The commercial CFD software Fluent 12.0 is used to simulate the fluid **flow** and temperature field. A preprocessor GAMBIT is used to generate the required mesh for the solver. The governing equations are discretized using the finite volume method. The simple algorithm is used for the convective terms in the solution equations. The second order up winding scheme is used to calculate the **flow** variables. The solver iterates the equations till the convergence is obtained for the set residuals.

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convective boundary-layer **flow** of a nanofluid past a vertical plate. They made a correlation for the reduced Nusselt number and investigated the effect of buoyancy ratio, Brownian motion parameter and thermophoresis parameter. They used a model for the nanofluid incor- porates the effects of Brownian motion and thermo- phoresis as proposed by Buongiorno [5]. Very recently, Syakila et al. [9] studied Blasius and Sakiadis problems in nanofluids for various values of volume fraction.

In this research work, a conjugate problem of laminar **convection** **flow** of radiating gas inside a duct with sudden expansion is analyzed by numerical scheme. Toward this end, the Navier-Stokes equations along with gas energy equations are solved by CFD method for computations of the velocity and temperature fields in the gas **flow**. Since, the present problem is a conjugate one, the Laplace equation for conduction process inside the solid element must be solved simultaneously with the energy equation for gas **flow**. Also, for computation of radiative term in gas energy equation, RTE is solve numerically by employing the DOM. It is worth mentioning that the analysis of conjugate problem of separated **forced** **convection** **flow** of radiating gas in a channel in which the set of governing equations in both solid element and gas **flow** are solved simultaneously is done here for the first time. Numerical results reveal that thermal behavior of such system is much affected by the conduction ratio. Such that under the condition of having high values for K, more heat transfer takes place from the solid element toward the gas **flow**. Numerical results show that increasing in the value of RC parameter causes considerable increase in radiative Nusselt number along the gas-solid interface, but the convective Nusselt number is not much affected by the radiation conduction parameter. In the present analysis, it is seen that high rate of heat transfer takes place between the gas **flow** and solid element under high values of solid to gas conduction ratio, such that the parameter K has a great effect on temperature pattern inside the convective **flow**. Also it is found that minimum temperature on the solid to gas interface takes place just at the reattachment point, such that this minimum temperature increases by increasing in RC parameter.

The analysis of **convection** boundary layer **flow** along a vertical surface embedded in porous media has received considerable theoretical and practical interest. The **convection** boundary layer **flow** occurs in several industrial and technical applications such as electro-chemistry, solar collectors and polymer processing. Studies of boundary layer flows in a saturated porous medium have been considered by several authors. The first study of the free **convection** **flow** over a horizontal flat plate embedded in a porous medium was reported by Cheng and Chang (1976) and followed by Cheng (1977) for the mixed **convection** **flow** case. Hong et al. (1987) studied the Darcy-Brinkman **forced** **convection** **flow** over a fixed impermeable heated plate embedded in a porous medium. Mukhopadhyay and Layek (2009) analyzed the **forced** **convection** boundary layer **flow** over a porous plate in porous media with the radiation effects. Mahdy and Chamkha (2010) reported the effects of chemical reaction and viscous dissipation on Darcy-Forchheimer mixed **convection** along a vertical surface in a fluid saturated porous media. The steady **forced** **convection** **flow** and heat transfer past a porous plate placed in a fluid saturated porous medium using the Darcy model with partial slip was discussed by Bhattacharyya et al. (2011). Later, Mukhopapadhyay et al. (2012) have studied the steady **forced** **convection** boundary layer **flow** past a porous plate placed in a fluid-saturated porous medium using the Darcy-Forchheimer model taking into account the effect of thermal radiation. Bakar et al. (2014) considered the **forced** **convection** **flow** past a permeable plate embedded in a Darcy- Forchheimer poeous medium.

