CHARACTERISTICS OF NEWTONIAN HEATING ON ELECTRICALLY CONDUCTING WATER-BASED NANO-FLUID WITH IN PERMEABLE VERTICAL MICRO-CHANNELS

Micro-channels are extensively used in the electrical and medical industries to advance the heat transfer of cooling devices. For the present study, the heat transfer from a porous vertical micro-channel heat sink here in this work, nanofluid, was considered a working fluid inside the micro-channel. The four most commonly used nanofluid is considered during the work, that is and. The mixture of nano-sized copper and alumina particles is considered to be cool the micro-channel heat sink. The said physical model is translated into mathematical expressions are solved the governing equations analytically. It was observed that all the nano-fluids thermophysical properties vary with the addition of nano-particles, and thermal conductivity is increasing. The consequences of solid nano-particle, porosity and heat source slip parameter, Darcy number, Hartmann number, and slip length are 2 MANI RAMANUJA, G GOPI KRISHNA, HARI KAMALA SREE, S.R. MISHRA computed.


INTRODUCTION
The examination of incompressible viscous nanofluid free convection processes due to the importance of their existence in diverse physical measures such as heat exchangers, petroleum reservoirs, combustion modeling, and fire engine. The flow phenomena over the micro-channel are also generating a lot of attention since they have practical implications in accumulating for electronics and computers. Researchers and scientists have persistent because nano-fluids act as a unique heat transfer medium. They can get better conductivity of the fluids by adding tiny solid nano-particles, resulting in increased heat transfer for various applications.
Tuckerman and Pease [1] first heat sink researchers introduced a method for draining heat from a chip by pushing coolant via closed channels imprinted on the underside of silicon water.
Experimental, numerical, and theoretical investigations are the three types of studies conducted in this area. Ozoe and Okada [2] analyzed the influence of the magnetic field path in a cubical enclosure was investigated it using a three-dimensional numerical model. Oztop et al. [3] analyses using a finite volume approach the heat transfer and fluid flow induced by magnetohydrodynamic buoyancy in a non-isothermally heated square enclosure. The entropy created in a simple engineering system is proportionate to the energy destroyed, which is always destroyed owing to the Second Law. Koo and Kleinstreuer [4] discussed with a temperature rise, there is a more significant augmentation in thermal conductivity. Nayak et al. [5] analyses the influence of physical parameters on a water-based 23 Al O nanofluid using the KKL model.
The concept of nanofluid is demonstrated experimentally by Choi et al. [6] and examined when compared to a simple base fluid, an increase in thermal efficiency. These findings were subsequently tested in the experiment (Kang et al. [7]). Further, Eastman et al. [8]  Heat transfer and skin friction's analytical and numerical effects were also highlighted.
Hayat et al. [11] investigated the MHD nanofluid flow across a stretched surface with power-law velocity as an analytical problem. Domairry et al. [12] have examined shows the thickness of the momentum bounding surface grows as the volume fraction of nanoparticles enhances, whereas the thickness of the thickness of the thermal boundary layer diminishes. Sheikholeslami et al. [13] have investigated a revolving system with two horizontal plates, the flow of nanofluids, and heat transfer properties; their findings show that raising the nanoparticle volume percentage and the injection/suction parameter enhances the heat transfer rate at the surface for suction/injection.
The increase in heat conductivity was proportional to the particle size, according to Esfahani and Toghraie [14] and Beck et al. [15], but Anoop et al. [16] found the reverse. Aysha et al. [17] found that Cu-water nanofluid showed improved thermal enhancement trends than 23 Al O -water nanofluid when the Reynolds number was increased. Kirsch and Thol [18] and concluded micro-channel pin fin arrays were created using laser powder bed fusion and tested for pressure loss and heat transfer over a range of Reynolds numbers. Ambreen and Kim [19] examined the flow of nanofluids in the tube under laminar and turbulent conditions. They discovered that Brownian motion in nanofluids causes an enhancement in the heat coefficient near the intake.
Sun et al. [20] the variations of nanofluid heat transfer rate was investigated experimentally ( 32 Fe O /water) under the influence of the magnetic field within the horizontal circular tubes.
They established a relation between the intensity of the magnetic field and the pace of heat transmission. Kumar et al. [21] evaluated heat transfer rates for conventional fluid and nanofluid were numerically compared. ( 23 Al O / 2 HO) claimed that nanofluid resulted in for the reduction in temperature as well as a 70% boost in the dependability of electronic chips. Lahmar et al. [22] examined including a squeezing flow of water, the behavior of thermal conductivity, and heat transfer rate 32 Fe O / water with the effect of the magnetic field within two parallel plates. Nada et al. [23] investigated mixed convection flow in a lid-driven inclined square enclosure filled with a nanofluid. Manoju Kumar et al. [24] investigated an MHD nanofluid flows and generates entropy in a vertical channel with a deformable porous medium. Younes et al. [25] are discussed Advances of nanofluids in heat exchangers-A review.
According to the author's knowledge and information based on the above literature, the influence of limited nanofluid particles was considered. In the present study, a comparison of vertical micro-channels with equal heat transfer areas in different conditions is suitable for heat transfer.
Also, the impact of water and on the thermal performance of vertical micro-channels was considered. Considering all of the articles mentioned above, we studied the influence of the magnetic field and nanoparticles on the flow of nanofluid, which is examined by the vertical micro-channel via permeable surface with convective conditions. We studied three different types of nanofluids to investigate these effects, namely 23 Al O -water, water and Cu-water. Various non-dimensional situations were presented and analyzed using an analytical solution, leading parameters on velocity, temperature, thermal radiation, heat source, slip parameter, Darcy number, and Hartmann number, slip length.

