This study investigates the heat augmentation and hydromagnetic flow of water-based carbon nanotubes (CNTs) inside a partially heated rectangular fin-shaped cavity. A thin heated rod is placed within the cavity to create a resistance or to provide a source for heat transfer. The obstacle is tested for the heated case, while the right side of the horizontal tip is tested for three different temperatures (adiabatic, cold, and heated). The left vertical side of the cavity is partially heated with temperature Th, and the rest of the sides are kept cold at temperature Tc except the right tip. Two different thermal boundary conditions (prescribed temperature and adiabatic) are employed on the fin tip. The CNTs and water are assumed to be in thermal equilibrium with no-slip velocity. The magnetic field and thermal radiation are introduced in the momentum and energy equations, respectively. The governing equations are obtained in dimensionless form by means of dimensionless variables. The numerical computation is performed via the finite element method using the Galerkin approach. The substantial effects of emerging parameters on the streamlines, isotherms, dimensionless velocities, and temperature are reported graphically and discussed. In the case of a cold or adiabatic fin-tip, a drop to minimum is found in the dimensionless temperature. The components of velocity are perceived maximum at a vertical corner while minimum at the horizontal corner. It is demonstrated that the local Nusselt numbers are increased by introducing both solid volume fraction of CNTs and radiation effects, while the Nusselt number noticed maximum at the corners.

Natural convection of water-based carbon nanotubes in a partially heated rectangular fin-shaped cavity with an inner cylindrical obstacle

This investigation reveals the flow patterns of natural convective hybrid nanofluid inside a square enclosure. The enclosure is presumed to be filled with water-based ferrous-graphene nanoparticles and multiple heated obstacles with various shapes. Three types of heated obstacles namely circular, square, and diamond are considered to visualize the flow patterns. The bottom and left-sided walls are presumed to be uniformly heated, whereas the top surface is adiabatic and the right-sided wall is made isothermally cooled. Moreover, thermal radiation and magnetic effects are supposed to exist within the flow region. A complete investigation is conducted to extract that how these different shaped heated obstacles influence the hydrothermal pattern. Appropriate similarity variables translate the dimensional equation into non-dimensional. Later on, Galerkin finite element scheme is introduced to deal with those nondimensional flow equations. The grid independence, comparison test, and experimental validation are conducted to exhibit the competency of the current model. Several isotherms, streamlines, velocity distribution, and average Nusselt number plots are depicted to perceive the parametric impact on such cavity flow. These plots are made for dimensionless factors such as Rayleigh number a $$\left( {10^{3} \le {\text{Ra}} \le 10^{5} } \right)$$
 , thermal radiation $$\left( {0.5 \le N \le 1.5} \right)$$
 , Hartmann number $$\left( {5 \le {\text{Ha}} \le 15} \right)$$
 , nanoparticle volume fraction $$\left( {0.00 \le \phi_{2} \le 0.04} \right)$$
 . The consequences imply that the isotherms intensify for Rayleigh number and extreme distortion is noted for circular obstacle, while other parameters disclose opposite scenario in isotherms. The average Nusselt number diminishes for Hartmann number but amplifies for nanoparticle concentration. The maximum increment in heat transport is predicted for Rayleigh number variation and circular obstacles. It is approximately 27.39%. The lowest enhancement is provided by diamond-shaped obstacles.

On the flow patterns and thermal control of radiative natural convective hybrid nanofluid flow inside a square enclosure having various shaped multiple heated obstacles

The constructal design-based model is reported to analyze the thermal control and heat augmentation inside a split lid-driven square cavity. A Y-shaped obstacle is placed within the cavity, which is filled with Al2O3–Cu–water hybrid nanofluids. The concept of the split-lid-driven cavity is utilized for the first time. The governing flow mathematical structure is obtained in terms of a system of partial differential equations and converted to a non-dimensional form through dimensionless variables. The numerical experiments are performed by employing a Galerkin finite element scheme for different values of involved physical parameters. The effects of pertinent parameters on the streamlines, isotherms, dimensionless temperature, and Nusselt numbers are investigated for different values of the Richardson number. Due to the simultaneous motion of the split-lids, the streamlines and isotherms show symmetrical distribution. The local Nusselt number increases with the moving split-lids and attains the maximum value when both lids meet. The average Nusselt number decreases with an increase in the Richardson number. It is important to note that the Y-shaped obstacle enhances the heat transfer rate in the cavity.

Finite element analysis of hybrid nanofluid flow and heat transfer in a split lid-driven square cavity with Y-shaped obstacle

This study investigates the free convection of Casson fluid inside a square cavity with intruded Y-shaped fin at the bottom surface. The Casson fluid is a non-Newtonian fluid and has an infinite viscosity at zero rates of shear. This is the first time that this fluid is used in the square cavity containing Y-shaped fin at the bottom surface. The Y-shaped fin helps in understanding the constructal theory and enhancing the heat transfer rate from the fin. The main objective of using this fin is to increase the convective heat transfer surface area. The sidewalls of the cavity are kept at cold temperature, the bottom surface at a hot temperature, and the top surface as adiabatic. The tips of the Y-shaped fin are considered as hot, cold, and adiabatic. The effects of the magnetic field and radiation are included in the momentum and energy equations. The influence of viscous heating is neglected. The buoyancy term is included in the momentum equation using Boussinesq approximation. The dimensionless governing equations are solved numerically using a Galerkin weighted residual technique of the finite element method. The effects of Rayleigh number (Ra = 104–106), radiation parameter (Rd = 0–103), Hartmann number (Ha = 0–103), and Casson parameter (γ = 0.1–1) on streamlines, isotherms, dimensionless velocity components, temperature, and local Nusselt numbers along the fin and the bottom heated wall are investigated and presented graphically. It is demonstrated that, in the presence of Y-shaped fin, all the pertinent parameters and dimensionless numbers help in enhancing the heat transfer rate along the bottom surface.