Nanofluids are best for applications in which fluid flows through small passages because nanoparticles are small enough to behave similarly to liquid molecules. Xuan and Roetzel[1] were showed that the thermal conductivity of the suspensions can increase by more than 20% causing increase in heat transfer rate. Maı¨ga et al.[2] developed numerical simulation for the hydrodynamic and thermal characteristics of a laminar **forced** **convection** **flow**. Results showed that heat transfer enhancement that appears to be more pronounced with the increase of the particle volume concentration is accompanied. Later, Akbarinia and Behzadmehr[3] Fully developed laminar mixed **convection** of a nanofluid numerically. they estimated water and Al 2 O 3 in 3-D horizontal curved tubes. They concluded that The nanoparticles volume fraction does not have a direct effect on the

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considers particle migration due to spatial gradients in both the viscosity and the shear rate, as well as the Brownian motion. Particle migration due to these effects could result in a significant non-uniformity in particle concentration over the tube cross-section, in particular, for large particles at high concentrations. The non- uniform particle concentration has a significant influence on the local thermal conductivity. Compared with the constant thermal conductivity assumption, the non uniform profile resulting from particle migration leads to a higher Nusselt number, which depends on the Peclet number and the mean particle concentration. Gilles Roy et. al. [28] in this paper they have investigated, by numerical simulation, the hydrodynamic and thermal characteristics of a laminar **forced** **convection** **flow** of Nanofluids inside a straight heated tube and a radial space between coaxial and heated disks. Two particular Nanofluids were considered, namely Ethylene Glycol- cAl 2 O 3 and

Abstract In the current work, a numerical analysis of the thermodynamic second law is investigated for the laminar **forced** **convection** **flow** in a duct adjacent to two inclined backward facing steps. For calculation of entropy generation from the second law of thermodynamics in a laminar **forced** **convection** **flow**, the velocity and temperature distributions are primarily needed. For this purpose, the governing equations including mass, momentum and energy equations are solved by computational fluid dynamic (CFD) techniques to obtain the temperature and velocity fields. For simulating the inclined surface, the blocked-off method is used. The effects of the inclination angle on the entropy generation and Bejan number are also presented. Comparison of numerical results with the available data published in open literature shows a good consistency.

In the present work, a numerical solution is described for turbulent **forced** **convection** **flow** of an absorbing, emitting, scattering and gray fluid over a two-dimensional backward facing step in a horizontal duct. The AKN low-Rey- nolds-number model is employed to predict turbulent flows with separation and heat transfer, while the radiation part of the problem is modeled by the discrete ordinate method (DOM). Discretized forms of the governing equations for fluid **flow** are obtained by finite volume approach and solved using SIMPLE algorithm. Results are presented for the distri- butions of Nusselt numbers as a function of the controlling parameters like radiation-conduction parameter (RC) and optical thickness.

Numerical simulations of a two-dimensional laminar **forced** **convection** **flow** adjacent to inclined backward-facing step in a rectangular duct are presented to examine effects of baffle on **flow**, heat transfer and entropy generation distribu- tions. The main aim of using baffles is to enhance the value of **convection** coefficient on the bottom wall. But the useful energy can be destroyed due to intrinsic irreversibilities in the **flow** by the baffle. In the present work, the amount of energy loss is estimated by the computation of entropy generation. The values of velocity and temperature which are the inputs of the entropy generation equation are obtained by the numerical solution of momentum and energy equations with blocked-off method using computational fluid dynamic technique. Discretized forms of the governing equations in the (x, y) plane are obtained by the control volume method and solved using the SIMPLE algorithm. Numerical expres- sions, in terms of Nusselt number, entropy generation number, Bejan number and coefficient of friction are derived in dimensionless form. Results show that although a baffle mounted onto the upper wall increases the magnitude of Nus- selts number on the bottom wall, but a considerable increase in the amount of entropy generation number takes place because of this technique. For validation, the numerical results for the Nusselt number and entropy generation number are compared with theoretical findings by other investigators and reasonable agreement is found.

In this study, the single phase model for numerical investigation of two dimensional symmetric steady, **forced** turbulence **convection** **flow** of nanofluid inside a horizontal circular tube was used. Moreover, nanofluids were assumed to be incompressible and non-Newtonian. Therefore, steady state conservation of mass, momentum, and energy equations were as follow [11]:

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where (c) is an unknown constant, and should be determined by matching experimental data. It depends on the diameter of the nanoparticles and flowing surface geometry. The comparison of the measured values of the nanofluid thermal conductivity with the calculated values from the proposed models indicates that the ther- mal dispersion is the main mechanism for enhancing fluid thermal conductivity inside channels filled with nanofluids under convective conditions. In fact, Equa- tion 11 is a first approximation considering the disper- sive effects of nanoparticles on the thermal conductivity of the nanofluid flowing through channels. According to the study of Khaled and Vafai [40] in which heat trans- fer of nanofluid **flow** in a channel was investigated, the range of the value of c was chosen to be from 0 to 0.4. Comparing this study (triangular duct) with the channel **flow** in the Khaled and Vafai ’ s investigation, the value of c = 0.3 is used in this study. In order to examine the exact value of constant (c), further experimental and numerical investigations are needed.

