non-intrusive techniques. The experimental results will complement ex- isting data at lower Rayleigh numbers available in literature. The main object is to extend the availability of accurate experimental data on natu- ral **convection** in differentialy heated cavities. This data can be exploited to validate different numerical methods, trying to capture the behavior of **turbulent** **natural** **convection** in the most efficient way. The work under- lined above is the graduation project of Andr´ e Popinhak, in which I was assigned to assist. The activities had already begun before the internship started and was not finished before the end of this period, therefore the subjects descibed are representative for the learned theory and performed tasks of the internee rather then a complete description of the research carried out.

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Due to the nature of the method employed to model this heat transfer process, obtaining justifiable approximation functions was among the first tasks to complete. The primary profiles to be determined were those of temperature and mean velocity in the vertical direction. Since the problem at hand involves **turbulent** **natural** **convection** along a vertical isothermal wall, the functions have to be representative of this type of flow. Initially, research focused on previous analyses and experiments conducted in flows where only air was present. It was felt that obtaining profiles from those problems would closely resemble the present problem.

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In the previous related research by Awuor (2012), the vorticity-vector potential formulation is used to eliminate the need to solve the pressure term in the momentum equation. In this particular research, the pressure term is instead solved using the PISO method and SIMPLEC methods which apply the primitive variable, and hence this is likely to change everything in terms of obtained numerical data for temperature and velocity, during the assessment of the performance of k- SST model in predicting heat transfer due to **natural** convention in an air filled cavity. Thus research will be important to engineering, industrial and agricultural systems that require engineering solutions which depend on this kind of mathematical model.

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Abstract: In present study a numerical analysis of complex heat transfer (**turbulent** **natural** **convection**, conduction and surface thermal radiation) in a rectangular enclosure with a heat source has been carried out. The finite volume method based on SIMPLEC algorithm has been utilized. The effects of Rayleigh number in a range from 10 8 to 10 11 , internal surface emissivity 0≤ε˂1 on the fluid flow and heat transfer have been extensively explored. Detailed results including temperature fields, flow profiles, and average Nusselt numbers have been presented. In this investigation it has been tried to study the shape of heat source influence on heat transfer and fluid field in the considered domain. According to results in low emissivity values usage of circular obstacles is recommended. Although in high emissivity values using rectangular obstacles lead to more efficiency.

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Wu and Lei (2015) studied **turbulent** **natural** **convection** in 2D and 3D with and without radiation transfer in heater cavities. Various Reynolds Average Navier-Stokes (RANS) turbulence model and the Discrete Ordinates radiation model were used in the numerical investigation. Further, Wu and Lei (2015) used quantitative and qualitative data for demonstration of the effects of three- dimensionality, thermal buoyancy condition and radiation transfer in surfaces that are horizontal. The derived simulation data from the numerical investigation are compared with the experimental data. The authors noted that when the radiation transfer was not accounted for the thermal boundary condition had an impact on the numerical solution on the horizontal surfaces. Moreover, it was deduced that variation of numerical results obtained when using three k-ε model were small. In the study, it was concluded that the k- ω SST model had the best overall performance while k- ω model had the worst performance.

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Abstract: In this Paper we will be dealing with **turbulent** **natural** **convection** in a long vertical pipe in which the flow is generated because of an unstable density difference across the two ends of the pipe. We create the density difference across the pipe using fresh water and brine. Since the density of brine is greater than that of fresh water, it tries to settle down while the fresh water tries to fill up the upper space. This creates collision of fluid masses in the pipe, leading to a **turbulent** flow at high levels of density differences. We will study the flow and its effect in the mid section of the pipe. Since water is an incompressible fluid, because of the density difference, the mass of fluid that goes up is equal to the mass of the fluid going down. Thus at any instant of time, the net flow will be zero at any cross section of the pipe. Since the length to diameter ratio (L/d ratio) of the pipe is around 9 to 10, the flow will be axially homogeneous. Thus we have an axially homogenous flow with zero mean velocity and which is purely buoyancy driven. This is the basic flow for our experiments.

Many analytical methods were employed previously to solve the problem of a vertical wall immersed in a thermally stratified environment. For instance, similarity solutions are used to extract a set of ordinary differential equations [44]. This method has been used in many cases such as non-isothermal vertical flat plate [45], an isothermal wall immersed in a partic- ular polynomial profile of thermal stratification [46], fixed wall temperatures [47], prescribed linearly increasing temperatures on both wall and the medium [48] and uniform heat flux [49]. Cheesewright [50] analytically studied **natural** **convection** heat transfer over a semi-infinite ver- tical plate immersed in a thermally stratified medium. The existing similarity solutions were generalized to include the effect of a non-isothermal surroundings. Scaling analysis was per- formed by Armfield et al. [51] on the **natural** **convection** boundary layer adjacent to an evenly heated semi-infinite plate with stratified ambient fluid. They obtained the scaling relations for the start-up, transitional and full development and reported that at full development, the stratified case had a region of two-dimensional flow near to the plate origin, while the remain- der of the flow, far from the plate origin, was one-dimensional. The scaling relations were confirmed by their numerical solutions, especially for the case of the one-dimensional region of the start-up, transitional and the fully developed flow as well as the two- to one-dimensional transition location.

