Research PaperNatural convection heat transfer enhancement using nanofluid and time-variant temperature on the square enclosure with diagonally constructed twin adiabatic blocks
Graphical Abstract
Introduction
Nanotechnology is considered by many as the most attractive invention of the present century. Scientists are exploring various ways to extend its advantage to wide number of industrial applications. Due to abnormal growth of population and industries, energy demand becomes the biggest challenge for the developing countries. Technocrats prefer conservation over generation due to political, environmental and investment aspects. Convection consumes more energy than any other industrial applications. Natural convection is the most economic mode of convection among all the viable modes. Even though natural convection occurs at slow pace, it conserves huge amount of energy with low or no pollution. Some of the industrial applications of natural convection are cooling of electronic equipments, nuclear reactors, green buildings, solar collectors, growth of crystals in liquids, liquid storage structures etc. De Vahl Davis [1] presented the benchmark solutions for natural convection inside the closed cavity with differentially heated vertical walls for Ra = 103 to 106. Bennett and Hsueh [2] gave the benchmark results for natural convection heat transfer inside the closed cavity using 3-dimensional analysis with all the four walls either as adiabatic or conductive walls for Ra = 103 to 106 and indicated that 2-dimensional analysis results are identical to 3-dimensional analysis for Ra < 105. Mahapatra et al. [3] performed numerical analysis on natural convection with and without blocks inside the square cavity and revealed that heat transfer enhances with the increase of the Ra up to a certain block size, and then tends to decrease. Kalidasan et al. [4] performed the numerical analysis inside the open cavity with diagonally placed twin blocks and indicated that size of the blocks have huge impact on the heat transfer. Natural convection inside the cavity with sinusoidal variation of temperature on the walls was studied in References [5], [6], [7]. Recently, Zhu Huang et al. [8] studied 3-dimensional analysis on natural convection with time-periodic side wall temperature and indicated that the heat transfer enhancement is strongly dependent on Ra, amplitude, and the period. All the above studies have been performed with air as the working fluid.
Ahmed and Eslamian [9] studied the effect of thermophoresis force in a differentially heated enclosure filled with water–CuO nanofluid and found that Nu increases by 13% when comparing with pure fluid, out of which 5% is due to the thermophoresis force. Sahin Yigit et al. [10] investigated the effects of aspect ratio on natural convection of Bingham fluids in rectangular enclosures with differentially heated horizontal walls and demonstrated that thermal transport weakens with increasing aspect ratio for both the Newtonian and Bingham fluids. Eslamian et al. [11] also studied the effect of thermophoresis on natural convection in a square enclosure filled with a nanofluid and concluded that the thermophoresis force is a significant contributor to heat transfer augmentation for high Ra numbers (Ra > 106). Alloui et al. [12] conducted the numerical analysis on a rectangular cavity filled with different types of nanoparticles and heated at the bottom by uniform heat flux. They indicated that the addition of nanoparticles reduced the strength of flow field, particularly at low Rayleigh number. Kyo Sik Hwang et al. [13] numerically investigated the buoyancy driven heat transfer of water based Al2O3 nanofluids in a rectangular cavity and concluded that when the ratio of Rayleigh number of nanofluid to water decreases, the average temperature of nanofluid increases. Seok Ki Choi et al. [14] studied the natural convection of nanofluid inside the square cavity and pointed out that controversies between the numerical and experimental studies are owing to the different definitions of the Nusselt number. They revealed that slip mechanism of the Brown diffusion and thermophoresis effects are negligible in the laminar natural convection. Sohel Murshed and Nieto de Castro [15] recently reviewed the superior thermal features of carbon nanotubes based nanofluid and ionanofluid and concluded that both the fluids have superior thermophysical and heat transfer properties when comparing with base fluid. Zhang and Liu [16] revealed that the natural convection heat transfer enhancement is feasible by inserting multi-scale plates into the boundary. Faroogh Garoosi et al. [17] investigated the natural convection inside the square cavity with a pair of heaters and coolers and demonstrated that increasing the number of heaters is efficient than increasing the size of heaters for the heat transfer enhancement. Nasrin and Alim [18] numerically investigated the free convection on a square cavity with a hot diamond cylinder at the center. They used water based nanofluid with two nanoparticles (Alumina and Copper) and remarked that the mean temperature of the nanofluid decreases with increasing Pr and Ra. Zi-Tao Yu et al. [19] studied the transient natural convection heat transfer of aqueous nanofluid with CuO nanoparticles in a differentially heated square cavity