Analysis of Steady State Conjugate Heat Transfer in a Circular Microtube Inside a Substrate

2004 ◽  
Author(s):  
P. Sharath C. Rao ◽  
Muhammad M. Rahman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Stainless Steel ◽  
Nusselt Number ◽  
Steady State ◽  
Maximum Temperature ◽  
Working Fluid ◽  
Thermal Conductivity Ratio ◽  
Interface Temperature ◽  
Outlet Temperature

The steady state heat transfer for laminar flow inside a circular microtube within a rectangular substrate has been investigated. Silicon, Silicon Carbide, and Stainless Steel were the substrates used and Water and FC-72 were the coolants employed. Equations governing the conservation of mass, momentum, and energy were solved in the fluid region. Within the solid wafer, the heat conduction was solved. A thorough investigation for velocity and temperature distributions for different substrates and coolants was performed by varying geometrical dimensions and Reynolds number. At a constant diameter and Reynolds number, for combinations comprising same coolant but different substrates, one with the lowest solid to fluid thermal conductivity ratio (ks/kf) attains the highest local peripheral average interface temperature. It was found that the Nusselt number is more for a system with Silicon as the substrate and FC-72 as the working fluid and the least for a system with Stainless Steel as the substrate and Water as the working fluid. The lower ks/kf ratio of Stainless Steel-Water combination is the main reason for the lower Nusselt number. With the increase in hydraulic diameter and Reynolds number, the average Nusselt number increased. It was also observed that the maximum temperature of the substrate and hence the outlet temperature of the fluid increased as the Reynolds number decreased.

scholarly journals Analysis of transient mixed convection in a horizontal channel partially heated from below

2021 ◽  
Vol 4 (8(112)) ◽  
pp. 16-22
Author(s):  
Mahmoud A. Mashkour
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Heat Source ◽  
Local Nusselt Number ◽  
Richardson Number ◽  
Stokes Equations ◽  
Heat Convection ◽  
Horizontal Channel ◽  
Outlet Temperature

The heat convection phenomenon has been investigated numerically (mathematically) for a channel located horizontally and partially heated at a uniform heat flux with forced and free heat convection. The investigated horizontal channel with a fluid inlet and the enclosure was exposed to the heat source from the bottom while the channel upper side was kept with a constant temperature equal to fluid outlet temperature. Transient, laminar, incompressible and mixed convective flow is assumed within the channel. Therefore, the flow field is estimated using Navier Stokes equations, which involves the Boussinesq approximation. While the temperature field is calculated using the standard energy model, where, Re, Pr, Ri are Reynolds number, Prandtl number, and Richardson number, respectively. Reynolds number (Re) was changed during the test from 1 to 50 (1, 10, 25, and 50) for each case study, Richardson (Ri) number was changed during the test from 1 to 25 (1, 5, 10, 15, 20, and, 25). The average Nusselt number (Nuav) increases exponentially with the Reynold number for each Richardson number and the local Nusselt number (NuI) rises in the heating point. Then gradually stabilized until reaching the endpoint of the channel while the local Nusselt number increases with a decrease in the Reynolds number over there. In addition, the streamlines and isotherms patterns in case of the very low value of the Reynolds number indicate very low convective heat transfer with all values of Richardson number. Furthermore, near the heat source, the fluid flow rate rise increases the convection heat transfer that clarified the Nusselt number behavior with Reynolds number indicating that maximum Nu No. are 6, 12, 27 and 31 for Re No. 1, 10, 25 and 50, respectively

Effect of Twist Ratio on Heat Transfer Enhancement by Swirl Impingement

2019 ◽  
Author(s):  
Kishore Ranganath Ramakrishnan ◽  
Srivatsan Madhavan ◽  
Prashant Singh ◽  
Srinath V. Ekkad
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Steady State ◽  
Heat Transfer Enhancement ◽  
Experimental Work ◽  
Working Fluid ◽  
Transfer Enhancement ◽  
Average Heat ◽  
Twist Ratio ◽  
Single Jet

Abstract Steady state experimental work has been carried out to compare a conventional single jet of diameter 12.7mm with a swirling impinging jet. In this study swirl inserts with three different twist ratios 3, 4.5 and 6 were used to induce the swirling motion to the working fluid. The Reynolds number based on conventional impinging jet’s diameter is varied from 10000 to 16000. It is observed that with increase in twist ratio, the average heat transfer enhancement is reduced. However, with higher twist ratios more uniform distribution of heat transfer enhancement is observed.

scholarly journals Heat Transfer Enhancement and Flow Physics Behavior of Fluid in Circular Tube with Insert

2019 ◽  
Vol 8 (3) ◽  
pp. 1708-1715
Keyword(s):  
Heat Transfer ◽  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Flow Behavior ◽  
Vortex Generator ◽  
Leading Edge ◽  
Working Fluid ◽  
Literature Study

