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When the temperature of an air conditioning unit’s fin surface goes below its dew point temperature, condensation forms on the unit’s surface. As a result, the cooling coil’s performance is compromised. By altering the cross-section and heat conductivity of the fins, the performance of such systems can be improved. This study aims to analyze the thermal performance of longitudinal fins made up of a variable thickness (assuming constant weight) and functionally graded material.

Different grading parameters are considered for an exponential variation of thermal conductivity. The humidity ratio and the corresponding fin temperatures are assumed to follow a cubic relationship. The Bvp4c solver in MATLAB^® is used to solve the differential heat transfer equation resulting from balancing heat transfer in a small segment.

Validation of the methodology is provided by previous research presented in this area. For different combinations of grading parameters, geometry parameters and relative humidity, the normalized temperature distribution along the fin length and fin efficiency contours are plotted, and the results are very promising.

When compared to the efficiency of an isotropic homogenous rectangular longitudinal fin with optimal geometry and grading parameters, a 17% increase in efficiency under fully wet conditions is measured. When it comes to fin design, these efficiency contour plots are extremely useful.

To find the optimal geometries of rectangular and cylindrical fins for maximum heat dissipation.

The objective function for finding the optimized profiles of fins are solved by using the genetic algorithms (GAs). A range of fin shapes are investigated and the optimum solutions for various profile area are obtained.

Provide information to thermal engineers to what extent any particular extended surface or fin arrangements could improve heat dissipation from a surface to the surrounding fluid. Smaller fin volume in fin design is preferable as the heat is dissipated more effectively.

A new method of using GA for optimization of fins is used here. The value of this paper lies in providing data for selecting suitable fins for thermal management in electronic systems.

Limited to cases where the correlations for heat transfer coefficients are valid.

A very useful finding for practising thermal engineer especially in the area of electronic packaging as the parameters for the fin design can easily be found for any chosen profile area.

The purpose of this paper is to study the thermal behaviour of a fully wet porous fin of longitudinal profile. The significance of radiative and convective heat transfer has been scrutinised along with the simultaneous variation of surface emissivity, heat transfer coefficient and thermal conductivity with temperature. The emissivity of the surface and the thermal conductivity are considered as linear functions of the local temperature between fin and the ambient. Darcy’s model was considered to formulate the heat transfer equation. According to this, the porous fin permits the flow to penetrate through it and solid–fluid interaction occurs.

Runge–Kutta–Fehlberg fourth–fifth-order method has been used to solve the reduced non-dimensionalized ordinary differential equation involving highly nonlinear terms.

The impact of pertinent parameters, such as convective parameter, radiative parameter, conductivity parameter, emissivity parameter, wet porous parameter, etc., on the temperature profiles were elaborated mathematically with the plotted graphs. The heat transfer from the fin enhances with the rise in convective parameter.

The wet nature of the fin enhances heat transfer and in many practical applications the parameters, such as thermal conductivity, heat transfer coefficient as well as surface emissivity, vary with temperature. Hence, the main objective of the current study is to depict the significance of simultaneous variation in surface emissivity, heat transfer coefficient and thermal conductivity with respect to temperature under natural convection and radiation condition in a totally wetted longitudinal porous fin.

This paper aims to study nonlinear heat transfer through a longitudinal fin of three different profiles.

A truly meshfree method is used to undertake a nonlinear analysis to predict temperature distribution and heat-transfer rate.

A longitudinal fin of three different profiles, such as rectangular, triangular and concave parabolic, are analyzed. Temperature variation, along with the fin length and rate of heat transfer in steady state, under convective and convective-radiative environments has been demonstrated and explained. Moving least square (MLS) approximants are used to approximate the unknown function of temperature T(x) with Th(x). Essential boundary conditions are imposed using the penalty method. An iterative predictor–corrector scheme is used to handle nonlinearity.

Modelling fin in a convective-radiative environment removes the assumption of no radiation condition. It also allows to vary convective heat-transfer coefficient and predict the closer values to the real problems for the corresponding fin surfaces.

The meshless local Petrov–Galerkin method can solve nonlinear fin problems and predict an accurate solution.

The purpose of this study is to conduct a numerical computation to analyse the thermal attribute and heat transfer phenomenon of a fully wetted porous fin of a longitudinal profile. The fin considered is that of a functionally graded material (FGM). Based on the spatial dependency of thermal conductivity, three cases such as linear, quadratic and exponential FGMs are analysed.