and showed that the convective flow consumes longer time to attain the steady state as Ra is increased. Sourtiji et al. [20] numerically simulated the mixed convective heat transfer in a ventilating cavity with Al2O3–water nanofluid and concluded that the maximum Nu is obtained when the outlet port is placed in any one of the three corners. Ben-Cheikh et al. [21] performed numerical study on natural convection inside the square cavity with non-uniform temperature on the bottom wall. They used water based nanoparticles of Copper, Silver, Alumina and Titanium and indicated that the best way to delay the transition to the unsteady state is the increase of volume of nanoparticles. Basak and Chamkha [22] made a comprehensive research on natural convection with various types of nanofluid and various types of boundary conditions including the sinusoidal variation of temperature on the bottom wall of square cavity and concluded that sinusoidal variation of temperature on the bottom wall increases the heat transfer for all nanofluid. Sivasankaran and Pan [23] numerically studied the natural convection inside the square cavity filled with water based Al2O3 nanofluid along with the vertical walls exposed to sinusoidal variation of temperature. They described that the variations of the amplitude ratio and the phase deviation of the sinusoidal temperature distribution has a significant effect on its own wall, but they have very little effect on the opposite wall. Wang et al. [24] studied the natural convection of Cu–water nanofluid inside the square cavity with time-periodic temperature on the left wall and indicated that the addition of copper nanoparticles causes a remarkable increase in time averaged Nusselt number. Mehrjou et al. [25] has experimentally studied the heat transfer performance of CuO/water nanofluid through a square cross-section duct in the turbulent flow regime. Zeinali Heris et al. [26] experimentally investigated the laminar flow convective heat transfer of oxide nanofluids (CuO and Al2O3) and indicated that Al2O3–water nanofluid exhibits more heat transfer than CuO water nanofluid.
Due to poor thermal conductivity, liquids like water and oil consume more energy during the heat transfer. Heat transfer inside the enclosure containing obstacles and filled with liquid is needed in many industrial applications. The presence of obstacles like adiabatic blocks acts as a retarder during the convection process. One of the best ways to overcome the retardation effect during the heat transfer inside the cavity is utilizing the nanoparticles of high thermal conductivity along with base fluid. The other method for enhancing the convection is enforcing the dynamic variation of temperature in the boundary condition on one or two walls. The present investigation is to extend the advantage of nanotechnology to natural convection inside the enclosure with adiabatic blocks as retarders and dynamic variation of temperature as accelerator with an ultimate aim of conservation of energy. The cumulative effect of nanofluid and time-variant temperature along with the presence of solid blocks has not been studied so far and hence the present nucleus of research is on the natural convection of nanofluid inside the closed cavity with two adiabatic blocks exposed to sinusoidal time-variant temperature on the bottom wall.
Section snippets
Mathematical formulation
The schematic diagram of the system is presented in Fig. 1a. The length and height of the enclosure are denoted by L and H respectively with an aspect ratio of 1. The depth of the enclosure perpendicular to the plane of the diagram is too long and hence the problem is considered as 2-dimensional. The vertical walls are assumed as hot while the top wall is assumed as cold. The bottom wall temperature is assumed to vary sinusoidal over time as elucidated in Fig. 1b. Two adiabatic square blocks
Numerical procedure
The energy equation (4) in time has been initially solved by the Alternating Direction Implicit scheme. The temperature results are plugged in to the vorticity equation. Then the unsteady vorticity transport equation (2) in time is solved by the Alternating Direction Implicit scheme. Constant time step of 1 × 10−3 is used for the entire simulation. The iterations are terminated after sufficient number of cycles in the periodic state. Convergence criteria of 10−5 are used for velocity and stream
Results and discussion
Numerical simulation has been performed on the square enclosure with an aspect ratio of unity. The parameters considered in the study are Rayleigh number (Ra), volumetric fraction of nanoparticles (ϕ), amplitude (a) and period (). The nanoparticle considered in this research is copper (Cu). The copper solid particles used in the research are assumed as spherical and its diameter is assumed as 100 nm. The percentages of particle loadings are 0, 1, 2 and 4% like in Sivasankaran and Pan [23]. The
Conclusions
Two-dimensional numerical analysis has been performed by streamline-vorticity approach on the square cavity containing two diagonally placed adiabatic blocks and filled with copper–water nanofluid. Constant as well as time-variant temperature is considered on the bottom wall and the results are presented with streamlines, isotherms and Nu plots. Based on the study, the following conclusions are arrived.
