Transient convective heat transfer to water near the critical region in a vertical tube

Numerical analysis has been carried out to investigate transient forced convective heat transfer to water near the critical region in developing flow through a vertical tube. With large variations of thermophysical properties such as density, specific heat, viscosity, and thermal conductivity near the thermodynamic critical point, heat transfer in the tube is strongly coupled with fluid flow. Buoyancy force parameter has also large variation with fluid temperature and pressure in the tube. Time dependent characteristics of fluid velocity, temperature, and heat transfer coefficient with water properties are presented and analyzed. Transient Nusselt and Stanton number distributions along the tube are also compared for various pressures in the tube. Because of heat transfer from the wall transition behavior from liquid-like phase to gas-like phase of heat transfer coefficient occurs when the fluid passes through pseudocritical temperature region in the tube. Turbulent viscosity ratio also has steep variation near the pseudocritical temperature close to the wall.     

Optimization of Mixed Convection in a Lid-Driven Enclosure with a Heat Generating Circular Body

The physical model considered here is a lid-driven enclosure with bottom heating and top cooling conditions, and a heat generating circular body is placed at the center. The vertical walls of the cavity are kept thermally insulated, and the top lid moves at a constant speed. The steady two-dimensional governing equations for the physical problem are transformed in a dimensionless form with dimensionless governing parameters that decide the fluid flow and heat transfer characteristics in the system. The solution of these transport equations is obtained numerically with the finite element approach using the Galerkin method of weighted residuals. The parametric study has been carried out for variation of the heat generation parameters, the Reynolds numbers, solid-fluid thermal conductivity ratios as well as the Richardson numbers. The working fluid is assigned as air with a Prandtl number of 0.71 throughout the simulation. Results are presented in the form of streamlines, isotherms, average Nusselt number, bulk temperature, and drag force for the afore mentioned parameters. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as average Nusselt number, average bulk temperature, and drag force. An optimum combination of the governing parameters would result in higher heat transfer and lower drag force.     

Visualization of heat flow using Bejan’s heatline due to natural convection of water near 4 °C in thick walled porous cavity

A numerical study on natural convection heat transfer of cold water near 4 °C in a thick bottom walled cavity filled with a porous medium has been performed. It is assumed that the cavity is isothermally heated from the outside of the thick bottom wall and cooled from ceiling. The finite-difference method has been used to solve the governing partial differential equations of heat and fluid flow. Effects of thermal conductivity ratio, Rayleigh number and bottom wall thickness on heat transfer from the bottom to the ceiling have been studied. The heatline visualization technique has been used to demonstrate the path of heat transport through the enclosure. Moreover, streamlines and isotherms have been used to present fluid flow and temperature distributions. The obtained results show that multiple circulation cells are formed in the cavity and the local Nusselt numbers at the bottom wall and solid–fluid interface are highly affected by formed cells. The increase of Rayleigh number and thermal conductivity ratio increases heat transfer through the cavity. However, the increase of thickness of the bottom wall reduces the mean Nusselt number. Almost one-dimensional conduction heat transfer is observed in the solid bottom wall of the cavity.     

Analysis of temperature-sensitive magnetic fluids in a porous square cavity depending on different porosity and Darcy number

Magnetic fluids are thermo-sensitive and whose flow and energy transport processes can be controlled by temperature and external magnetic field. In the natural convection of porous cavity, magnetic force is not only the driving force, the effective gravity is also a force related to the natural convection, and the effective gravity is closely depending on the porosity and permeability of porous medium. As is known, the porous medium is in solid state with high heat capacity but low heat transfer coefficient, while the magnetic fluid is a kind of fluid with high heat transfer coefficient and easy to be controlled. Combining the complementary characteristic of magnetic fluids and porous medium, we present a study for temperature-sensitive magnetic fluids in a porous square cavity. In the study, a Lattice Boltzmann method is developed to simulate the laminar convection of temperature-sensitive magnetic fluids in a porous square cavity. We present numerical results for the streamlines, isotherms, magnetization for different values of porosity and Darcy number. In addition, Nusselt numbers on heated and cooled wall and the average Nusselt numbers are also investigated.     