The governing equations are nondimensionalised and solved by applying Runge-Kutta-Fehlberg fourth-fifth order technique.

The parametric investigation is executed to access the significance of the pertinent parameters on the thermal feature of the fin and heat transmit rate. The outcomes are portrayed in a graphical form.

No such study has yet been published in the literature.

The integral transform method is employed for the hybrid numerical‐analytical solution of two‐dimensional, steady‐state heat conduction within extended surfaces of variable longitudinal profile and temperature dependent thermal conductivity. Numerical results are then obtainable with automatic accuracy, allowing for the establishment of benchmark results and for the validation of approximate solutions. Convergence rates are illustrated for longitudinal fins with trapezoidal and parabolic profiles, and for different values of the governing parameters, Biot number and aspect ratio. In addition, the classical one‐dimensional approximate solutions are critically examined for these typical non‐straight profiles, and the applicability limits are investigated.

The purpose of this paper is to determine the heat transfer and fluid flow characteristics of an internally finned tube for different flow conditions.

Numerical investigation have been performed by solving the conservation equations of mass, momentum, energy with two equation-based k-eps model to determine the wall temperature, outlet temperature and Nusselt number of an internally finned tube.

It has been found from the numerically investigation that there exists an optimum fin height and fin number for maximum heat transfer. It was also found that the heat transfer in T-shaped fin was highest compared to other shape. The saw type fins had a higher heat transfer rate compared to the plane rectangular fins having same surface area and the heat transfer rate was increasing with teeth number. Keeping the surface area constant, the shape of the duct was changed from cylindrical to other shape and it was found that the heat transfer was highest for frustum shape compared to other shape.

The present computations could be used to predict the heat transfer and fluid flow characteristics of an internal finned tube specifically used in chemical and power plants.

The original contribution of the paper was in the use of the two equation-based k-eps turbulent model to predict the maximum heat transfer through optimum design of fins and duct.

This study aims to numerically investigate the thermal-hydrodynamic performance of silicon oxide/water nanofluid laminar flow in the heat sink miniature channel with different fin cross-sections. The effect of the fin cross-section including semi-circular, rectangular and quadrant in two directions of flat and curved, and channel substrate materials of steel, aluminum, copper and titanium were examined. Finally, the analysis of thermal and frictional entropy generation in different channels is performed.

According to the numerical results, the highest heat transfer coefficients belong to the rectangular, quadrant 2, quadrant 1 and semi-circular fins compared to the channel without fin is 38.65%, 29.94%, 27.45% and 17.1%, respectively. Also, the highest performance evaluation criteria belong to the rectangular and quadrant 2 fins, which have 1.35 and 1.29, respectively. Based on the thermal conductivity of the substrate material, the best material is copper. According to the results of entropy analysis, the reduction of thermal irreversibility of the channel with rectangular, quadrant 1, quadrant 2 and semi-circular compared to non-finned channel is equal to 72%, 57%, 63% and 48%, respectively.

The rectangular and quadrant 2 fins are the best fins and the copper substrate material is the best material to reduce the entropy generation.

The silicon oxide/water nanofluid flow in the heat sink miniature channel with various fin shapes and the curvature angle against the fluid flow was simulated to increase the heat transfer performance. The whole test section is simulated in three-dimensional. Different channel materials have been investigated to find the best channel substrate material.

The purpose of this paper is to conduct a numerical study of the convection heat transfer in porous media by the homotopy analysis method (HAM). The geometry considered is that of a rectangular profile fin. The porous fin allows the flow to infiltrate through it and solid-fluid interaction takes place. This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The theory section addresses the derived governing equation. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed. The results suggest that the radiation transfers more heat than a similar model without radiation. The auxiliary parameter in the HAM is derived by using the averaged residual error concept which significantly reduces the computational time. The use of optimal auxiliary parameter provides a superior control on the convergence and accuracy of the analytic solution.

This study is performed using Darcy's model to formulate heat transfer equation. To study the thermal performance, three types of cases are considered namely long fin, finite length fin with insulated tip and finite length fin with tip exposed. The effects of the porosity parameter Sh, radiation parameter G and temperature ratio CT on the dimensionless temperature distribution and heat transfer rate are discussed.