The paper presents computational fluid dynamics study of non-conventional insert vortex generator using Commercial software, to analyze the effect of vortex generator insert on heat transfer augmentation and fluid flow behavior. The study was done for Reynolds number 10000, 15000, 25000, 35000 and 45000 with working fluid as air flowing through a tube with a constant heat flux of 1000 w/m2. Current study validates the experimental results from the literature study. The heat transfer of these inserts with various geometrical arrangements viz. pitch to projected length ratio, angle of attack and height to inner diameter ratio are investigated here with the help of computational fluid dynamics software. The physical mechanism of formation and development of vortex flow from the leading edge to trailing edge of the insert is studied and it is observed that Nusselt number increases as an increment in Reynolds number. The ratio of augmented Nusselt number to smooth tube Nusselt number is found to be decreasing with increase in Reynolds number.

Effects of a High Porous Material on Heat Transfer and Flow in a Circular Tube

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
Koichi Ichimiya ◽  
Tetsuaki Takeda ◽  
Takuya Uemura ◽  
Tetsuya Norikuni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Porous Material ◽  
Entropy Generation ◽  
Circular Tube ◽  
Flow Characteristics ◽  
Reynolds Numbers ◽  
Working Fluid ◽  
Equivalent Diameter

This paper describes the heat transfer and flow characteristics of a heat exchanger tube filled with a high porous material. Fine copper wires (diameter: 0.5 mm) were inserted in a circular tube dominated by thermal conduction and forced convection. The porosity was from 0.98 to 1.0. The working fluid was air. The hydraulic equivalent diameter was cited as the characteristic length in the Nusselt number and the Reynolds number. The Nusselt number and the friction factor were expressed as functions of the Reynolds number and porosity. The thermal performance was evaluated by the ratio of the Nusselt number with and without a high porous material and the entropy generation. It was recognized that the high porous material was effective in low Reynolds numbers and the Reynolds number, which minimized the entropy generation existed.

Transient Response of Microchannel Heat Sinks in a Silicon Wafer

1997 ◽  
Vol 119 (4) ◽  
pp. 239-246 ◽  
Author(s):  
J. R. Rujano ◽  
M. M. Rahman
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Local Heat ◽  
Momentum Equation ◽  
Heat Sinks ◽  
Maximum Temperature ◽  
Thermal Conductivity Ratio ◽  
Channel Depth ◽  
Steady State Condition ◽  
Time Required

The transient conjugated heat transfer in forced convection for simultaneously developing laminar flow inside a microchannel heat sink is studied by solving the steady momentum equation and the transient energy equation. A parametric study is performed to understand the effects of channel depth and width, Reynolds number, spacing between channels, and solid to fluid thermal conductivity ratio. Silicon as well as indium phosphide are used as wafer’s material. Step and pulsed variations of the heat load are analyzed. Results show that the time required for the heat transfer to reach steady state condition is longer for the system with larger channel depth or spacing and smaller channel width or Reynolds number. Characteristic results for the fluid mean temperature at the exit, solid maximum temperature, local Nusselt number, and local heat flux are presented graphically as functions of position and time.

Heat Transfer Characteristics of High Heat Generating Integrated Circuit Chips Cooled Using Liquid Cold Plate—A Combined Numerical and Experimental Study

2020 ◽  
Vol 13 (1) ◽  
Author(s):  
Naveen G. Patil ◽  
Tapano Kumar Hotta
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Integrated Circuit ◽  
Convective Heat Transfer Coefficient ◽  
High Heat ◽  
Vital Role ◽  
Maximum Temperature ◽  
Cold Plate ◽  
Error Band

Abstract This paper deals with the experimental and numerical investigations of seven integrated circuit (IC) chips cooled using the water flowing inside the cold plate at different flowrates. The study includes the supply of three different heat input cases under four different flowrates (0.063 kg/s, 0.125 kg/s, 0.25 kg/s, and 0.5 kg/s) to cool the high heat-generating IC chips mounted on the SMPS board at various positions. The optimal configuration (71-11-74-76-65-24-15) for the arrangement of the 7 IC chips is considered for the analysis. The numerical simulations are carried out using the commercial software ansys fluent (R-16) to support the experiments. Both the results (IC chips temperature) agree with each other in the error band of 8–14%. The smallest chip U6 attains the maximum temperature, as its heat attenuation rate is very high. The water flowing inside the cold plate absorbs the heat from the IC chips; by increasing the flowrate (Reynolds number increases), there is an increase in the convective heat transfer coefficient of the chips (Nusselt number increases) and ultimately cools these faster. A correlation is proposed for the Nusselt number of the chips with the Reynolds number of the flow. The results suggest that the liquid cold plate plays a vital role in the cooling of the IC chips and leads to better thermal management.

