The extended technology applications of Micro-Electro-Mechanical systems have promoted abundant surveies of its fluid flow and heat transportation features. This work presented numerical simulation of to the full developed flow for characteristic laminar faux pas flow and heat transportation in diamond microchannels with the presence of radiation. The faux pas speed and temperature leap boundary conditions at the wall are performed. The effects of Reynolds figure, speed faux pas and temperature leap on Poiseuille figure and impact of the presence of radiation on Nusselt figure for different facet ratio is reported.

Analysis of unstable conveyance at microscale is of a great importance non merely for playing a cardinal function in the biological systems, but besides in a broad assortment of modern-day technology applications, affecting micro-scale devices such as microsensors, micropumps, and chilling electronic equipments. Microchannels nevertheless are the basic construction of these systems. Peoples realize that there are many differences between heat and flow transportation in Microchannels and channels with conventional size.

A figure of practical state of affairss involve heat transportation between a low-density gas and a solid surface. In using the term low denseness, we shall intend those fortunes where the average free way of the gas molecules is no longer little in comparing with a characteristic dimension of the heat transportation surface. The average free way is the distance a molecule travels, on the norm, between hits. The larger this distance becomes, the greater the distance required to pass on the temperature of a hot surface to a gas in contact with it. Obviously, the parametric quantity which is of chief involvement is a ratio of the average free way to a characteristic organic structure dimension. This grouping is called the Knudson figure which is defined as:

( 1 )

Beskok and Karniadakis [ 1 ] classified the gas flow in microchannels into four flow governments. They are continuum flow government ( Kn?0.001 ) , slip flow government ( 0.001 & A ; lt ; Kn?0.1 ) , passage flow government ( 0.1 & A ; lt ; Kn?10 ) and free molecular flow government ( kn & amp ; gt ; 10 ) .

In faux pas flow government, the Navier-Stokes and energy equations remain applicable, provided a speed faux pas and temperature leap are taken into history at the walls. Research workers have investigated theoretical, numerical and experimental surveies in microchannels along with speed faux pas and temperature leap boundary status at the walls [ 2-8 ] . Numeric analysis of to the full developed laminar faux pas flow and heat transportation in trapezoidal microchannels had been studied by Bin et Al. [ 3 ] with unvarying wall heat flux boundary status. In their probe, the influence of speed faux pas and temperature leap on clash factor and Nusselt figure were investigated in item. M. Shams and C. Aghanajafi has studied numerical simulation of faux pas flow through diamond microchannels without the impact of heat transportation through radiation [ 9 ] . Wei et Al. [ 10 ] investigated the steady province convective heat transportation for laminar, two dimensional, incompressible rarefied gas flow by the finite volume finite difference strategy with faux pas flow and temperature leap boundary conditions.

In this paper, a to the full developed laminar flow in a diamond microchannel with the presence of radiation is investigated. Numeric consequences are obtained utilizing a continuum based three dimensional, incompressible, steady theoretical account which is solved by a finite-volume method with slip speed and temperature leap boundary conditions applied to the impulse and energy equations, severally. The effects of rarefaction and aspect ratio on Poiseuille figure and Nusselt figure are studied. The influence of the presence of radiation on Nusselt figure is obtained.

## 2. Model apparatus

In this paper, microchannels with diamond cross subdivision are analyzed. The simulations are performed based on the undermentioned premises:

( 1 ) The regulating equations based on Navier-Stokes equations associated with slip boundary conditions that can depict faux pas flow governments in microchannels.

( 2 ) The flow is laminal.

( 3 ) The procedure is 3-dimensional incompressible steady flow.

( 4 ) The organic structure forces are neglected.

( 5 ) The energy equation with the presence of radiation is applied.

The ensuing governing equations are following:

Continuity equation:

( 2 )

Momentum equation:

( 3 )

where, u is the speed constituent, P is force per unit area, ? is the unstable denseness, µ is the dynamic viscousness.

Energy equation:

( 4 )

where, T is temperature, and cp is the specific heat at changeless force per unit area.

( 5 )

where is the Stefan-Boltzman invariable and K is the Rosseland average soaking up coefficient. Assuming that the optical deepness of the gas is sufficiently big and the temperature gradients are sufficiently little so that the local strength consequences from local emanations and besides can be expressed as a additive map of temperature

( 6 )

where the higher order footings of the enlargement are neglected.

The most common agencies of analytically or numerically patterning a rare flow within the faux pas flow government, 0.01?Kn?0.1, is through the usage of faux pas speed and temperature leap boundary conditions applied to the conventional continuum impulse and energy equations. The original faux pas speed boundary status and temperature leap boundary status were derived by Maxwell [ 11 ] and Smoluchowski [ 12 ] , severally.

( 7 )

( 8 )

where, u is the digressive speed, ? is the mean-free way of the molecules, ?? is the digressive impulse adjustment coefficient, ?T is the thermic adjustment coefficient, ? is the specific heat ratio of the gas, Pr is the Prandtl figure, µ is the viscousness, ? is the denseness and T is the temperature of the gas at the wall.