The HAM has been successfully applied for the thermal performance of a porous fin of rectangular profile. Solutions are derived for three cases of tip condition: an infinitely long fin with tip in thermal equilibrium with the ambient, a finite fin with an insulated tip and a finite fin with a convective tip. The performance of the fin depends on three dimensionless parameters; porosity parameter Sh, radiation-conduction parameter G and a dimensionless temperature relating the ambient and base temperatures. The results show that the base heat flow increases when the permeability of the medium is high and/or when the buoyancy effect induced in the fluid is strong. The base heat flow is enhanced as the surface radiation or the tip Biot number increases.

The analysis is made for the Darcy's model. Non-Darcy effects will be investigated in a future work.

The approach is useful in enhancing heat transfer rates.

The results of the study will be interested to the researchers of the field of heat exchanger designers.

In hydraulically‐operated retractable wheels for aircraft the actuating member comprises a jack having a piston connected on one side with a motive pump and an exhaust, and on the other side with a hydro‐pneumatic pressure accumulator into which the liquid is forced by the jack during each lifting operation, the stored energy in the accumulator actuating the jack to assist the action of gravity when lowering the wheels. The retractable wheels R (Fig. 1) are each pivoted at A and connected to a fluid‐operated piston in a cylinder V pivoted at T, the wheels being drawn up into the machine through spring‐operated doors C1, D1 which are opened by fluid‐operated means G2 (Fig. 2) when the wheels are lowered. The cylinder V is connected by pipe 3 and non‐return valve 4 to a pump 1 supplied from a reservoir 2, surplus liquid being bye‐passed from the pump through a pipe 16. A pipe 5 for exhausting the cylinder V is connected through a manually‐operated valve 6 to the reservoir 5 and a branch 3a from the pipe 3 is connected to a cylinder 8 whereby pressure is applied to move valve 12 and non‐return valve 10 to place the other end of the cylinder V to discharge through pipes 3b, 3e to a pneumatic accumulator 9 supplied with air from a cylinder 14. When pressure is supplied by the pump 1 to the cylinder V to retract the wheels, a projection on the valve 12 opens the valve 10 and the liquid in the other end of the cylinder is forced into the accumulator 9, and when the wheels are to be lowered the valve 6 is opened by the lever 7 to exhaust one end of the cylinder into the reservoir 2 while the other end of the cylinder is supplied with pressure fluid from the accumulator. A pipe 17 from the pump 1 is connected to a cylinder G2 and is provided with a branch 18 and manually‐operated valve 19 whereby the cylinder may be exhausted. The cylinders G2 (Fig. 5) are connected by links to the doors C1, C2 maintained in the closed position by springs r1, r2, the doors C1, C2 being interconnected to open smaller doors D1 (Fig. 1) which remain open when the wheels R are lowered. The levers 25, 20, 7 (Fig. 2) are connected to a single control lever. In Fig. 10, the wheel arm J is pivoted at A and is connected by piston rod P to the cylinder V pivoted at T. A wire 35 connected to the arm J passes over pulleys 36, 37, and is connected to a piston in a horizontal cylinder 41 open to a pneumatic reservoir 9. When the wheel R is raised to the position R1 by the admission of fluid under the piston P, the wire 35 rapidly withdraws the piston in the cylinder 41 to compress the air in the accumulator 9, and since the effect of gravity is not so pronounced between the positions R, R1 as between R1, R2 and the fact that the air pressure on R tends to raise the wheel, the pressure applied to the piston P is mainly stored in the accumulator 9. From the position R to R1 the effect of air pressure is less and gravity greater, so that between these positions the wire 35 is adapted to lap around a pulley 43 on the axis A whereby the movement of the piston in the cylinder 41 is small and less power is stored in the accumulator 9, the pressure on the piston P being primarily expended in raising the wheel from R1 to R2. Similarly when lowering the wheel the accumulator expends the greatest power between R1, R. A device for recovering any leakage from the pump 1 when the reservoir 2 is at a higher level is shown in Fig. 9. A leakage pipe 28 is connected by a housing 29 and pipe 30 to the suction pipe 33, and the housing contains a float 31 with upper and lower needle valves. When the housing 29 is full of liquid, the pipe 28 is closed by the upper needle valve and the liquid in the housing is withdrawn through pipe 30 and when the housing is empty the float falls and closes the pipe 30.