Non-Newtonian fluid flow around a Y-shaped fin embedded in a square cavity

Natural convection arising over vertical and horizontal heated flat surfaces is one of the most ubiquitous flows at a range of spatiotemporal scales. Despite significant developments over more than a century contributing to our fundamental understanding of heat transfer in natural convection boundary layers, certain “hidden” characteristics of these flows have received far less attention. Here, we review scattered progress on less visited fundamental topics that have strong implications to heat and mass transfer control. These topics include the instability characteristics, laminar-to-turbulent transition, and spatial flow structures of vertical natural convection boundary layers and large-scale plumes, dome, and circulating flows over discretely and entirely heated horizontal surfaces. Based on the summarized advancements in fundamental research, we elaborate on the selection of perturbations and provide an outlook on the development of perturbation generators and methods of altering large-scale flow structures as a potential means for heat and mass transfer control where natural convection is dominant.

Natural convection over vertical and horizontal heated flat surfaces: A review of recent progress focusing on underpinnings and implications for heat transfer and environmental applications

The phenomenon of natural convection in a square cavity filled with a copper-water nanofluid is investigated numerically. The studied domain is a square cavity with hot and cold isothermal walls at x = 0 and x = L, respectively, while the other walls are adiabatic. The fins are considered perfectly conductive with different lengths (Lf) and positioned at different locations. We examined the situation for Rayleigh numbers ranging between 104 and 106. The governing equations are expressed in the vorticity, stream function, and temperature formulation. The system of equations was solved by the finite difference method, using the upwind scheme. The computation code thus developed was used to analyze the effect of the different locations of the fins on the thermal performances. The obtained results were validated by comparing with those of a previously published work and with those obtained using COMSOL Multiphysics. It has been found that adding fins on the cold and adiabatic walls results in an increase in the average Nusselt number, while it decreases when the fin is located on the hot wall. That is to say, placing the fins on the cold and adiabatic walls increases the thermal performances of the transfer.

Numerical study of natural convection in a differentially heated square cavity filled with nanofluid in the presence of fins attached to walls in different locations

In this paper, we have studied the problem of natural convection in an inclined square cavity filled with a Cu/water nanofluid; this is done under a differentially heated configuration in the presence of a magnetic field which tracks the cavity in its inclination. The dimensionless governing equations formulated using stream function, vorticity and temperature have been solved by the finite difference method of second-order accuracy, where the upwind scheme is employed to discretize the convective terms. It turned out that the developed code requires a numerical validation. To do this, a comparison with previously published numerical and experiments results, as well as with the result of simulations under the COMSOL Multiphysics software was performed. The results thus found express very good agreement with the results of the developed code. Heat transfer and fluid flow are examined for parameters of nanoparticles volume fraction ($0\% \leq \phi \leq 20\%$), Grashof number ($ 10^{3}\leq Gr\leq 10^{5}$, Hartmann number ($ 0\leq Ha^{2}\leq 100$), and the cavity inclination angle ($ 0^{\circ}\leq\gamma \leq\pi/2$). Thus, it is found that a good enhancement in the heat transfer rate can be obtained by adding copper nanoparticles to the base fluid, as well as the increasing of Grashof number. However, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics.

Numerical modeling of natural convection in horizontal and inclined square cavities filled with nanofluid in the presence of magnetic field

In this study, we investigate the thermal behaviour of nanofluids in a double-pipe heat exchanger. It is about a counterflow configuration, designed to cool a lubrication unit of a thermoelectric power plant. The subject of this work is to evaluate the thermal performances of the exchanger by using a nanofluid based on alumina suspension comparing with deionized water. In order to evaluate the thermal performance of the studied configuration, we carried out numerical experiments in an application developed on COMSOL Multiphysics environment, these experiments are utilized to show the feasibility of this application. As result, we found that the nanofluid with an increase in its volume fraction leads to an increase in the overall exchange coefficient, the convective heat transfer coefficient, as well as the efficiency and the power of the exchanger. It is noted that an increase of 1% in volume fraction, can enhance the overall exchange coefficient, the power and the effectiveness of the exchanger by 17.62%, 1.473% and 10.80% respectively. Besides, it is noted that the increase in the concentration of nanofluids leads to a narrowing of the pinch points of the inlet and outlet temperatures, which means that nanofluids are more efficient in cooling temperatures than conventional fluids.

/pdf/numerical-and-experimental-investigation-of-alumina-based-3rryk06csb.pdf

Numerical and experimental investigation of alumina-based nanofluid effects on double-pipe heat exchanger thermal performances

Upwind scheme to solve time-periodic temperature effect on convective nanofluid flow in a square cavity

Numerical Study Of Natural Convection In Square Cavity Using Lattice Boltzmann Method: Obstacles Effect

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