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diameter and 900 mm heated length (L/D = 30), is subjected to a constant wall heat flux boundary condition. The study covers a Reynolds number ranges from 400 to 1600, the heat flux varied from 60 W/m 2 to 400 W/m 2 and with the cylinder inclination angle of h = 0 o (horizontal). The entrance sections included two long, calming sections, one with a length of 180 cm (L/D = 60), another one with a length of 240 cm (L/D = 80) and two short calming sections with length 60 cm (L/D = 20), 120 cm (L/D = 40). In all entrance sections, it found an increase in the Nusselt number values as the heat flux increases. It was reasoned that the free **convection** effects tended to diminish the heat transfer results at low Re while to increase the heat transfer results for high Re. Dogan et-al [5], (2006), with arrays of discrete heat sources studied experimentally mixed **convection** heat transfer within the horizontal channel. With insulated and adiabatic sides, upper and lower walls, from the experimental measurements, row- average surface temperature and Nusselt number distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers of these numbers were looked into. The answers establish that top and bottom heater surface temperatures increase with the increasing Grashof number. For high values of Grashof numbers where **natural** **convection** is the dominant heat transfer regime (Gr*/Re2 >> 1), temperatures of top heaters can deliver much larger value. Mare et-al [6], (2005), Laminar mixed **convection** in isothermal tubes has been studied numerically and experimentally The present work considers the three dimensional developing laminar flow of water with constant viscosity and conductivity in an isothermal pipe inclined of 60˚ from horizontal. At the beginning, the elliptic partial differential equations modeling, mixed **convection**, have been numerically solved using a control volume based finite difference solver for Re = 90, Pr = 7 and Gr = 3.3 × 10 5 .

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There is a fundamental difference between the maximal ray and the surface- or volume-based length approximations that becomes particularly important with regard to deformations of the convex hull: the maximal ray by deﬁnition runs along the direction of maximum extent of the convex hull. In contrast, the other two quantities yield averaged and isotropized approximations of the length scale probed by the hull, i.e. the radius of a reference sphere of same surface or volume. Spherical geometry is a **natural** ﬁ rst-order approximation of a convex hull or, more precisely, the convex polyhedron, which we use as its numerical representation, since convexity implies that the hull has no corner pointing inwards. This constraint severely restricts the complexity of the hull’s surface structure, since any such corner vertex would turn into an interior point enclosed by the hull. This results in an object which can mainly be deformed by ﬂattening of the inscribed spheroid along some direction perpendicular to the maximal ray. The convex hull is not material and therefore is not constrained by volume conservation in incompressible ﬂ ow. Although the possible length de ﬁ nitions do not show large qualitative differences compared to the maximal ray, their behavior relative to each other reﬂects the different responses of hull area and volume to deformations of the convex hull. This will be exploited in section 5.

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fluid exceeds a critical value of the Rayleigh-number, it starts moving, controlled by the temperature difference of the vertical, heated walls. The Prandtl number lies in this study at Pr = 0.71. The simulation assumes a non- Boussinesq fluid, consequently, temperature dependent fluid properties are calculated by the Sutherland model as stated in [2]. The computational geometry consists of a Cartesian block-structured mesh with 27 blocks. A scheme of the mesh can be seen in Figure 1, right picture. This mesh partition enables an exterior zone where a finer resolution can easily be chosen independently of the other blocks. Directly at the walls the mesh is clus- tered and the cell ratios decrease to the walls. In this way, all relevant **turbulent** scales can be resolved and no wall functions have to be considered. In the middle of the geometry, large scales of the flow are dominant. Thus, the mesh can have a coarser resolution in this region than close to the walls. The final mesh consists of

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Heat is a form of energy that can be transferred from one system to another system. There are three different ways for heat to be transferred which is: conduction, **convection** and radiation (A. Cengel, 2015). A temperature distinction is required for these methods of heat transferred to happen, and the heat dependably exchanges from areas of high temperature to lower temperature. The amount of heat transferred during the three process is denoted by Q while the heat transferred rate is denoted by .

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The present work is a continuation of the efforts discussed above. In order to introduce the hypothesis on the **turbulent** vortex dynamo into tropical cyclone research, a recent discovery of vortical moist **convection** in the tropics is empha- sized. Based on this finding, we discuss and substantiate the crucial role of ro- tating cumulonimbus clouds, known as vortical hot towers (VHTs), as a neces- sary element to provide the dynamo effect in conditions of tropical cyclone for- mation. Based on the mathematical model of the **turbulent** vortex dynamo in a convective system [13] and results of numerical simulation carried out for this model, an analogy is traced between the role of interaction “moist convec- tion—vertical wind shear” (described by a hypothetical “vortex-motive” force in the model) in creating the vortex dynamo in the atmosphere and the role of the mean electromotive force providing the magnetohydrodynamic (MHD) dynamo in electrically conducting medium. Bearing in mind an existence of excitation threshold for the large-scale helical-vortex instability predicted within the theo- retical model and confirmed by numerical analysis for this model, we propose introducing quantitative criteria, which take into account helicity, convective available potential energy (CAPE), and vertical wind shear (similarly to those applied for midlatitude severe storms), in order to use them for study and diag- nosis of tropical cyclogenesis.