Numerical simulation of natural convection heat transfer from a heated square cylinder in a square cavity filled with micropolar fluid

A numerical investigation has been performed to visualize the magnetohydrodynamic natural convective heat transfer from a heated square cylinder situated within a square enclosure subjected to nonuniform temperature distributions on the left wall. The flow inside the enclosure is unsteady, incompressible, and laminar and the working fluid is micropolar fluid with constant Prandtl number (Pr = 7). The governing equations of the flow problem are the conservation of mass, energy, and linear momentum, as well as the angular momentum equations. Governing equations formulated in dimensionless velocity and pressure form has been solved by Marker and Cell method with second-order accuracy finite difference scheme. Comprehensive verification of the utilized numerical method and mathematical model has shown a good agreement with numerical data of other authors. The results are discussed in terms of the distribution of streamlines and isotherms and surface-averaged Nusselt number, for combinations of Rayleigh number, Ra (10³–10⁶), Vortex viscosity parameter, K (0–5), and Ha parameter (0–50). It has been shown that an increase in the vortex viscosity parameter leads to attenuation of the convective flow and heat transfer inside the cavity.     

Analysis of mixed convection in an inclined square cavity using nanofluids with Vajjha and Das' nanofluid model

In this article, the effects of angle of inclination on heat transfer by mixed convection have been analyzed numerically in a square cavity packed with a CuO nanofluid. Cavity boundaries are constructed by having sinusoidal varying temperature on sidewalls, inactive horizontal walls, and the hot passing plate at the center of the cavity. The transport equations for fluid and heat are solved using the finite-volume method with SIMPLE algorithm. The Richardson number (Ri) varying from 0.01 to 100, inclination angle (γ) from 0° to 90°, wall speed ratios (λ) from 0 to 3 and volume fraction of nanoparticles (φ) from 0.0 to 0.1 are given and represented in the form of flow fields, temperature fields, and mean heat transfer graphs. It is detected that the principal flow constraints have a substantial impact on the flow lines and thermal lines. Specifically, the structures of cavity inclination, existence of copper nanoparticles, and the hot wall in motion at the midpoint of the cavity are established to enrich the overall rate of heat transfer. Correspondingly, in the present study, the Vajjha and Das model is taken into account for the effective thermal conductivity and viscosity of the nanofluid; application of this model is beneficial for the industries working in a high-temperature environment.     

Natural Convection Heat Transfer in a Cubic Cavity Submitted to Time-Periodic Sidewall Temperature

The laminar unsteady natural convection in a cubic cavity is comprehensively studied here using a high accuracy temporal-spatial pseudospectral method. In this study, the cavity is filled with air and one of its sidewalls is submitted to sinusoidally varying temperature, while constant lower temperature is imposed on the opposing sidewall and other sidewalls are adiabatic. Computations are performed to explore the effects of several influential factors on the fluid flow patterns and heat transfer performances within the cavity, including Rayleigh number and the amplitude and period of pulsating sidewall temperature. Numerical results reveal that the heat transfer enhancement is complexly determined by the above influential factors, and the heat transfer resonance is observed in the case of a large Rayleigh number and amplitude of pulsating sidewall temperature. The three-dimensional effects on fluid flow patterns and heat transfer are discussed. Finally, the backward heat transfer is quantitatively studied.     

Flow over porous blocks in a square cavity: Influence of heat flux and porosity on heat transfer rates

The heat transfer due to the flow over two porous blocks situated in a square cavity is investigated and the effects of heat flux and the porosity on the flow structure and the heat transfer in the cavity are examined. In the simulations, four heat fluxes and three porosities are accommodated while air is used as the working fluid. The flow conditions at the cavity inlet are kept the same for all the cases simulated. The equilibrium equations pertinent to the flow over porous blocks in the cavity are used to predict the velocity and temperature fields. It is found that increasing porosity of the blocks modifies the flow field in the cavity, which is more pronounced as the heat flux increases. The Nusselt number enhances with the increasing porosity and heat flux.     

Numerical analysis of mixed convection heat transfer of a high viscosity fluid in a rectangular tank with rolling motion

A numerical analysis is presented for the mixed convection heat transfer of a high viscosity fluid contained in a two-dimensional rectangular tank subject to rolling motion. The study is motivated by the thermal design of heating systems of a tanker in a wavy sea. Basic equations are given for the body (tank)-fixed coordinate system considering inertia forces acting on the fluid in the tank including centrifugal force, Coriolis force, etc. The isotherms and flow velocity vectors are determined by the numerical solutions of the basic equations. Similarity parameters are introduced, and their influence on the heat transfer is systematically examined.     