The first term in combining weight. ( 7 ) is the speed faux pas due to the shear emphasis at the solid surface, and the 2nd term is the thermic weirdo speed due to a temperature gradient tangential to the wall. These equations are presented in a format presuming a Cartesian co-ordinate system, a wall normal way ( Y ) , and a streamwise way ( x ) .

It should be noted that the streamwise speed and the temperature at the recess are unvarying and other constituent of speed are zero. The wall temperature is changeless. The speed gradients along the axial flow way are zero which means the boundary status at the mercantile establishment boundary is outflow. Obviously, the channel length is chosen so that the developing length can be neglected in comparing with the developed flow length and there is thermally and hydrodynamically developed flow at the mercantile establishment boundary.

The digressive impulse adjustment and the thermic adjustment coefficients vary between nothing and integrity. The digressive impulse adjustment coefficient is zero for mirrorlike molecular contemplation at the wall and it is unity for diffuse contemplation [ 13 ] . The thermic adjustment coefficient is zero if molecules hold their original temperature upon hit and it is unity if they gain the wall temperature. In this paper these coefficients are assumed as integrity. The specific heat ratio of the gas ? is equal to 1.4.

## 3. Numeric theoretical account

In this paper the diamond microchannel is studied. The aspect ratio AR is defined as:

( 9 )

where, H and B are horizontal and perpendicular diameters of the diamond channel, severally. In order to make to the full developed status the length is sufficiently long.

The 3D, incompressible, laminal, steady province impulse and energy equations are used. The commercial CFD package FLUENTTM [ 15 ] version 6.0.12 is employed to work out the regulating equations. The SIMPLEC is used to associate the force per unit area and speeds. In order to guarantee the choiceness of the computational grid spacing a grid independence trial is performed. To look into the influences of the faux pas boundary conditions a codification is included in FLUENTTM v.6.0.12. The remainders are considered 10-6 to make accurate consequences and convergence of the solution. A grid independence cheque is included to guarantee that the solution is independent of grid size.

## 4. Validation

To set up that the numerical process accurately theoretical accounts the faux pas flow government, some comparings are performed. Poiseuille Numberss have been compared with analytical values harmonizing to Po=24/ ( 1+12Kn ) in Table 1 that shows good understanding. In Table 2, the Nusselt figure have been compared with the consequences of Reinksizbulut [ 7 ] for Kn=0 through a scope of Reynolds figure. The comparings have been performed for parallel home bases. The facet ratio has been chosen sufficiently big that the channel geometry tends to parallel home bases. Another instance of proof is presented in Table 3 in which contains the consequences of this research and the consequences of Morini [ 14 ] . The consequences are wholly in agreement with the Morini ‘s consequences for different value of ? ( ? is the ratio of Poiseuille figure at Kn=0 to Poiseuille figure at non-zero Kn ) .

Table 1

Fully developed Poiseuille figure for parallel home bases.

Knudsen figure

Poiseuille figure

Analytic Consequences

Present Consequences

## %

0

24

23.9741

0.11

0.005

22.64

22.6117

0.13

0.01

21.43

21.3524

0.36

0.05

15

15.064

0.43

0.1

10.91

10.9845

0.68

Table 2

Fully developed Nusselt figure for parallel home bases.

Reynolds figure

Consequences of Reinksizbulut [ 7 ]

Present Consequences

0.1

8.105

8.124

1

8

8.046

5

7.741

7.801

10

7.624

7.660

Table 3

Fully developed Poiseuille figure for rectangular microchannel.

Kn=0

Kn=0.001

Kn=0.01

Kn=0.1

Consequences of [ 14 ]

Present consequences

Consequences of [ 14 ]

Present consequences ?

Consequences of [ 14 ]

Present consequences ?

Consequences of [ 14 ]

Present consequences ?

Aspect ratio

1

14.227

14.211

0.992

0.992

0.926

0.928

0.565

0.571

0.6

14.979

14.939

0.992

0.992

0.923

0.924

0.551

0.556

0.2

19.071

18.944

0.99

0.99

0.907

0.91

0.496

0.506

## 5. Consequences and treatment

## 5.1. Fully developed non-dimensional speed

The non-dimensional maximal speed and speed faux pas for AR=1 and changing Knudson figure are shown in Fig. 1. As shown in this figure the speed at the wall is zero for Kn=0. This figure shows that the speed faux pas at the wall increases with increasing Kn, which means that the faux pas speed increases as the consequence of rarefaction becomes more important. Besides it is obvious in this figure that the maximal speed in the centre of the channel decreases, when Knudson figure additions. The fluctuations of the to the full developed non-dimensional maximal speed and speed slip with different facet ratio and Kn=0.01 are shown in Fig. 2. As shown in this figure, the maximal speed in the centre of the channel decreases when the facet ratio of the channel increases. It is shown that, increasing the value of aspect ratio augments the faux pas speed.

## 5.2. Hydrodynamic features

Poiseuille figure is one of the most of import parametric quantities in fluid flow which is the merchandise of clash factor and local Reynolds figure. The effects of rarefaction, aspect ratio and Reynolds figure on Poiseuille figure on diamond microchannels are shown below. Fig. 3 shows the influence of Reynolds figure on Poiseuille figure for different rarefactions and unity facet ratio. As seen in Fig.