- •
The diagonal placement of adiabatic square blocks ensued different intensities of heat
References (31)
- et al.
Buoyancy-driven flow in an enclosure with time periodic boundary conditions
Int. J. Heat Mass Transfe
(1992) - et al.
Natural convection in a differentially-heated square enclosure filled with a nanofluid: significance of the thermophoresis force and slip-drift velocity
Int. Commun. Heat Mass Transfer
(2014) - et al.
Effects of aspect ratio on natural convection of bingham fluids in rectangular enclosures with differentially heated horizontal walls heated from below
Int. J. Heat Mass Transfe
(2015) - et al.
Effect of thermophoresis on natural convection in a Rayleigh-Benard cell filled with a nanofluid
Int. J. Heat Mass Transfe
(2015) - et al.
Natural convection of nanofluids in a shallow cavity heated from below
Int. J. Therm. Sci
(2011) - et al.
Buoyancydriven heat transfer of water-based Al2O3 nanofluids in a rectangular cavity
Int. J. Heat Mass Transfe
(2007) - et al.
Optimum geometric arrangement of vertical rectangular fin arrays in natural convection
Energy Conv. Manage
(2010) - et al.
Numerical simulation of natural convection of nanofluids in a square cavity with several pairs of heaters and coolers inside
Int. J. Heat Mass Transfe
(2013) - et al.
Free convective flow of nanofluid having two nanoparticles inside a complicated cavity
Int. J. Heat Mass Transfe
(2013) - et al.
A numerical investigation of transient natural convection heat transfer of aqueous nanofluids in a differentially heated square cavity
Int. Commun. Heat Mass Transfer
(2011)
Natural convection of nanofluids in a shallow cavity heated from below
Int. J. Heat Mass Transfe
Experimental investigation of oxide nanofluids laminar flow convective heat transfer
Int. Commun. Heat Mass Transfer
Buoyancy-driven heat transfer enhancement in a two-dimensional enclosure utilizing nanofluids
Int. J. Heat Mass Transfe
Numerical simulation of natural convection of nanofluid in a square enclosure: effects due to uncertainties of viscosity and thermal conductivity
Int. J. Heat Mass Transfe
Natural convection in a square cavity containing a nanofluid and an adiabatic square block at the center
Superlattices Microstruct
Cited by (34)
MRT-LB simulation and response surface analysis of natural convection of non-Newtonian ferrofluid in an enclosure with non-uniformly heated radiator through GPU computing
2023, Engineering Analysis with Boundary ElementsApplication of nanofluids: natural convection in cavities
2023, Nanofluid Applications for Advanced Thermal SolutionsNatural convection cooling of aircraft wingbox structures during turnaround period
2022, Applied Thermal EngineeringEffect of different magnetic field angles on the relationship between nanofluid concentration and heat transfer
2022, International Communications in Heat and Mass TransferCitation Excerpt :Especially, the change in heat transfer rate due to the increasing nanoparticle concentration is one of the focuses of the free convection flow within a cavity. It can be found that the heat transfer rate is enhanced with the increasing nanoparticle concentration [9,10]. However, Sheikhzadeh et al. [11] and Esfandiary et al. [12] demonstrated that the slip mechanism accompanied by the adding nanoparticle will lead to a deterioration in the heat transfer rate.
Nanomaterial transportation and exergy loss modeling incorporating CVFEM
2021, Journal of Molecular Liquids