Convective Heat Transfer Investigation of a Confined Air Slot-Jet Impingement Cooling on Corrugated Surfaces With Different Wave Shapes

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Recep Ekiciler ◽  
Muhammet Samet Ali Çetinkaya ◽  
Kamil Arslan
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Flow Characteristics ◽  
Jet Impingement ◽  
Working Fluid ◽  
Bottom Surface ◽  
Air Jet ◽  
Corrugated Surfaces ◽  
Energy Equations

In this study, air jet impingement on flat, triangular-corrugated, and sinusoidal-corrugated surfaces was numerically investigated. Bottom surface was subjected to constant surface temperature. Air was the working fluid. The air exited from a rectangular shaped slot and impinged on the bottom surface. The Reynolds number was changed between 125 and 500. The continuity, momentum, and energy equations were solved using the finite volume method. The effect of the shape of bottom surface on heat and flow characteristics was investigated in detail. Average and local Nusselt number were calculated for each case. It was found out that Nusselt number increases by increasing the Reynolds number. The optimum conditions were established to get much more enhancement in terms of performance evaluation criterion (PEC). It was revealed that the shape of the cooling surface (bottom wall) influences the heat transfer substantially.

Effects of a High Porous Material on Heat Transfer and Flow in a Circular Tube

2007 ◽  
Author(s):  
Koichi Ichimiya ◽  
Tetsuaki Takeda ◽  
Takuya Uemura ◽  
Tetsuya Norikuni
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Porous Material ◽  
Entropy Generation ◽  
Circular Tube ◽  
Copper Wire ◽  
Flow Characteristics ◽  
Working Fluid ◽  
Equivalent Diameter

This paper describes the heat transfer and flow characteristics of a heat exchanger tube filled with a high porous material. Fine copper wire (diamete: 0.5 mm) was inserted in a circular tube dominated by thermal conduction and forced convection. The porosity was from 0.98 to 1.0. Working fluid was air. Hydraulic equivalent diameter was cited as the characteristic length in Nusselt number and Reynolds number. Nusselt number and friction factor were expressed as functions of Reynolds number and porosity. Thermal performance was evaluated by the ratio of Nusselt number with and without a high porous material and the entropy generation. It was recognized that the high porous material was effective in low Reynolds number and the Reynolds number which minimized the entropy generation existed.

Enhancement of Heat Transfer by an Electric Field for a Drop Translating at Intermediate Reynolds Number

2005 ◽  
Vol 127 (10) ◽  
pp. 1087-1095 ◽  
Author(s):  
Rajkumar Subramanian ◽  
M. A. Jog
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Nusselt Number ◽  
Steady State ◽  
Field Strength ◽  
Electric Field ◽  
Electric Field Strength ◽  
Continuous Phase ◽  
Dispersed Phase ◽  
Enhancement Of Heat Transfer

The enhancement of heat transfer by an electric field to a spherical droplet translating at intermediate Reynolds number is numerically investigated using a finite volume method. Two heat transfer limits are considered. The first limit is the external problem where the bulk of the resistance is assumed to be in the continuous phase. Results show that the external Nusselt number significantly increases with electric field strength at all Reynolds numbers. Also, the drag coefficient increases with electric field strength. The enhancement in heat transfer is higher with lower ratio of viscosity of the dispersed phase to the viscosity of the continuous phase. The second heat transfer limit is the internal problem where the bulk of the resistance is assumed to be in the dispersed phase. Results show that the steady state Nusselt number for a combined electrically induced and translational flow is substantially greater than that for purely translational flow. Furthermore, for a drop moving at intermediate Reynolds number, the maximum steady state Nusselt number for a combined electrically induced and translational flow is slightly greater than that for a purely electric field driven motion in a suspended drop.

Confined Jet Impingement Thermal Management Using Liquid Ammonia as the Working Fluid

2002 ◽  
Author(s):  
Muhammad M. Rahman ◽  
Padmaja Dontaraju ◽  
Rengasamy Ponnappan
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Numerical Models ◽  
Strong Dependence ◽  
Working Fluid ◽  
Interface Temperature ◽  
Fluid Interface ◽  
First Case

The focus of the study was the conjugate heat transfer during impingement of a confined liquid jet. Two numerical models of a heat transfer process with heat transmission through a fluid-solid interface have been developed. In the first case only the fluid region has been considered while in the second case the solid region has been modeled along with the fluid region as a conjugate problem. The inlet nozzle Reynolds number has been kept at values where laminar flow can be assumed in all cases. The solid-fluid interface temperature shows a strong dependence on several geometric, fluid flow, and heat transfer parameters. The Nusselt number increased with Reynolds number. For a given flow rate, a higher heat transfer coefficient was obtained with smaller slot width and lower impingement height. A higher heat transfer coefficient at the impingement location was seen at a smaller thickness, whereas a thicker plate provided a more uniform distribution of heat transfer coefficient. Compared to Mil-7808 and FC-77, ammonia provided much smaller solid-fluid interface temperature and higher heat transfer coefficient.

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