Convective Heat Transfer in Microchannels of Noncircular Cross Sections: An Analytical Approach

2012 ◽  
Vol 134 (9) ◽  
Author(s):  
S. Shahsavari ◽  
A. Tamayol ◽  
E. Kjeang ◽  
M. Bahrami
Keyword(s):  
Heat Flux ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Thermal Characteristics ◽  
Temperature Fields ◽  
Constant Property ◽  
Nusselt Numbers ◽  
Parametric Studies ◽  
Predicted Values ◽  
Newtonian Constant

Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels of hyperelliptical and regular polygonal cross sections. The considered geometries cover several common shapes such as ellipse, rectangle, rectangle with round corners, rhombus, star-shape, and all regular polygons. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. A linear least squares point matching technique is used to minimize the residual between the actual and the predicted values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical and numerical solutions from the literature for a variety of cross sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.

Analytical Velocity and Temperature Distributions for Flow in Microchannels of Various Cross-Sections

2010 ◽  
Author(s):  
S. Shahsavari ◽  
E. Kjeang ◽  
M. Bahrami
Keyword(s):  
Heat Flux ◽  
Cross Sections ◽  
Analytical Solutions ◽  
Thermal Characteristics ◽  
Temperature Fields ◽  
Constant Property ◽  
Nusselt Numbers ◽  
Temperature Distributions ◽  
Parametric Studies ◽  
Newtonian Constant

Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels for a wide variety of cross-sections. The considered geometries include hyper-elliptical channels and regular polygon ducts, which covers several common shapes. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. The boundary conditions are applied using a linear least-squares point matching technique to minimize the residual between the actual and the modeled values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical solutions from literature for a variety of channel cross-sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.

Estimation of Nusselt Number in Microchannels of Arbitrary Cross-Section With Constant Axial Heat Flux

2008 ◽  
Author(s):  
Ehsan Sadeghi ◽  
Majid Bahrami ◽  
Ned Djilali
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Cross Section ◽  
Cross Sections ◽  
Numerical Solutions ◽  
Arbitrary Cross Section ◽  
Geometrical Parameters ◽  
Thermal Systems ◽  
Cross Sectional ◽  
Axial Heat

In many practical instances such as basic design, parametric study, and optimization analysis of thermal systems, it is often very convenient to have closed form relations to obtain the trends and a reasonable estimate of the Nusselt number. However, finding exact solutions for many practical singly-connected cross-sections, such as trapezoidal microchannels, is complex. In the present study, the square root of cross-sectional area is proposed as the characteristic length scale for Nusselt number. Using analytical solutions of rectangular, elliptical, and triangular ducts, a compact model for estimation of Nusselt number of fully-developed, laminar flow in microchannels of arbitrary cross-sections with “H1” boundary condition (constant axial wall heat flux with constant peripheral wall temperature) is developed. The proposed model is only a function of geometrical parameters of the cross-section, i.e., area, perimeter, and polar moment of inertia. The present model is verified against analytical and numerical solutions for a wide variety of cross-sections with a maximum difference on the order of 9%.

Numerical Investigation on Simultaneous Effects of Surface Roughness and Variable Properties on Laminar Flow in Annular Tubes

2018 ◽  
Author(s):  
Morteza Heydari ◽  
AmirHossein Bagheri ◽  
Hamid Sadat ◽  
Huseyin Bostanci ◽  
Seifollah Nasrazadani
Keyword(s):  
Surface Roughness ◽  
Thermal Characteristics ◽  
Maximum Velocity ◽  
Nanofluid Flow ◽  
Constant Property ◽  
Nusselt Numbers ◽  
Smooth Channel ◽  
Thermo Physical Properties ◽  
Annular Tube ◽  
Comprehensive Study

A comprehensive study is conducted to evaluate the heat transfer characteristics of laminar nanofluid flow in an annular tube. Thermo-physical properties of the nanofluid is considered to be variable and for the inner and outer walls, there exists serrated surface roughness. The study focuses on the velocity distribution, friction factor and Nusselt number. All results are compared with those for the smooth channel and constant property nanofluid as well. The results show that the tube with serrated wall experiences greater maximum velocity. Moreover, decrease in velocity gradient and some other thermal characteristics result in decrease in average Poiseuille and Nusselt numbers for the rough tube with variable-property fluid.

