Heat Transfer Optimization For Smooth Circular Tubes Biology Essay

An optimisation of heat transportation for smooth round tubing has been carried out to get minimal mercantile establishment temperature and maximal heat flux by utilizing Multi Objective Genetic Algorithm ( MOGA II ) . The tubing diameter with scope from 7 millimeters to 13 millimeters and length of tubing with scope from 0.5m to 1.2 m, have been varied to analyze the consequence the fluid flow and heat transportation of round tubings. The numerical analysis was performed by utilizing finite element commercial codification and the optimisation consequences show that the best design of round tubing is 7 millimeter for the diameter and 1.2 m for the tubing length which give the minimal temperature of 8.2 & A ; deg ; C at the mercantile establishment and maximal heat flux of 16190 W/m2.


With the increasing demand in power and energy over the universe, a batch of research has been conducted to analyze the little capacity system of soaking up chilling systems that can be used in residential and domestic applications. However, to redesign and optimise the overall system based on minimisation of refrigerating charge, the cost of production and running still a ambitious undertaking ( Misra et al. 2006 ) .

X. Zeng et Al. ( 2001 ) have conducted an experimental work of spray vaporization of ammonium hydroxide by utilizing spray noses. They found that spray vaporization heat transportation coefficient additions with the addition of heat flux along the tubings and consequences besides show that square-pitch package has higher spray vaporization coefficient when compared with the triangular-pitch package at low impregnation temperature. At a high impregnation temperature, triangular-pitch tubing is more likely to bring forth higher spray vaporization coefficient.

Ghajar and Tam ( 1995 ) proposed a new flow government map for forced flow laminar, passage and turbulent in horizontal round tubing with three different entrywaies ( re-entrant, square-edged and bell-mouth ) under uniform wall heat flux. The recommended map hpears to be really general for experimental but it still can be used to foretell the dath development and to the full developed flows. With cognition of Re and the parametric quantity Gr Pr at peculiar x/D location the government map can be used to place the convection heat transportation flow government pure forced or assorted for any three recesss.

H.A. Mohammed and Y.K. Salman ( 2007 ) investigated an by experimentation laminal combined convection heat transportation to thermally developing air flow inside a uniformly horizontal round cylinder. The consequence of Reynolds figure and the consequence of heat flux were determined. They found that the fluctuation of the surface temperature along the cylinder has the same form, and it would be higher for low Re than for high Re figure due to tip convection domination. It was concluded that the free convection effects tended to diminish the heat transportation consequences at low Re and to increase the heat transportation consequences for high Re.

Another survey on the flow inside the tubing was presented by ( Lap-Mou Tam and Afshin J. Ghajar 1998 ) . They investigated the behaviour of local heat transportation coefficient for the passage part of a round tubing with a bell-mouth entryway and uniform wall heat flux around the boundary. An experimental trial was carried out on the tubing with interior diameter of 1.584 centimeter and ethene ethanediol H2O mixture used as a working fluid. It was established that for a bell-mouth entryway the fluctuation of local heat transportation coefficient with the length is unusual and doing a dip in the Nu-x/D curve. The length of this dip is really short ( about 25 diameters ) in the disruptive part, nevertheless, the length of the dip in the passage part is much longer than in the disruptive part. This phenomenon causes a important influence on both the local and the mean heat transportation features of the tubing.

( B. Shome and M. k. Jensen 1995 ) analysis the thermic development and at the same time developing assorted convection flow with variable viscousness for both warming and chilling in isothermal horizontal round canals. From their analysis, the analysis that used in this survey is for unvarying wall temperature boundary status. It was found that consequence of variable viscousness was more marked on the fraction factor than Nusselt Number. They proposed correlativities that can be used for broad applications and acquire more accurate consequences.

( Alper Yilmaz 2008 ) Studied the optimisation of heat transportation in the tubing length for a turbulent flow in a smooth wall tubing, at changeless wall temperature for a given force per unit area loss. He found that for a certain tubing length to diameter ratio ( L/D ) in turbulent flow, the maximal heat transportation flux was depended on force per unit area Reynolds figure, Prandtl figure and local force per unit area loss coefficient, optimal value of L/D addition with Pr and Numberss. The maximal heat transportation flux addition with and lessening with Pr figure.

