © 2001 Scripta Technica, Heat Trans Asian Res, 31(1): 56–67, 2002     

An experimental and three-dimensional numerical study of natural convection heat transfer between two horizontal parallel plates

In this study, experimental and three-dimensional numerical studies were performed to investigate the effects of plate spacing and temperature difference on natural convection between isothermally heated upward-facing lower horizontal plate and externally insulated horizontal upper plate. Air is used as the heat transfer medium. Rayleigh number varied in the 1108–2.339 × 10⁵ range. Several numerical simulations for three-dimensional steady laminar and turbulent flows heat transfer were carried out using a commercial CFD code Fluent 6.2. Results have shown that there is a good agreement between the numerical and present experimental results as well as with available data in literature.     

Natural convection heat transfer from upward-facing plates in saline water

Saltwater or brackish water is used as a coolant in most industries. Therefore, understanding the heat transfer processes and hydrodynamics during the natural convection in saline water is crucial for enhancing the efficiency of a heat exchanger. This study elaborates on the natural convection heat transfer in saline water under atmospheric conditions. A DC power supply is used to regulate the power given to the heater in a liquid pool for thermal analysis. The pool liquid comprises solutions with varying salinity from 0%, 0.2%, 0.5%, and 2%. The effect of varying salinity on the heat transfer coefficient and the thermal aspects encountered during the desalination process is analyzed. The temperature distribution across the surface of the heater is monitored using an infrared camera. It is studied for the solution of different salinities. The heat transfer coefficient and Nusselt number are investigated during natural convection for normal water and salt solution of different concentrations. It is inferred from the study that in the regime of natural convection, there is no significant difference in the Nusselt number for normal water and saltwater for the lower value of temperature difference between the plate and pool. The heat transfer coefficient in 0.2% saline water is higher as compared to the other solutions.     

Viscous dissipation effects on parallel plates with constant heat flux boundary conditions

This paper investigates basic analytical expressions for Nusselt number with the effect of viscous dissipation on the heat transfer between infinite fixed parallel plates, where the focus is on hydro-dynamically and thermally fully developed flow of a Newtonian fluid with constant properties, neglecting the axial heat conduction. Thermal boundary conditions considered are: both the plates kept at different constant heat fluxes, both the plates kept at equal constant heat fluxes, and one plate insulated. From the analysis, new expressions for Nusselt numbers have been found, as a function of various definitions of the Brinkman number.     

Effect of surface radiation on conjugate natural convection in a horizontal annulus driven by inner heat generating solid cylinder

This paper reports a numerical study of the laminar conjugate natural convection heat transfer with and without the interaction of the surface radiation in a horizontal cylindrical annulus formed between an inner heat generating solid circular cylinder and an outer isothermal circular boundary. Numerical solutions are obtained by solving the governing equations with a pressure correction method on a collocated (non-staggered) mesh. Steady-state results are presented for the flow and temperature distributions and Nusselt numbers for the heat generation based Grashof number ranging from , solid-to-fluid thermal conductivity ratios of 1, 5, 10, 50 and 100, radius ratios of 0.226 and 0.452 and surface emissivities of 0–0.8 with air as the working medium. It is observed that surface radiation reduces the convective heat transfer in the annulus compared to the pure natural convection case and enhances the overall Nusselt number.     

Non—Darcian and Anisotropic Effects on Natural Convection in Horizontal Porous Media Enclosure

Natural convection heat transfer in a horizontal enclosure filled with anisotropic porous media,being isothermally heated at bettom and cooled at top while the vertical walls being adiabatic,is numerically studied by applying the Brinkman model-a modified form of Darcy model giving consideratioin to the viscous effect.The results show that:(1)a larger permeability ratio(K^*) causes a lower flow intensity in the enclosure and a smaller Nusselt number,all Nusselt numbers approach unity in the limit of K^*→∞;a larger thermal conductivity ratio(λ^*) causes a stranger distortion of isotherms in the enclosure and a higher flow velocity near the walls,all the Nusselt numbers approach unity in the limit of λ^*-→0,the permeability and thermal conductivity ratios generally have opposing effects on the Nusselt number.(2) an increasing Darcy number decreases the flow intensity and heat tansfer rates,which is more significant at a lower permeability ratio.In particular,with K^*≤0.25,the Nusselt number for Da=10^-3 would differ from that of Darcy flow up to an amount of 30%,an analysis neglecting the non-Darican effect will inevitably be of considerable error.     