Combined Forced and Free Convection in the Entrance Region of an Isothermally Heated Horizontal Pipe

1982 ◽  
Vol 104 (1) ◽  
pp. 153-159 ◽  
Author(s):  
Mikio Hishida ◽  
Yasutaka Nagano ◽  
M. S. Montesclaros
Keyword(s):  
Numerical Solutions ◽  
Entrance Region ◽  
Temperature Fields ◽  
Horizontal Pipe ◽  
Uniform Wall Temperature ◽  
Nusselt Numbers ◽  
Developing Flow ◽  
Uniform Wall ◽  
Secondary Velocity ◽  
Laminar Convection

Numerical solutions are given without the aid of a large Prandtl number assumption for combined forced and free laminar convection in the entrance region of a horizontal pipe with uniform wall temperature. The steady-state solutions have been obtained from the asymptotic time solutions of the time-dependent equations of momentum and energy with the Poisson equation for pressure. Results are presented for the developing primary and secondary velocity profiles, developing temperature fields, local wall shear stress, and local and average Nusselt numbers, which reveal how the developing flow and heat transfer in the entrance region are affected by the secondary flow due to buoyancy forces.

Thermal Drag and Critical Heat Flux for Natural Convection of Air in Vertical Parallel Plates

1993 ◽  
Vol 115 (1) ◽  
pp. 124-129 ◽  
Author(s):  
Zeng-Yuan Guo ◽  
Xiao-Bo Wu
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Critical Heat Flux ◽  
Numerical Solutions ◽  
Vertical Channel ◽  
Wall Heat Flux ◽  
Uniform Heat Flux ◽  
Parallel Plates ◽  
Constant Property ◽  
Flux Boundary Condition

Variable property effects on vertical channel natural convection in air are studied systematically. Numerical solutions of the governing equations show that both the mass flow rate and heat transfer in the channel are not only lower than the constant property results, but also show a nonmonotonic variation with increasing wall temperature or wall heat flux. This phenomenon, which seemingly conflicts with the conventional knowledge, has also been identified by experiments. For a vertical channel with a uniform heat flux boundary condition, the wall may experience a sharp rise in temperature up to damage of the channel if the wall heat flux is greater than the critical heat flux. This implies that the crisis phenomenon (or burnout) may occur in channel natural convection in gas as well as in the boiling process.

Natural Convection in a Rectangular Porous Cavity With Constant Heat Flux on One Vertical Wall

1984 ◽  
Vol 106 (1) ◽  
pp. 152-157 ◽  
Author(s):  
V. Prasad ◽  
F. A. Kulacki
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Local Heat ◽  
Constant Heat Flux ◽  
Heated Wall ◽  
Width Ratio ◽  
Constant Heat ◽  
Nusselt Numbers

Numerical solutions for two-dimensional, steady, free convection are presented for a rectangular cavity with constant heat flux on one vertical wall, the other vertical wall being isothermally cooled. The horizontal walls are insulated. Results are presented in terms of streamlines and isotherms, local and average Nusselt numbers at the heated wall, and the local heat flux at the cooled wall. Flow patterns are observed to be quite different from those in the case of a cavity with both vertical walls at constant temperatures. Specifically, symmetry in the flow field is absent and any increase in applied heat flux is not accompanied by linearly proportional increase in the temperature on the heated wall. Also, for low Prandtl number, the heat transfer rate based upon the mean temperature difference is higher as compared to experimental results for the isothermal case. Heat transfer results, further, indicate that the average Nusselt number is correlated by a relation of the form Nu = constant Ra*mAn, where Ra* is the Rayleigh number and A the height-to-width ratio of the cavity.

scholarly journals Unsteady Laminar Free Convection from a Vertical Cone with Uniform Surface Heat Flux

2008 ◽  
Vol 13 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Bapuji Pullepu ◽  
K. Ekambavanan ◽  
A. J. Chamkha
Keyword(s):  
Heat Flux ◽  
Free Convection ◽  
Surface Heat Flux ◽  
Numerical Solutions ◽  
Surface Heat ◽  
Temperature Fields ◽  
Vertical Cone ◽  
Linear Partial Differential Equations ◽  
Average Skin ◽  
Good Agreement

Numerical solutions of, unsteady laminar free convection from an incompressible viscous fluid past a vertical cone with uniform surface heat flux is presented in this paper. The dimensionless governing equations of the flow that are unsteady, coupled and non-linear partial differential equations are solved by an efficient, accurate and unconditionally stable finite difference scheme of Crank-Nicolson type. The velocity and temperature fields have been studied for various parameters Prandtl number and semi vertical angle. The local as well as average skin-friction and Nusselt number are also presented and analyzed graphically. The present results are compared with available results in literature and are found to be in good agreement.

scholarly journals Effects of operating and material parameters on the thermal characteristics of a wet clutch

2021 ◽  
Vol 13 (7) ◽  
pp. 168781402110341
Author(s):  
Zhigang Zhang ◽  
Ling Zou ◽  
Hang Liu ◽  
Yonglong Chen ◽  
Benzhu Zhang
Keyword(s):  
Heat Flux ◽  
Applied Pressure ◽  
Thermal Characteristics ◽  
Thermal Models ◽  
Material Parameters ◽  
Heat Transfer Theory ◽  
Friction Disk ◽  
Viscous Shear ◽  
Wet Clutch ◽  
Transient Thermal