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Although previous investigations on the slip flows in porous micro-channels are important, many parts of the **flow** and heat transfer need to be resolved, especially when the thermal field is developing or LTNE prevails. In the present paper, attention is focused to analyze these effects simultaneously. For this purpose, **forced** **convection** heat transfer in porous micro-tubes is simulated numerically. Computations are undertaken for distinct cases with different values of the Knudsen number, the Darcy number, the Peclet number, the Forchheimer number, the Biot number, and the modified conductivity ratio. Results are presented in terms of velocity field, distributions of the fluid and solid temperatures, the local Nusselt number, and the thermal entry length.

**Convection** is the transfer of energy from one place to another by the motion of a mass of fluids between the two points. **Convection** occurs when particles with a lot of heat energy in a liquid or gas move and take the place of particles with less heat energy. Heat energy is transferred from hot places to cooler places by **convection**. Naturally, **convection** occurs when a solid surface is in contact with a fluid of different temperature from a surface. Density differences provide the force required to move the fluid (moisture) in the food. In the oven, the fluid involved is the enclosed air and the burner surface, which provides the solid surface, while the oven walls serve as the solid surfaces.

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packed porous medium for a Newtonian fluid **flow**, incorporating the variable porosity, permeability, thermal conductivity and solutal diffusivity in the presence of Internal heat generation (IHG) are varied. Here, the equations governing the physical system are highly coupled which are involved with non-linear partial derivatives are converted to ordinary equations analytically and solved numerically by shooting technique using Runge Kutta Fehlberg algorithm and Newton-Raphson corrector method to find the graphical representations for transport processes for different physical parameters.

and a portion of the liquid remains as a film on the wall. This type of venturi is recommended for hot gas **flow**, adhesives and corrosives dust [9]-[11]. They have shown that the fraction of liq- uid streaming as a film influences the collect efficiency and the pressure drop across the device. In the ejector type, the liquid is injected through nozzles by a pressure atomizer at the throat. This king of venturi is efficient for both particles and gaseous pollutants. Moreover, it is ideal for handling sticky or abrasive materials [12]. Despite their dangerousness for human health [13] [14], submicron particles have not been received much atten- tion in venturi scrubbing process. In these studies cited above, only large particles are considered and the collect hypothesis is only based on inertial impaction. To improve the submicron particles removal efficiency by im- paction, others mechanisms such as electrostatic attraction and condensation of water vapor on particles may be used [15] [16] to increase particles size. In others wet scrubbers, diffusion mechanism has been widely studied. Slinn [17], using dimensional analysis coupled with experimental data, gives correlation for single rain droplet collect efficiency. Jung and Lee [18] derive the collision efficiency due to Brownian diffusion and interception for a multiple fluid sphere system. As seen, diffusive effects have been neglected in venturi scrubbing process.

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branches of science and technology, such as its applications in transportation cooling of re-entry vehicles and rocket boosters, cross-hatching on ablative surfaces and film va- porization in combustion chambers. **Forced** convective boundary layer flows have a great interest from both theoretical and practical point of views because of its vast and significant applications in cosmic fluid dynamics, solar physics, geophysics, electronics, paper production, wire and fiver coating, composite processing and storage system of agricultural product etc.

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The three-dimensional characteristics of a **flow** undergoing an abrupt contraction inside a rectangular confined geometry under **forced** **convection** conditions are investigated in this work. A common practice to enhance the thermal performance of a heat exchanging configuration is to increase the total heat exchanging area using fins or multiple passages of the cooling fluid. Based on this concept, the heat sink under investigation comprises a series of rectangular channels that sustain an abrupt width reduction at the configuration mid-length. The first objective of the present study is to scrutinize the effect of the contraction on the **flow** field by illustrating the topology of the emerging vortical structures and identifying the mechanisms that cause their onset. Subsequently, the influence of the developing secondary-**flow** pattern on the temperature field and the overall heat transfer rate of the heat sink is investigated. The numerical results are presented for three values of the Reynolds number (Re 1 =519,1038,1557) that cover the entire laminar steady **flow** region.