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Forced **convection** heat transfer in non-circular ducts can find its application in many fields. Dittus-Boelter equation is widely used to calculate the heat transfer coefficient in the non-circular tubes (Batra et al., 1979; Barrow et al., 1985; Colombo et al., 2015; Ragueb et al., 2013). And the hydraulic diameter is used as the characteristic length for the Reynolds number in the Dittus-Boelter equation. However, Malák et al. (1975) studied several kinds of non-circular tubes using experiment method, and demonstrated that it is not accurate to calculate the **turbulent** **convection** heat transfer in the non-circular tubes using the hydraulic diameter method. Wang et al. (2014) also showed that this theory through numerical simulation and found that the maximum deviation would be 27.5% for the square cross-section. Aly et al. (2006) investigated the fully developed air-flows in an equilateral triangular duct over a Reynolds number range of 53,000-107,000, while friction factors were found to be about 6% lower than for pipe flow. Eckert et al. (1960) reported a numerical simulation of the isosceles triangle pipe with the length ratio of 5, and found that the coefficient of friction resistance that was calculated by using the hydraulic diameter method resulted in a relative deviation of about 20%. Based on the references above, it can be concluded that it is inaccurate to use the Dittus-Boelter equation to calculate heat transfer of **turbulent** **convection** in noncircular pipes.

nanofluids **turbulent** flow within an inclined copper tube under non-uniform heat flux of the upper wall and insulation of the lower wall by using two phase mixture model. According to the obtained numerical results, some equations are extracted to calculate the average Nusselt number and the wall surface friction coefficient in terms of Reynolds number changes and different inclinations of tube.

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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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); y: transversal coordinate (m); z: axial coordinate (m); Greek letters b: coefficient of thermal expansion (K -1 ); ε: dissipation of **turbulent** kinetic energy (m 2 s -3 ); : parti- cle volume concentration; l: thermal conductivity of the fluid (W m -1 K -1 ); ν: kinematics viscosity (m 2 s -1 ); μ: dynamic viscosity (kg m -1 s -1 ); r: density (kg m -3 ); τ: wall shear stress (Pa); Subscripts av: average value; b: bulk value; eff: effective; f: primary phase (base fluid); F: friction; k: kth phase; m: mixture (nanofluid); opt: optimum; out: outlet section; p: particle property; r: nanofluid/base-fluid ’ ratio; t: **turbulent**; T: heat transfer; w: channel wall; 0: inlet condition

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2) Process steps of thermal resistance measurement. The thermocouple made by K-Type wires was welded by hydrogen-oxygen welding machine. The temperature cor- rection was performed as follows: Fix the K-type ther- mocouple wires on the chip and place in the tempera- ture-controlled adiabatic oven. Adjust oven temperature within defined range of this experiment, the temperature output signals were collected by data capture device and kept for chip temperature in a stable condition. Then, setup three-dimensional closed test box, which was made of low thermal conductivity balsa wood in the size of 40 × 40 × 40 cm and placed it under **natural** **convection**. The device of sing

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Use of an internal energy distribution function gives stable results [16] as it considers pressure work and viscous heat dissipation [17] and thus the most stable thermal LBM method. Raisi et al. [18] simulated Cu–water nanofluid in a microchannel for both slip and no-slip conditions, ignoring temperature jump effects and applying the classic Navier–Stokes equations. Theoretical results of fluid flow in slip flow regimes or nanofluid flow simulation using LBM in a single or multi-phase mixture model has been reported [19]. Few studies of nanofluid simulation in microchannels using LBM [20] and [21] have ignored slip velocity and temperature jump effects, except in [1]. An accurate understanding of **convection** heat transfer of nanofluids in a microtube in the slip flow regime and the effect of temperature jump is not yet available in the literature.

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A prototype of motorcycle helmet fitted with three number of Peltier module (TEC 1-12706) is fabricated to study the cooling effect .as a second case heat sinks were fixed to each of the module at the outer surface of the helmet. The prototype is tested for its cooling performance under **natural** **convection** and forced **convection** conditions .The experimental results in the form of peltier inside and outside temperatures are presented at time intervals of 3 mins.The experiments were conducted during May 2017 when the ambient temperature are close to 400C.The experiment results indicate that the inside temperature of the helmet is reduced by about 60C as compared to ambient temperature within 20 mins.The temperature drop is found to be higher when heat sinks are attached.

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.