3, the fluctuations of Reynolds figure have small consequence on Poiseuille figure for a fixed rarefaction. It can be concluded from this figure that Poiseuille figure decreases with increasing value of Knudson figure. Fig. 4 shows the Poiseuille figure as a map of aspect ratio for different Reynolds figure and at Kn=0.01. As seen in Fig. 4, Poiseuille figure additions with increasing value of aspect ratio, and as shown in this figure, the fluctuations of Reynolds figure have small influences on Poiseuille figure. Variation of to the full developed Poiseuille figure with aspect ratio for different Knudsen figure at Re=10 is the intent of Fig. 5. It is obvious in Fig. 5 that Poiseuille increases with increasing value of aspect ratio for a fixed Knudsen figure. As seen in this figure the facet ratio is more effectual when it is less than 0.7 and at greater values than this aspect ratio, the Poiseuille figure is changeless for a fixed rarefaction. This figure besides shows that Knudsen figure can well impact on Poiseuille figure, in which Poiseuille figure reaches its upper limit when Knudsen figure is equal to zero, i.e. no slip status, and so increasing the value of rarefaction reduces the value of Poiseuille figure.

## 5.3. Heat transportation

The most of import parametric quantity in heat transportation is the ratio of convective to conductive heat transportation across the boundary which is called Nusselt figure. The mean local heat transportation or the local Nusselt figure is defined as:

( 10 )

where, H is the heat transportation coefficient, is the circumferentially mean temperature gradient to the wall and is the majority average temperature.

In order to analyze the influence of the presence of Radiation the heat transportation coefficient is defined as:

( 11 )

where, is the convective heat transportation coefficient and is the heat transportation coefficient of radiation. Obviously, when the radiation is neglected, the entire heat transportation coefficient is equal to convective heat transportation coefficient.

The figures following are the consequences of probes which show the effects of Reynolds figure, Prandtl figure, Knudsen figure and channel aspect ratio on to the full developed Nusselt figure for microchannel with rhombus cross subdivision. The consequence of the presence of radiation on Nusselt figure is shown and discussed in inside informations. Fig. 6 shows the consequence of Prandtl figure on Nusselt figure for different facet ratio at Re=10 and Kn=0.01. It is obvious that increasing the value of Prandtl figure causes the decrease in temperature leap and accordingly reduces the heat transportation rate and the Nusselt figure. It is shown in this figure that the Nusselt figure additions by increasing the value of aspect ratio of the channel. Besides it can be seen in this figure that the presence of the radiation augments the value of Nusselt figure. Fig. 7 shows the Nusselt Numberss as a map of aspect ratio for different Reynolds

Numberss for Kn=0.01 and Pr=0.74.it is clear in this figure that the heat transportation rate lessenings with increasing the value of Reynolds figure and this decrease is greater between lower value of Reynolds figure. Besides it is shown that the Nusselt figure additions when the facet ratio of the channel increases for a fixed Reynolds figure. The influence of the presence and absence of radiative heat transportation is besides depicted in this figure. Fig. 8 shows the Nusselt figure as a map of rarefaction for different Reynolds figure at Pr=0.74 and aspect ratio of integrity. The consequence of radiation is clearly shown in this

figure. It is shown in this figure that the value of Nusselt figure is greater for lower Reynolds figure, and besides the Nusselt figure decreases with increasing the value of rarefaction. The fluctuation of to the full developed Nusselt figure as a map of aspect ratio and Knudsen figure is investigated and shown in Fig. 9 at Re=10 and Pr=0.74. As seen in Fig. 9, the Nusselt figure has its maximal value when there are no rarefaction and it is obvious in this figure that the rarefaction causes decrease in heat transportation rate and Nusselt figure for a fixed facet ratio. It is clearly shown in this figure that diminishing the value of aspect ratio for a fixed Knudsen figure affects the Nusselt figure in which it reduces and lower facet ratios have more considerable effects on this decrease. We can besides see in this figure that the presence of radiation has a brilliant consequence on the heat transportation rate i.e. Nusselt figure.

## 6. Decision

A three dimensional incompressible steady theoretical account has been developed to look into the effects of Reynolds figure, aspect ratio, rarefaction, Prandtl figure and radiation heat transportation on Poiseuille and Nusselt figure for to the full developed laminar flow over a scope of faux pas flow government in a microchannel with rhombus cross subdivision. Constant wall temperature, faux pas speed and temperature leap boundary conditions were included. The Nusselt and Poiseuille figure both lessening with diminishing the value of aspect ratio, but rarefaction has reverse consequence on Poiseuille and Nusselt figure in which Poiseuille and Nusselt figure decreases with increasing in Kn. It is observed from the figures that Reynolds figure has more consequence on Nusselt figure so Poiseuille figure. It is concluded from the figures and consequences that the presence of the radiation augments the heat transportation rate and Nusselt figure to approximately 3 % in comparing by the absence of radiation.