Based on the frictional mechanism of a wet clutch, frictional models of wet clutch engagement were established using the modified Reynolds equation and the elastic contact model between frictional pairs. Then, the heat flux models for the viscous shear and asperity friction were built, and the two-dimensional transient thermal models for the separator plate, friction disk, and ATF heat convection model were deduced based on the heat transfer theory and conservation law of energy. Finally, the Runge–Kutta numerical method was used to solve the frictional and thermal models. The average temperature of the separator plate, friction disk, and ATF were calculated. The effects of operating and material parameters, such as applied pressure, initial angular velocity, friction lining permeability, surface combined roughness RMS, equivalent elastic modulus, and ATF flow, on the thermal characteristics of friction pairs and ATF during engagement, were studied. The simulation results show that the temperature characteristics of the separator plate, friction disk, and ATF depend mainly on the viscous shear and asperity friction heat flux, and that the operating and material parameters of the wet clutch also have significant impacts on the overall variation trend of the thermal characteristics of the separator plate, friction disk, and ATF.

Effects of Insulated and Isothermal Baffles on Pseudosteady-State Natural Convection Inside Spherical Containers

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Yuping Duan ◽  
S. F. Hosseinizadeh ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Heat Transfer Enhancement ◽  
Numerical Procedure ◽  
Boussinesq Approximation ◽  
Transfer Enhancement ◽  
Nusselt Numbers ◽  
Extended Surface ◽  
Parametric Studies ◽  
Thermal Layer

The effects of insulated and isothermal thin baffles on pseudosteady-state natural convection within spherical containers were studied computationally. The computations are based on an iterative, finite-volume numerical procedure using primitive dependent variables. Natural convection effect is modeled via the Boussinesq approximation. Parametric studies were performed for a Prandtl number of 0.7. For Rayleigh numbers of 104, 105, 106, and 107, baffles with three lengths positioned at five different locations were investigated (120 cases). The fluid that is heated adjacent to the sphere rises replacing the colder fluid, which sinks downward through the stratified stable thermal layer. For high Ra number cases, the hot fluid at the bottom of the sphere is also observed to rise along the symmetry axis and encounter the sinking colder fluid, thus causing oscillations in the temperature and flow fields. Due to flow obstruction (blockage or confinement) effect of baffles and also because of the extra heating afforded by the isothermal baffle, multi-cell recirculating vortices are observed. This additional heat is directly linked to creation of another recirculating vortex next to the baffle. In effect, hot fluid is directed into the center of the sphere disrupting thermal stratified layers. For the majority of the baffles investigated, the Nusselt numbers were generally lower than the reference cases with no baffle. The extent of heat transfer modification depends on Ra, length, and location of the extended surface. With an insulated baffle, the lowest amount of absorbed heat corresponds to a baffle positioned horizontally. Placing a baffle near the top of the sphere for high Ra number cases can lead to heat transfer enhancement that is linked to disturbance of the thermal boundary layer. With isothermal baffles, heat transfer enhancement is achieved for a baffle placed near the bottom of the sphere due to interaction of the counterclockwise rotating vortex and the stratified layer. For some high Ra cases, strong fluctuations of the flow and thermal fields indicating departure from the pseudosteady-state were observed.

Numerical Prediction of Flow and Heat Transfer in a Parallel Plate Channel With Staggered Fins

1987 ◽  
Vol 109 (1) ◽  
pp. 25-30 ◽  
Author(s):  
K. M. Kelkar ◽  
S. V. Patankar
Keyword(s):  
Heat Transfer ◽  
Local Heat Transfer ◽  
Periodic Variation ◽  
Local Heat ◽  
Temperature Fields ◽  
Parallel Plates ◽  
Constant Property ◽  
Cross Sectional ◽  
Flow And Heat Transfer ◽  
Order Of Magnitude

Fluid flow and heat transfer in two-dimensional finned passages were analyzed for constant property laminar flow. The passage is formed by two parallel plates to which fins are attached in a staggered fashion. Both the plates are maintained at a constant temperature. Streamwise periodic variation of the cross-sectional area causes the flow and temperature fields to repeat periodically after a certain developing length. Computations were performed for different values of the Reynolds number, the Prandtl number, geometric parameters, and the fin-conductance parameter. The fins were found to cause the flow to deflect significantly and impinge upon the opposite wall so as to increase the heat transfer significantly. However, the associated increase in pressure drop was an order of magnitude higher than the increase in heat transfer. Streamline patterns and local heat transfer results are presented in addition to the overall results.

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