Peristaltic flow under the effects of an induced magnetic field and heat and mass transfer

Influence of heat and mass transfer on the peristaltic flow of pseudoplastic fluid in the presence of an induced magnetic field has been considered. The fluid is considered in a channel with non-conducting walls. Analysis have been made out under the assumptions of long wavelength and low Reynolds number. Series solution for the stream function, pressure gradient, magnetic force function, temperature and concentration distributions have been computed. The flow quantities have been examined for various interesting parameters. The pressure rise and heat transfer coefficient are also analyzed.     

Unsteady flow and heat transfer of a ferrofluid between two rotating,vertical moving and stretching disks

Unsteady flow and heat transfer of a magnetic fluid between two rotating disks is investigated. Both the disks are stretchable and the lower disk moves in the vertical direction. A new approach of similarity transformation is adopted to transform the equation of continuity, momentum, and the energy equation into ordinary nonlinear coupled differential equations. The numerical solution of the converted nonlinear differential equations is obtained using the finite element method. The effects of magnetization force, rotational viscosity, Prandtl number, and Eckert number on the velocity and temperature distributions are studied. The impact of stretching, movement, and rotation of the disk is also considered in this computational study. The skin friction coefficients and heat transfer rate on the lower disk for different physical parameters are calculated. Different types of motion of the disks and the magnetization force are crucial aspects in the stress distribution and heat transfer rate near the lower disk.     

Thermally dependent viscosity and non-Newtonian flow in a double-pipe helical heat exchanger

A double-pipe helical heat exchanger was numerically studied to determine the effects of thermally dependent viscosity and non-Newtonian flows on heat transfer and pressure drop for laminar flow. Thermally dependent viscosities were found to have very little effect on the Nusselt number correlations for Newtonian fluids; however significant effects on the pressure drop in the heat exchanger were predicted. Changing the flow rate in the annulus can significantly affect the pressure drop in the inner tube, since the average viscosity of the fluid in the inner tube would change due to the change in the average temperature.The effects of non-Newtonian power law fluids on the heat transfer and the pressure drop were determined for laminar flow in the inner tube and in the annulus. The Nusselt number was correlated with the Péclet number for heat transfer in the inner tube. For the annulus, the Nusselt number was found to correlate best with the Péclet number and the curvature ratio. Pressure drop data were compared by using ratios of the pressure drop of the non-Newtonian fluid to a Newtonian fluid at identical mass flow rates and consistency indices.     

Entropy generation and pumping power in a turbulent fluid flow through a smooth pipe subjected to constant heat flux

In a heat exchange process, heat transfer and pumping power requirements are the two main considerations. Efforts made to increase heat transfer in a fluid flow usually cause increase in the pumping power requirement. In an effort to avoid inefficient utilization of energy through excessive entropy generation, a thermodynamic analysis of turbulent fluid flow through a smooth duct subjected to constant heat flux has been made in this study. The temperature dependence of the viscosity was taken into consideration in determining the heat transfer coefficient and friction factor. It was shown that the viscosity variation has a considerable effect on both the entropy generation and the pumping power. Pumping power to heat transfer ratio and the entropy generation per unit heat transfer can become very large especially for low heat flux conditions.     

Numerical study of fluid flow and heat transfer in microchannel cooling passages

Numerical investigation was conducted for fluid flow and heat transfer in microchannel cooling passages. Effects of viscosity and thermal conductivity variations on characteristics of fluid flow and heat transfer were taken into account in theoretical modeling. Two-dimensional simulation was performed for low Reynolds number flow of liquid water in a 100 μm single channel subjected to localized heat flux boundary conditions. The velocity field was highly coupled with temperature distribution and distorted through the variations of viscosity and thermal conductivity. The induced cross-flow velocity had a marked contribution to the convection. The heat transfer enhancement due to viscosity-variation was pronounced, though the axial conduction introduced by thermal-conductivity-variation was insignificant unless for the cases with very low Reynolds numbers.     

