Analytical Modeling of Fluid Flow and Heat Transfer in Micro/Nano-Channel Heat Sinks (original) (raw)
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Analytical Modeling of Fluid Flow and Heat Transfer in Microchannel/Nanochannel Heat Sinks
Journal of Thermophysics and Heat Transfer, 2008
Laminar forced convection in two-dimensional rectangular microchannels and nanochannels under hydrodynamically and thermally fully developed conditions is investigated analytically in the slip-flow regime. Closed-form solutions for fluid friction and Nusselt numbers are obtained by solving the continuum momentum and energy equations with the first-order velocity slip and temperature jump boundary conditions at the channel walls. An isoflux thermal boundary condition is applied on the heat sink base. The results of the present analysis are presented in terms of the channel aspect ratio, hydraulic diameter, momentum and thermal accommodation coefficients, Knudsen number, slip velocity, Reynolds number, and Prandtl number. It is found that fluid friction decreases and heat transfer increases compared with no-slip flow conditions, depending on the aspect ratios and Knudsen numbers that include the effects of the channel size or rarefaction and the fluid/wall interaction.
International journal of scientific research in mathematical and statistical sciences, 2018
This study analyzes laminar forced convection flow in parallel plate micro-channel with slip velocity and temperature jump. Closed-form solutions are obtained for temperature, bulk temperature and rate of heat transfer when both walls of the channel are kept at unequal temperatures. The effects of various controlling parameters such as rarefaction parameter, fluid-wall interaction parameter and Brinkman number on the thermal behavior and rate of heat transfer are discussed with the aid of line graphs. Interesting result from the present work is that increase in rarefaction parameter leads to enhancement in fluid temperature while increase in fluid-wall interaction parameter leads to increase in temperature jump on the walls of the channel. In addition, the rate of heat transfer represented as the Nusselt number at the both walls of the channel displays an unbounded swing which varies with increase in fluid-wall interaction and rarefaction parameters.
Slip-flow and heat transfer in rectangular microchannels with constant wall temperature
International Journal of Thermal Sciences, 2006
A control-volume numerical approach has been used to study rarefaction effects in simultaneously hydrodynamically and thermally developing 3D micro flows in rectangular channels for Kn ≤ 0.1. The effects of velocity slip, thermal creep and temperature jump on the key flow parameters are examined in detail. Low Reynolds number flows (Re ≤ 1) for different channel aspect ratios (0 ≤ α * ≤ 1) are considered. The effects of rarefaction on the global features of the flow and thermal development in the entrance region are studied. Dramatic reductions in the friction coefficient are observed in the entrance region due to rarefaction effects, which are enhanced by thermal creep. For the fluid heating case considered here, thermal creep increases slip at the wall and thereby further reduces the friction coefficient and enhances heat transfer. For an identical heat flux applied to the microchannel walls, thermal creep effects become more pronounced at lower Reynolds numbers since it results in higher axial temperature gradients. Present results for Kn = 0.1 indicate that the flow and thermal fields are greatly influenced by thermal creep at Re = 0.1.
NUMERICAL INVESTIGATION OF LAMINAR NANOFLUID FLOW IN MICRO CHANNEL HEAT SINKS
The effect of using nanofluids on heat transfer and aerodynamics characteristics in rectangular shaped micro channel heat sink (MCHS) is numerically investigated for Reynolds number range of (100-400 ) and different value of heat flux (50 , 100, 150 ) . In this study, the MCHS performance using tow type of nanofluid ( ) with volume fraction 10% was used as a coolant is examined. The three-dimensional steady, laminar flow and heat transfer governing equations are solved using The computational fluid dynamics code (FLUENT). The MCHS performance is evaluated in terms of temperature profile, heat transfer, velocity profile, pressure drop and friction factor. The results reveal that both heat transfer and pressure drop will be increasing with increasing Reynolds number, while the friction factor of the MCHS is decreased. However, heat transfer from micro channel heat sink with metal nanofluids ( ) improves compared with that of a micro channel heat sink with oxide metal nanofluids ( ). Only a slight increase in the pressure drop across the MCHS is found compared with the pure water-cooled MCHS
Slip-¯ow heat transfer in rectangular microchannels
Laminar slip-¯ow forced convection in rectangular microchannels is studied analytically by applying a modi®ed generalized integral transform technique to solve the energy equation, assuming hydrodynamically fully developed¯ow. Results are given in terms of the¯uid mixed mean temperature, and both local and fully developed mean Nusselt numbers. Heat transfer is found to increase, decrease, or remain unchanged, compared to non-slip-¯ow conditions, depending on two dimensionless variables that include eects of rarefaction and the¯uid/wall interaction. The transition point at which the switch from heat transfer enhancement to reduction occurs is identi®ed for dierent aspect ratios. Ó : S 0 0 1 7 -9 3 1 0 ( 0 1 ) 0 0 0 7 5 -8
International Journal of Heat and Fluid Flow, 2007
Slip-flow in rectangular microchannels heated at constant and uniform heat flux (H2 boundary condition) is studied. The study is 11 extended to the eight possible thermal versions that are formed of different combinations of heated and adiabatic walls. The paper aims 12 to show the effect of different thermal versions on heat transfer in microchannel. The velocity distribution that is required in determining 13 of temperature distribution is obtained from the literature. Mathematical similarity between the heat conduction and convection prob-14 lems is used to determine the temperature distribution in the microchannel. The solution of a heat conduction problem, available in the 15 literature, is adapted to the heat convection problem in the microchannel. The velocity and temperature distributions thus found are used 16 to determine the average Nusselt number for all the eight thermal versions. For the case studied, it is found that rarefaction has a decreas-17 ing effect on heat transfer in the microchannels exposed to any of the eight thermal versions. The results of the paper for the special case 18 of no-slip-flow agree exactly with the results found for macrochannels in the literature. 19
Numerical simulation of heat transfer in rectangular microchannel
Advances in Applied …, 2009
Numerical simulation of heat transfer in a high aspect ratio rectangular microchannel with heat sinks has been conducted, similar to an experimental study. Three channel heights measuring 0.3 mm, 0.6 mm and 1 mm are considered and the Reynolds number varies from 300 to 2360, based on the hydraulic diameter. Simulation starts with the validation study on the Nusselt number and the Poiseuille number variations along the channel streamwise direction. It is found that the predicted Nusselt number has shown very good agreement with the theoretical estimation, but some discrepancies are noted in the Poiseuille number comparison. This observation however is in consistent with conclusions made by other researchers for the same flow problem. Simulation continues on the evaluation of heat transfer characteristics, namely the friction factor and the thermal resistance. It is found that noticeable scaling effect happens at small channel height of 0.3 mm and the predicted friction factor agrees fairly well with an experimental based correlation. Present simulation further reveals that the thermal resistance is low at small channel height, indicating that the heat transfer performance can be enhanced with the decrease of the channel height.