PHYSICAL MODEL AND GOVERNING EQUATIONS
The laminar fully developed nanofluid flow and heat transfer in a vertical micro-channel are analyzed and the results. The two plates are separated apart by a distance h . We should have used a y-axis is perpendicular to the x-axis and the x-axis is vertically upwards in the plates. The fluid is a water-based nanofluid with three different types of nano-particles in it Cu and 23 Al O . The base fluid and incomplete nano-particles are considered to be in thermal equilibrium. Table 1 shows the thermophysical characteristics of nanofluids. In the equations of motion, temperature buoyancy forces are thought to have a linear effect on density.
Following ( [26, 27 & 28]) the MHD mixed convective vertical micro-channel nanofluid flow phenomena can be expressed as; Where u is the velocity of the fluid along the x -direction, The conditions of their respective boundaries are ( ) Using the dimensionless similarity variables listed below The governing equations (1) and (2) along with the boundary conditions (4) and (5)

SOLUTION OF THE PROBLEM
For the coupled differential equations, analytical solutions were obtained (7 and 8) given the view of boundary conditions (9 and 10) are presented here.

Case II: (The no-slip surface being heated -NSS)
For the coupled differential equations, analytical solutions were obtained (7 to 8) given view of boundary conditions (13 and 14) are presented here

VOLUME FRACTION
The Volume flow rate in the vertical micro-channel, which is given by

SKIN FRICTION
The between pure fluid, Cu -water, and water- 23 Al O . Nanofluid decreases with an increase in the thermal radiation parameter. It is evident that nanofluid Cu -nanofluid heat transfer rate is greater than 23 Al O nanofluid. The temperature profiles of the flow are seen to improve as the radiation parameter is increased. Physically, a rise in radiation allows heat to move, which improves to enhance momentum and the thickness of the thermal wall layer.
Supplementary, fig. 3 illustrates the impact of internal heat source parameter  on the temperature for pure water, Cu -Nano and 23 Al O nanofluid. By increasing  , exothermic reaction generates internal heat in the thermal system, This leads to a faster of the thermal field nanofluid Cu -water- 23 Al O . It is observed that high thermal conductivity nanoparticles improve heat transmission more than low thermal conductivity nanoparticles. The influence of rising values of the heat source parameter is to enhance the temperature of nanofluid particles namely Cu water and 23 Al O and water. The rate of transfer of heat energy on the surface can be enhanced by the addition of nanoparticles. Fig.4 shows the behaviour of velocity slip parameter  on pure water, Cu -nano and 23 Al O -nanofluid temperature. We observed an interesting effect that the profiles of nanofluid temperature, pure water, Cu -nano and 23 Al O nanofluid increase respectively, with the decrease in velocity slip parameter  . In coolants, the 23 Al O -water nanofluid provided better heat transfer velocity as contrast to a condensed water and Cu -nanofluid. However, as compared to water, the Cu -nanofluid has a higher thermal performance. Cu -nano and 23 Al O nanofluid velocity profile. Also, the curves displaying the influence of Darcy number for 23 Al O -water nanofluid lie connection the curves of Cu -water nanofluid, which indicates that Cu -water nanofluid displays higher stability as a comparison to Cu -water nanofluid in the current structure. Al O -water nanofluid is more than that of Cu -water nanofluid. The base fluid, water, has lower specific gravity than both the nanofluid and the nanofluid. Fig.8  Al O nanoparticles. Thermal conductivity increases with large particle size. Thermodynamic performance of two distinct nanofluids 23 Al O and Cu water nanofluids gives enhanced heat transfer than the base fluids water but Cu /water the MCHS has shown better thermal advantages than the water-based than the water-based 23 Al O . Fig.10 depicts the impact of  of nanofluid on the velocity profile of the flow. In particular, the 23 Al O nanofluid diminishes the thickness of the thermal boundary layer , which would be higher than the thickness of the Cu water solution. It shows that velocity has decreasing behaviour for large values of velocity slip parameter. It is effects for large slip parameter values; Cu water/nanofluid is slower than the hybrid nanofluid.    Table II shows the validation of the present analysis for the volume flow rate with the earlier work of Mani et al. [27] in case of pure fluid and the non-appearance of thermal radiation (SHS condition). Also it presents the behaviour in the case of nano-fluids. Further, it is observe that with an increase in M , the volume flow rate of nano-fluids in the vertical micro-channel decreases significantly. 16 MANI RAMANUJA, G GOPI KRISHNA, HARI KAMALA SREE, S.R. MISHRA  Table III illustrates the validation of the present investigation with the earlier study of [27] as well as the variation on the volume flow rate (NSS condition). In case of pure fluid both the results show their good correlation and it clarifies the convergence of the present methodology. It shows that with an increase in M , the volume flow rate of nanofluids in the vertical micro-channel decreases.

CONCLUSION
The effects of using common nano-fluids (e.g., 23 Al O / Cu /water) as a effective fluid for various thermal appliances should be examined. All of the investigations explored point to nano-fluids as a viable choice for the next generation of heat transfer fluids. Analyzing the effectiveness of ( 23 // Al O Cu water ) allows researchers to understand better the variables that influence thermo-physical properties and is highly reliant on nano-particle characteristics, temperature, and concentration. The influence of each component on 23 // Al O Cu water nano-fluids is shown in the following points.
• Comparative study of the current investigation concerning the earlier due to the flow of pure fluid exhibits the gateway to proceed for the further investigation with the help of metal and oxide nano-particles.