From the old surveies, most of the research workers have investigated the behavior of the fluid flow inside the pipes with different recess geometry and flow governments for free and force convection. Several surveies were besides carried out to analyze on the effects of boundary bomber bed on the heat transportation coefficient and different types of tubings packages.

However, the mercantile establishment temperature of the tubing in shell and tubes heat money changer has yet to be investigated.

Therefore, the aim of this survey is to optimise the design the round tubings inside the evaporator by utilizing Multi Objective Genetic Algorithm ( MOGA II ) method. The Navier-Stokes equation was employed to analysis the fluid flow and heat transportation inside the round tubing.

The usage of shell and tubing and spray vaporization with triangular tubing package as the heat money changer in the evaporators are broad, and the most of import point is how to acquire the optimal design for the heat transportation and to acquire the lower temperatures value in the tubes interior. The consequence of the sum of heat flux that additions from the chilled H2O inside the pipes should be studied.

In this survey probe of the fluid flow and the heat transportation inside a pipe which used in the evaporator of soaking up chilling system of 1.5 Ton refrigerant has been proposed. A fixed sum of flow rate of H2O inside the round tubing is studied. The survey on the design parametric quantities of different diameters and Lengths on the fluid flow and the heat transportation sum, at changeless wall temperature has been studied.

The survey on the design parametric quantity

The survey on the design parametric quantities for the tubings inside the shell and tubing heat money changer for an evaporator used in the soaking up chilling system is explain below. The consequence of tubing diameter and the length of the tubing is been studied to acquire the optimal heat flux from the tubing boundary and to acquire the minimal temperature organize the tubing outside. The consequence of design parametric quantity is studied for changeless mass flow rate inside the tubing, with variable physical belongingss depends on the temperature. The H2O is used inside the pipes ; the flow inside the tubing is laminal with different Reynolds.

? , u, T, In Water Out ? , U, T,

Mathematical theoretical account

This survey focuses on the optimisation of the fluid flow and the heat transportation inside round tubing. The equations that used in this survey to analysis the heat and fluid flow are:

The Energy equation

The cardinal jurisprudence regulating for the heat transportation is the first jurisprudence of thermodynamics, normally referred to as the rule of preservation of energy. Therefore the basic jurisprudence is normally rewritten in term of temperature, T. For a fluid, the ensuing heat equation is

( 1-1 )


Is the denseness ( Kg/m3 )

Is the specific heat capacity at changeless force per unit area ( j/ ( Kg.K ) )

Is absolute temperature ( K )

Is the speed vector ( m/s )

Is the heat flux by conductivity ( W/m2 )

Is the force per unit area ( dad )

Is the syrupy emphasis tensor ( dad )

Is the strain rate tensor ( 1/s ) :

Contains heat beginnings other than syrupy warming ( W/m3 )

By utilizing Fourier ‘s Law of conductivities, which states that conductive heat flux, Q, is relative to the temperature gradient:

( 1-2 )

Inserting equation 1-2 into equation 1-1, reordering the footings and disregarding syrupy warming and force per unit area work puts the heat equation on this signifier:

( 1-3 )

The Continuity and Momentum Equations:

The equations below represent continuity equation that refer to the preservation of mass, and the 2nd equation is the preservation of impulse and the 3rd one represented the preservation of energy, these three equations represent The Navier-Stokes equation used for the single-phase fluid- flow

( 1-4 )

( 1-5 )

( 1-6 )


Is the denseness ( Kg/m3 )

Is the speed vector ( m/s )

Is force per unit area ( dad )

Is the syrupy emphasis tensor ( dad )

Is the volume force vector ( N/m3 )

Is the specific heat capacity at changeless force per unit area ( j/ ( kg.K ) )

Is the absolute temperature ( K )

Is the heat flux vector ( W/m2 )

Contains the heat beginnings ( W/m3 )

Is the strain rate tensor: = )