Effects of heat and mass transfer on MHD nonlinear free convection non-Newtonian fluids flow embedded in a thermally stratified porous medium

This communication examines heat alongside mass transport in a nonlinear free convection magnetohydrodynamics (MHD) non-Newtonian fluid flow with thermal radiation and heat generation deep-rooted in a thermally stratified penetrable medium. The Casson and Williamson fluid considered in this communication flos simultaneously across the boundary layer and are mixed together. The model of heat alongside mass transport is set up with chemical reaction and thermal radiation alongside heat generation to form a system of partial differential equations (PDEs). Appropriate similarity variables are used to simplify the PDEs to obtain systems of coupled ordinary differential equations. An efficiently developed numerical approach called the spectral homotopy analysis method was used in providing solutions to the transformed equations. A large value of Casson term is observed to degenerate the velocity plot while the Williamson parameter enhances the velocity profile. The parameter of thermal stratification is found to enhance the rate of heat transport within the boundary layer. An incremental value of the magnetic parameter declines the velocity of the fluid and the entire boundary layer thickness. The present result was compared with previous studies and was seen to be in good agreement.     

Natural convection heat transfer of high temperature gas in an annulus between two vertical concentric cylinders

Water cooling panels have been adopted as the vessel cooling system of the High Temperature Engineering Test Reactor (HTTR) to cool the reactor core indirectly by natural convection and thermal radiation. In order to investigate the heat transfer characteristics of high temperature gas in a vertical annular space between the reactor pressure vessel and cooling panels of the HTTR, we carried out experiments and numerical analyses on natural convection heat transfer coupled with thermal radiation heat transfer in an annulus between two vertical concentric cylinders with the inner cylinder heated and the outer cylinder cooled. In the present experiments, Rayleigh number based on the height of the annulus ranged from 2.0 × 10⁷ to 5.4 × 10⁷ for helium gas and from 1.2 × 10⁹ to 3.5 × 10⁹ for nitrogen gas. The numerical results were in good agreement with the experimental ones regarding the surface temperatures of the heating and cooling walls. As a result of the experiments and the numerical analyses, the heat transfer coefficient of natural convection coupled with thermal radiation was obtained as functions of Rayleigh number, radius ratio, and the temperatures and emissivities of the heating and cooling wall surfaces. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 293–308, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20070     

Soret and Dufour effects on free convection flow of non-Newtonian fluids along a vertical plate embedded in a porous medium with thermal radiation

This article numerically studies the combined laminar free convection flow with thermal radiation and mass transfer of non-Newtonian power-law fluids along a vertical plate within a porous medium. The solution takes the diffusion-thermo (Dufour), thermal-diffusion (Soret), thermal radiation and power-law fluid index effects into consideration. The governing boundary layer equations along with the boundary conditions are first cast into a dimensionless form by a similarity transformation and the resulting coupled differential equations are then solved by the differential quadrature method (DQM). The effects of the radiation parameter R, the power-law index n, the Dufour number D_f, and the Soret number S_r on the fluid flow, thermal and concentration fields are discussed in detail. The results indicate that when the buoyancy ratio of concentration to temperature is positive, N > 0, the local Nusselt number increases with an increase in the power-law index and the Soret number or a decrease in the radiation parameter and the Dufour number. In addition, the local Sherwood number for different values of the controlling parameters is also obtained.     

Influence of transverse vibrations on convective heat transfer in parallel flow tube-in-tube heat exchanger

Tube-in-tube heat exchangers are widely used in food processing industries and wastewater treatment for both heating and cooling. Enhancement techniques namely active, passive, and compound are developed to reduce the thermal resistance in heat exchangers by improving convective heat transfer with or without increase in surface area. The present experimental study is aimed at analyzing the influence of vibrations on the convective heat transfer of a parallel flow tube-in-tube heat exchanger. The heat exchanger is placed in horizontal position and is subjected to transverse vibrations under turbulent fluid flow conditions. Experiments were performed at four frequencies (20, 40, 60, and 100 Hz), three amplitudes (1, 2, and 3 m/s²), and three vibration generator positions along its length, in the Reynolds number range of 10 710 to 21 420. An enhancement in Nusselt number is found with vibration than without vibration throughout the entire range of Reynolds numbers. A maximum enhancement of 33% at 40 Hz frequency, 3 m/s² amplitude, and vibration generator position at three-fourth of the tube length was observed. Empirical correlations are developed for Nusselt number to determine the heat transfer coefficient with vibration with an error of $\pm$10%.     