Chebyshev Spectral Collocation Method for Unsteady Mhd Flow and Heat Transfer of a Dusty Fluid Between Parallel Plates

The unsteady magnetohydrodynamic flow of a dusty fluid and heat transfer between parallel plates in which the electrically conducting fluid has temperature-dependent viscosity is studied. Both the fluid and the dust particles are governed by the coupled set of momentum and energy equations. The Chebyshev spectral method in space and implicit backward difference in time procedure is presented, introducing physically Navier-slip conditions for both the fluid and dust particle velocities. The Hartmann number, viscosity parameter, and Navier-slip parameter influences on the flow and temperature are simulated.     

Transient natural convection with temperature-dependent viscosity in a square partially porous cavity having a heat-generating source

A numerical study is performed on the transient natural convection with a temperature-dependent viscosity inside a square partially porous cavity with a local heat-generating and heat-conducting source. The vertical walls of the cavity are kept at constant cooling temperature while the horizontal walls are adiabatic. The discrete heat-conducting and heat-generating source is located on the bottom wall. A porous layer is located under the clear fluid layer. Governing equations formulated in dimensionless stream function, vorticity and temperature variables with corresponding initial and boundary conditions are solved using implicit finite difference schemes of the second order. The control parameters are the Darcy number, Ostrogradsky number, viscosity variation parameter, height of the porous layer, and dimensionless time. The effects of these parameters on the average Nusselt number along the heat source surface, average temperature of the heater, fluid flow rate inside the cavity, as well as on the streamlines and isotherms are analyzed. The results show that porous layer thickness and viscosity of the working fluid are very good control parameters for optimization of the passive cooling system.     

The effects of variable viscosity and thermal conductivity on heat transfer for hydromagnetic flow over a continuous moving porous plate with Ohmic heating

A numerical study of heat transfer from boundary layer flow driven by a continuous moving porous plate is proposed. The flow with electrically fluid due to the plate in the presence of a transverse magnetic field and Ohmic heating was molded as a steady, viscous, and incompressible. Both viscosity and thermal conductivity were variable and considered only a function of temperature. Similar analysis with Chebyshev finite difference method (ChFD) was developed to solve the governing equations for momentum and energy and determine the skin-friction coefficient and heat transfer rate. As the magnetic parameter and variable viscosity parameter increase, the fluid temperature and skin-friction coefficient increase and the fluid velocity and heat transfer rate decrease. The fluid temperature increases and heat transfer rate decreases with an increasing Eckert number and thermal conductivity parameter. The skin-friction coefficient and heat transfer rate increase, whereas the fluid velocity and temperature decrease as the wall suction velocity increase.     

Effect of magnetic field on two-layered natural/thermocapillary convection

Heat transfer in a two-layered fluid system is of great importance in a variety of applications. Control and optimization of convective heat transfer of the immiscible fluids needs complete understanding of all phenomena, especially those induced by surface tension at the fluid interface. The present work is focused on rather complex convective flow and heat transfer phenomena in a cavity, which can be subject to both buoyancy and thermocapillary effects in addition to the influence of magnetic field applied for flow control. With the encapsulant liquid posing magnetic properties, a magnetic force can arise to either enhance or counterbalance the gravity effect when the cavity is placed in a non-uniform magnetic field. In our study, the velocity and temperature distribution of the system can be significantly altered to change the heat transfer by varying intensity and gradient of the applied magnetic field. Preliminary results of numerical computation presented here are for a two-layered liquid cavity MnCl₂·4H₂O and Fluorinert FC40 under various magnetic fields intensities.     

Convective heat transfer combined with surface radiation in a rotating square cavity with a local heater

The effect of surface radiation on laminar natural convection in a rotating cavity with a discrete heater has been analyzed numerically. The enclosure is insulated at the bottom and top, heated by a constant temperature from the discrete heater located on the bottom wall, and cooled by a constant temperature from the side walls. Governing equations with corresponding initial and boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The effects of surface emissivity, Rayleigh number, and Taylor number on the fluid flow and heat transfer have been studied. Obtained results have revealed that rotation can be a very good control parameter for heat transfer and fluid flow.     

An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannels

An analytical solution is presented to study the heat transfer characteristics of the combined pressure – electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier–Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt number is obtained for a constant wall heat flux boundary condition. The fully-developed temperature profile and the Nusselt number depend on velocity field, channel height, solid/liquid interface properties and the imposed wall heat flux. A parametric study is presented to evaluate the significance of various parameters and in each case, the maximum heat transfer rate is obtained.