Boundary conditions

The boundary status premise for the present survey is presented, for the tubing inlet the temperature of the fluid ( H2O ) is 293.15oK and the mean average speed from 0.34 m/s to 0.0662 m/s harmonizing to the different of interior diameter from 7mm to 13mm. the temperature of the mercantile establishment wall of the tubing is changeless and it ‘s equal to 278.15oK. The convective flux boundary status applied at the escape from the round tubing, this status states that the lone heat transportation over a boundary is by convection, the temperature gradient in the normal way is zero and there is no radiation ( COMSOL user ‘s usher heat transportation faculty ) . No-slip status of the flow on the inner wall pipe was applied. The fluid is Newtonian, Incompressible, with conveyance belongingss in depended of clip and place. The physical belongingss for the fluid inside the pipe depend on Temperature utilizing the Liquids and gases material library by COMSOL MULTIPHYSICS. The flow inside the pipe is laminal and developed with different Reynolds Number from 2089 to 1141. Incompressible Navier-Stockes equation with Convection and conductivity faculty is used in the analytic simulation. The tubing with Different Diameter between ( 7-16 m ) millimeter and the length of tubings from ( 0.5-1.2 m ) is used and the overall flow rate is 0.1197 kg/s. the changeless physical belongingss of stuff used for the pipes. The stuff used for the pipe is [ Steel AISA 4340 ] .

Numeric method

A COMSOL Multiphysics 3.5a is employed to work out this instance of survey. It is a powerful synergistic environment for patterning and work outing all technology and scientific job based on partial differential equations. COMSOL Multiphysics used Finite Element Method to work out the theoretical account. The package runs the finite component analysis together with adaptative engagement and mistake by utilizing different numerical convergent thinker ( user ‘s usher comsol multiphysics ) . . The convergent thinker that used is stationary analysis type and the additive system convergent thinker type used direct ( SPOOLES ) .

By utilizing excess all right engaging the figure of grade of freedom are 536118 and figure of mesh points 25443. Fig. 2. Show the mesh statistics, and fig. 3. The temperature profile and the speed profile for the fluid flow inside a 3D axisymmetric pipe theoretical account.

Fig. 2. Shows the mesh statistics

Fig. 3. Shows the profile temperature and speed for the flow inside the pipe

Consequences and treatment for the mathematical theoretical account simulation

The consequence of the Diameter and Length of the tubing on the heat transportation and fluid flow inside the pipe has studied. As reference antecedently the flow inside the pipe is Laminar and the instance survey assumes the flow inside the tubing is non to the full development harmonizing to the computation of hydrodynamic entry length computations. The consequence of Diameter and Length of the pipe are discussed.

Consequence of Tube diameter and Length on the heat flux

The heat Flux consequences present in Figs. 4 and Fig. 5 for different Lengths and Diameters, the consequences show that the best heat flux within the smallest diameter 7 millimeter and shortest length 0.5 m of the pipe, because of high Reynolds figure with high speed. And the ground of the shortest length pipe is referred to the changeless flow rate through the pipe. So the temperature difference between the recess and the out Lashkar-e-Taiba will be higher, harmonizing to the Newton ‘s jurisprudence of chilling for changeless wall temperature and changeless heat transportation coefficient. Therefore as the pipe length increases the heat flux will diminish. Besides from Figs. 4 the heat flux addition once more particularly for the big tubing diameter 10-13 millimeter this phenomena because the flow will be hydrodynamically to the full development and the difference between the majority temperature and surface temperature addition and at the same time the heat flux addition.

Fig. 4. Variation of heat flux at different Tube Diameter and Length

Fig. 5. Variation of heat flux at Different Tube Diameter and Length

Consequence of Tube diameter and Length on the mercantile establishment temperature

In fig. 6. And fig. 7. the temperature mercantile establishment of the fluid at different Diameter and tubing length is shown, the minimal temperature got within the smallest tubing diameter 7 ( millimeter ) and Longest Length of the tubing 1.2 ( m ) the ground behind that is for the highest Reynolds figure and largest surface country that conducted better heat transportation. Besides from the Figs it is obvious that the effects of the changing Length in little diameters are beggar than the big diameters.

Fig. 6. Variation of out let temperature with Different Tube Diameter and Length

Fig. 7. Variation of out let temperature with Different Tube Diameter and Length

Consequence of Tube diameter and Length on the Pressure Drop

The force per unit area drops along the tubing for different diameter has been presented. In Figs. 8. The force per unit area bead is a measure of involvement in the analysis of pipe flow. It is straight related to the power consume in the pump. In this survey the consequence of the Diameter and the length are explain for the changeless mass flow rate inside the tubing, from the figure the soap force per unit area bead appear in the smallest diameter and longest tubing and it is 7 ( millimeter ) Diameter and 1.2 ( m ) this phenomenon can explicate harmonizing to the Darcy equation

( 2-1 )

Where is the dynamic force per unit area and is the Darcy clash factor.