Numerical simulation of natural convection heat transfer in the open space between two horizontal circular planes

Numerical simulations were conducted for natural convection heat transfer in a narrow gap between two horizontal plates in air. The lower plate is an infinite plate with a circular heating zone. The upper one is the bottom of a vertical cylinder, which is placed right above the circular heated plate and kept at room temperature. A set of Navier–Stokes equations and an energy equation are analyzed for a variety of combinations of gap clearance and Rayleigh number. The calculated average heat transfer values are shown to be in good agreement with the experimentally obtained ones reported in a previous paper. From the obtained isotherms, streamlines, and local Nusselt numbers, it is found that two types of convection appear in the gap space according to the conditions of Rayleigh number and gap clearance: one is a simple convection due to a single renewal flow which replaces heated air with ambient air and the other is a combined convection due to several vortex flows and a renewal flow. Furthermore, the flow rate of each flow controls the rate of heat transfer from the limited area which is covered by each flow. From this fact, the validity of the previously proposed heat transfer correlation is briefly discussed. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 485–502, 2001     

Natural convection heat transfer in the open space between two horizontal circular planes with different temperatures

A vertical cylinder maintained at room temperature is located right above a horizontal circular heated plane to constitute a narrow air space between the plane and the cylinder bottom surface. Natural convection heat transfer in the space is experimentally investigated. Average heat transfer coefficients of the heated plane are presented with the variation of space distance and Rayleigh number, and are compared with the predictions of the correlation equations which have been proposed for the space between two infinite parallel plates. Visualized flow patterns above the heated plane are also shown. The relation between the flow pattern and the heat transfer coefficient is discussed to clarify the mechanism of heat transfer in the narrow space. As a result, a heat transfer correlation is proposed, which is applicable over a wide range of space distances. © 2001 Scripta Technica, Heat Trans Asian Res, 30(6): 521–531, 2001     

Influence of Hall current on hydromagnetic natural convective flow between two vertical concentric cylinders in presence of heat source/sink

The fully developed laminar magnetohydrodynamic free convection between two concentric vertical cylinders with Hall currents and heat source/sink, in the presence of the radial magnetic field, are studied. The governing thermal energy and momentum equations are changed into ordinary differential equations whose solutions are determined in closed‐form expressions of the Bessel and modified Bessel functions of order zero. A parametric investigation illustrating the impacts of the Hall current, magnetic field, heat source, and radii ratio has been accomplished graphically to examine the changes in temperature as well as velocity while the Nusselt number, mass flux, and skin friction values have been presented in tabular forms. The results ensure that the Hall current has a strong and direct impact on the flow character, such that the influence of the Hall parameter enhances the velocity fields in the appearance of heat source and sink. The velocity remains almost constant as the Hall parameter value is greater than four. Moreover, the velocity and temperature fields have an increasing tendency due to the heat source and inversely for the heat sink.     

Internal gravity wave resonance of thermal convection fields in rectangular cavities with heat‐flux vibration (effects of aspect ratio on the fields)

In this paper the thermal convection field and its resonance phenomena in a rectangular cavity with heat‐flux vibration are numerically examined and the results are compared with those of a square cavity. As in the case of α=1, the critical angular velocity at which the relative amplitude of the midplane Nusselt number α_m has a local maximum agrees very well with the resonance angular velocity of the internal gravity wave ω_r, estimated by the theoretical equation proposed by Thorpe, even when the aspect ratio is α=5 and the Prandtl number is Pr=0.71 for a range of the Rayleigh number Ra. However, α_m has two local maxima for a larger Ra, which is peculiar to the case of larger α. The time variation of sub‐components of the fluctuating component of the midplane Nusselt number shows that the phase at the maximum value of α_m agrees well with that of the sub‐component of velocity for the first resonance angular velocity ω_r. For the other angular velocity ω_r2, the phase of α_m agrees with that of the sub‐component of temperature. Moreover, we found that the boundary angular velocity ω₀ between the first two of the five ω regions, which classify the thermal convection fields against ω, can be expressed by a function of α, Ra, and Pr and that α_m is independent of α and Ra for a relatively wide range of ω/ω₀. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(3): 158– 171, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20149     

Statistical approach on 3D hydromagnetic flow of water-based nanofluid between two vertical porous plates moving in opposite directions

The nanofluid flow between two plates is a common topic of research. However, studies dealing with the flow between two vertical plates moving in different directions have not been largely accounted for. The main aim of this study is to analytically and statistically investigate the MHD flow of water-based nanofluid between two vertical porous plates moving in opposite directions using perturbation technique and multiple linear regression, respectively. The consequence of various parameters on concentration, temperature, and velocity are examined via graphs using MATLAB software. It is observed that the main flow velocity profile is greater when the magnetic field is applied on the upward moving plate as compared to the main flow velocity when the magnetic field is applied on the downward-moving plate. The physical quantities are scrutinized using statistical tools like probable error and multiple linear regression and an excellent agreement is noted. It is noted that the Nusselt number is highly positively correlated with the injection parameter and highly negatively correlated with nanoparticle volume fraction. Furthermore, the simultaneous effects of parameters on drag coefficients are studied with the aid of three-dimensional surface plots.