Slip Flow and Heat Transfer in Rectangular and Cirular Microchannels
2010
Rarefied gas flows typically encountered in MEMS systems are numerically investigated in this study. Fluid flow and heat transfer in rectangular and circular microchannels in the slip flow regime are studied in detail by our recently developed implicit, incompressible, hybrid (finite volume/finite element) flow solver. The hybrid flow solver methodology is based on the pressure correction or projection method, which involves a fractional step approach to obtain an intermediate velocity field by solving the original momentum equations with the matrix-free, implicit, cellcentered finite volume method. The poisson equation resulting from the fractional step approach is then solved by node based Galerkin finite element method for an auxiliary variable which is closely related to pressure and is used to update the velocity field and pressure field. The hybrid flow solver has been extended for applications in MEMS by incorporating first order slip flow boundary conditions. Extended inlet boundary conditions are used for rectangular microchannels, whereas classical inlet boundary conditions are used for circular microchannels to emphasize on the entrance region singularity. In this study, rarefaction effects characterized by Knudsen number (Kn) in the range of 0 ≤ Kn ≤ 0.1 are numerically investigated for rectangular and circular microchannels with constant wall temperature. Extensive validations of our hybrid code are performed with available analytical solutions and experimental data for fully developed velocity profiles, friction factors, and Nusselt numbers. The influence of rarefaction on rectangular microchannels with aspect ratios between 0 and 1 is thoroughly investigated. Friction coefficients are found to be decreasing with increasing Knudsen number for both rectangular and circular microchannels. The reduction in the friction coefficients is more pronounced for rectangular microchannels with smaller aspect ratios. Effects of rarefaction and gas-wall surface interaction parameter on heat transfer are analyzed for rectangular and circular microchannels. For most engineering applications heat transfer is decreased with rarefaction. However for fluids with very large Prandtl numbers velocity slip dominates the temperature jump resulting in an increase in heat transfer with rarefaction. Depending on the gas-wall surface interaction properties extreme reductions in the Nusselt number can occur. Present results confirm the existence of a transition point below and above which heat transfer enhancement and reduction can occur.
Study of Fluid Flow and Heat Transfer In Rectangular Micro Channel
The computational fluid dynamics (CFD) model equations are solved to predict the hydrodynamic and thermal behaviour of the exchanger. The geometry of the problem and meshing of it have been made in ANSYS 14.0. The models have been solved by ANSYS Fluent 14.0 solver. Water and its Nano fluids with alumina (A2O3) are used as the coolant fluid in the micro channel heat sink. The relation between heat transfer coefficient and thermal conductivity of the fluid i.e. h ∝ k is proved in the present study. Thus use of Nano fluids has been found beneficial both in laminar and turbulent zone. The result shows that Nano fluids help to increase the heat transfer coefficient by 15% and 12% respectively in laminar and turbulent zone. The entrance length for the fully developed velocities depends on Reynolds number. The temperature rise between outlet and inlet depends on the Reynolds number, Re and Peclet number, Pe Temperature distribution is found to be independent of radial position even for Pe<<1.0. The hydrodynamic and thermal behaviour of the system have been studied in terms of velocity, pressure and temperature contours. The velocity contours at the exit show that wall effect penetrates more towards the center and the thickness of the zone with maximum velocity shrinks with increase in Re. The pressure drop across the channel increases with increase in Re. The experimental work done by Lee and Mudawar (2007) has been predicted by the present CFD results. The hydrodynamics and thermal behaviour of a rectangular micro channel are studied here. The variation wall temperature, pressure drop in the channel and the friction factors calculated using ANSYS Fluent can well predict the experimental data. The effect of Re on the behaviour the channel are also studied. Its behaviour also has been analyzed with the help of temperature, pressure and velocity contours.
Analytical solutions of heat transfer for laminar flow in rectangular channels
Archives of Thermodynamics, 2014
The paper presents two analytical solutions namely for Fanning friction factor and for Nusselt number of fully developed laminar fluid flow in straight mini channels with rectangular cross-section. This type of channels is common in mini- and microchannel heat exchangers. Analytical formulae, both for velocity and temperature profiles, were obtained in the explicit form of two terms. The first term is an asymptotic solution of laminar flow between parallel plates. The second one is a rapidly convergent series. This series becomes zero as the cross-section aspect ratio goes to infinity. This clear mathematical form is also inherited by the formulae for friction factor and Nusselt number. As the boundary conditions for velocity and temperature profiles no-slip and peripherally constant temperature with axially constant heat flux were assumed (H1 type). The velocity profile is assumed to be independent of the temperature profile. The assumption of constant temperature at the channel’s ...