Fig. 8. Variation of Pressure bead with Different Tube Diameter and Length


Nowadays there is a tendency to increase the hardiness and public presentation of the design. The purpose of the optimisation is to increase the public presentation of the parametric quantities that used in the design. In the present work the optimisation undertaking has been carried out, by utilizing the powerful optimisation package viz. Mode FRONTIER. There are two design parametric quantities taken into history and three chief aims that needed to be achieved. Multi Objective Genetic Algorithm ( MOGA-II ) has been used to accomplish a set of optimum solution. MOGA-II proposed a set of alternate optimal solution named the Pareto frontier ( Augusto et al. 2006 ) . The aim of the optimisation is to maximise the heat flux along the tubing and maximise the temperature different between the recess and mercantile establishment flow, with logical force per unit area bead.

To get down the optimisation procedure, there is a parametric quantities should be arranged and puting in modeFRONTIER for the coveted design. Get downing with initial design of experiment ( DOE ) which consist of top angle angle and underside slant angle had been generated by utilizing Face Centered Cubic ( FCC ) method. The choice of the FCC method was to bring forth a good starting point for multi-objective familial algorithm ( MOGA-II ) which is available in manner FRONTIER. By utilizing the Data Wizard Tool, the initial consequences of simulations were imported into the Mode FRONTIER. The optimisation strategy was automatically generated as shown in Fig.9.

Fig. 9 ModeFRONTIER optimisation strategy

Before the multi-objective familial algorithm ( MOGA-II ) tally. The imported consequences were interpolated by Response Surface Modeling ( RSM ) based on the Gaussian Processes algorithm. Where ( RSM ) is a aggregation of mathematical and statistical techniques utile for the mold and analysis of jobs in which a response of involvement is influenced by several variable. The Gaussian Processes algorithm is a powerful arrested development theoretical account. This method is best suited for non-polynomial responses. After that the multi-objective familial algorithm ( MOGA-II ) has been run. In the concluding measure of the optimisation procedure the Multi Criteria Decision Making ( MCDM ) will be used. The MCDM help the determination shaper in happening the best solution from among a set of sensible options. In the MCDM attributes panel the determination measure has been done ( the input or end product of the undertaking and there dealingss ) . The purpose of the aims is to maximise the heat flux, minimise the temperature out and the force per unit area bead along the tubing. The weight of these aims is different harmonizing to the significance of these factors. In the present work the consequence of the force per unit area bead is negligible comparing with the consequence of heat flux and temperature bead. Because of the little sum of flow rate, so the consequence of the caput force per unit area with power consuming is little when you compare with the consequence of addition in heat flux. The heat flux is of import in this survey to see that the concentrated liquid ammonium hydroxide can be evaporated and changed to the saturated vapour by acquire the sum of heat. The weight of the temperature is more than the heat flux variable because in this theoretical account we need the minimal temperature out of the chilled H2O that supply to the fan spirals used in the air conditioning procedure and this is the purpose of good evaporator. From above the premise in the MCDM property panel is:

Temperature out E? 2.00 heat flux,

Heat Flux E? 2.00 Pressure bead,

Temperature out E? 4.00 Pressure bead.

Fig. 10. Shows the MCDM public-service corporation chart, besides shows the weights of different aims.

Fig. 10. MCDM public-service corporation chart

There are 1918 design points were generated by MOGA-II analysis from initial 19 initial populations. To do the concluding solution MCDM was used. The consequences of MCDM show that the best design that give the higher rank is the design 1 ( the tubing diameter 7mm and the Length 1.2 m ) . Fig 11 shows the Rank of the given designs.

Fig 11. The Rank of the given design


Numeric analysis and optimisation of heat transportation and fluid flow for round smooth tubing has been studied. The consequence of the tubing diameter and length was studied. It was found that the maximal heat flux occurs within smallest tubing diameter and shortest length for changeless wall temperature at changeless flow rate. The temperature out from the tubing has been presented and the lowest value founded within the smallest tubing diameter 7 ( millimeter ) and longest length of the tubing 1.2 ( m ) . The maximal force per unit area bead appears in the smallest diameter and longest tubing. It was concluded that the best design for the pipes has been found with 7 ( millimeter ) diameter and 1.2 ( m ) for 0.0133 ( kg/s ) by utilizing Multi Objective Genetic Algorithm. This method gave a set of optimum solution with different rank harmonizing to the weight of the input variables and aims.