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In recent years the process industries aim at the maximum output with reduced equipment size so as to minimize the unit product cost. This is particularly true in the design of electrolytic cells where the mass transfer limiting conditions exists. Various techniques have been adopted to augment the transfer rates. Use of rough surfaces is one of the several enhancement techniques reported by Bergler (Bergler, 1969), through which it is possible to achieve a two-fold objectives of maximum mass transfer rate with a minimum frictional pressure drop. Considerable work has been reported on the use of surface roughness elements and insert promoter. Augmentation is in mass transfer coefficient was reported with use of string of spheres (Sitaraman, 1997), string or discs (Venkateswarlu and Jagannadha Raju, 1987), spiral coil (Sethumadhavan and Raja Rao, 1983), coaxially placed cones (Sarveswara Rao, 1983) or twisted tapes mounted on a central annual rod (Sujatha, 1991), Discs (Venkateswarlu, 1987) and orifices[8] placed across the **flow** in conduit generate form friction both in upstream and downstream sides, thus generated friction continuous to show their effect on wall mass transfer coefficient along the cell. In earlier investigation where coaxially placed twisted tape–disc assembly (Sujatha kumara, 2003) employed as turbulence promoters in circular conduit, significant augmentation in mass transfer was reported. Studies on effect of coaxially placed square- grooved serrated disc in circular conduit on mass transfer rates in case of **forced** **convection** **flow** of electrolyte have not been reported.

and orientation. These are also known as hairpin vortices and have also been identified as a mechanism in near-wall turbulence [10] and in the **flow** field surrounding bluff bodies [11], [12]. Bubbles sliding under an inclined surface differ from rising bubbles in that they only experience the component of the buoyancy force parallel to the surface. This is true until the surface inclination angle is increased above a critical angle, at which point they begin to bounce. It is the sliding regime without bouncing that is under consideration here. Maxworthy [13] studied a bubble rising under a flat inclined plate, finding that the terminal sliding velocity did not scale linearly with Reynolds number or surface inclination angle. A later investigation by Perron et al. [14] showed that this terminal velocity instead had distinct regimes corresponding to different bubble shapes. Cornwell [7] identified the main contributions due to heat transfer from a vapour bubble as bubble nucleation, liquid disturbance and micro-layer evaporation. Houston and Cornwell [5] showed that the liquid disturbance induced by a sliding gas bubble with no phase change could account for significant heat transfer at low wall superheats. Qiu & Dhir [15] studied the heat transfer associated with a single vapour bubble as it grew and slid under a downward facing heated surface. The study found that a vortex located immediately behind the bubble enhanced heat transfer from the wall by introducing cooler liquid from the bulk to the surface. This was supported by the 3-D simulations of Li et al. [16]. Donoghue et al. [17] showed that the impact of an air bubble on a horizontal heated surface generated local heat transfer enhancement of up to 18 times natural **convection** levels.

straight microtube for efficient cooling purpose in various applications. Single-phase approach method is used to perform the simulations. In this analysis Reynolds numbers taken as a constant; from results studied that the heat transfer characteristics enhanced in case of nanofluids compared to water but for constant pumping power the results achieved from nanofluids were very close to water case coolant. That indicates; here nanoparticles did not effectively reduce surface temperature as compared to water base fluids. W. Escher et al. [7] used silica nanoparticles suspensions in aqueous medium for electronics device cooling through microchannels sinks. Authors studied nanofluids for three different sizes of nanoparticles and find out the thermal- characteristics by varying the **flow** rate through microchannels. They observed that size of nanoparticles affects the thermal-characterises of system. From all the above literature survey, it is evident that sufficient research has been carried with regard to mini or microchannels heat sink using different concentration of nanoparticles in base fluid and also for different geometry models for various applications. However, little has been reported with respect to specific study in case of IC chips for various combinations of nanoparticles and also by varying their concentration in different base fluids like in case of Ethylene glycol and water mixture type base fluid. Further optimises the dimensions of geometry, velocity, nanoparticles concentration and also study nanofluids effects on pressure drop which affect the pumping power. Therefore, in the present work this particular aspect will be investigated thoroughly with a view that an optimum geometric configuration and nanoparticles concentration in particular base fluid ought to have greater heat transfer coefficient and consequently leading to better cooling

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