Determination of Heat Transfer in Ducts With Axial Conduction by Variational Calculus

2009 ◽  
Vol 131 (9) ◽  
Author(s):  
A. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Numerical Procedure ◽  
Variational Calculus ◽  
Bulk Temperature ◽  
Similar Data ◽  
Square Duct ◽  
Axial Conduction ◽  
Circular Pipes

This study uses a methodology based on the calculus of variation to determine the heat transfer in passages with two-dimensional velocity fields such as rectangular channels and in the presence of axial conduction. The mathematical procedure is presented and the subsequent numerical computations provide the Nusselt number values. To verify the accuracy of this numerical procedure, the Nusselt number values are acquired for parallel-plate channels and circular pipes and compared with similar data from the Graetz-type exact analyses. Then, rectangular passages are selected to show the capability and a square duct is used to study the domain of accuracy for this procedure. The results for small Peclet numbers lead to a simple correlation for determination of the bulk temperature and they compare well with those obtained from an asymptotic solution.

Determination of Flow Characteristics and Turbulent Heat Transfer in a Ribbed Roughened Square Duct, Part 2: Numerical Simulations

2011 ◽  
Vol 110-116 ◽  
pp. 2364-2369
Author(s):  
Amin Etminan ◽  
H. Jafarizadeh ◽  
M. Moosavi ◽  
K. Akramian
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Flow Characteristics ◽  
Turbulence Models ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Square Duct ◽  
Optimized Model ◽  
Rsm Model

In the part 1 of this research, some useful turbulence models presented. In that part advantages of those turbulence models has been gathered. In the next, numerical details and procedure of solution are presented in details. By use of different turbulence models, it has been found that Spallart-Allmaras predicted the lowest value of heat transfer coefficient; in contrast, RSM1 has projected the more considerable results compared with other models; besides, it has been proven that the two-equation models prominently taken lesser time than RSM model. Eventually, the RNG2 model has been introduced as the optimized model of this research; moreover.

Transient Internal Forced Convection Under Arbitrary Time-Dependent Heat Flux

2013 ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
M. Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Forced Convection ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel’s integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict: i) fluid temperature distribution inside the tube ii) fluid bulk temperature and iii) the Nusselt number. A new definition, cyclic fully-developed Nusselt number, is introduced and it is shown that in the thermally fully-developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ANSYS to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannels

2009 ◽  
Author(s):  
Zhanyu Sun ◽  
Yogesh Jaluria
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Conjugate Heat Transfer ◽  
Fused Silica ◽  
Maximum Temperature ◽  
Bulk Temperature ◽  
Uniform Heat Flux ◽  
Substrate Thickness ◽  
Variable Properties ◽  
Axial Conduction

This paper is directed at the numerical simulation of pressure-driven nitrogen slip flow in long microchannels, focusing on conjugate heat transfer under uniform heat flux wall boundary condition. This problem has not been studied in detail despite its importance in many practical circumstances such as those related to the cooling of electronic devices and localized heat input in materials processing systems. For the gas phase, the two-dimensional momentum and energy equations are solved, considering variable properties, rarefaction, which involves velocity slip, thermal creep and temperature jump, compressibility, and viscous dissipation. For the solid, the energy equation is solved with variable properties. Four different substrate materials are studied, including commercial bronze, silicon nitride, pyroceram and fused silica. The effects of substrate axial conduction, material thermal conductivity and substrate thickness are investigated in detail. It is found that substrate axial conduction leads to a flatter bulk temperature profile along the channel, lower maximum temperature, and lower Nusselt number. The effect of substrate thickness on the conjugate heat transfer is very similar to that of the substrate thermal conductivity. That is, in terms of axial thermal resistance, the increase in substrate thickness has the same impact as that caused by an increase in its thermal conductivity. By comparing the results from constant and variable properties models, it is found that the effects of variation in substrate material properties are negligible.

Roughness Effect on the Heat Transfer Coefficient for Gaseous Flow in Microchannels

2010 ◽  
Author(s):  
Metin B. Turgay ◽  
Almila G. Yazicioglu ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Nusselt Number ◽  
Flow Regime ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Roughness Height ◽  
Working Fluid ◽  
Axial Conduction ◽  
Slip Flow Regime

Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.

Heat Transfer Coefficient in Ducts With Constant Wall Temperature

1983 ◽  
Vol 105 (4) ◽  
pp. 878-883 ◽  
Author(s):  
A. Haji-Sheikh ◽  
M. Mashena ◽  
M. J. Haji-Sheikh
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Numerical Calculation ◽  
Transfer Coefficient ◽  
Cross Sections ◽  
Wall Temperature ◽  
Constant Wall Temperature ◽  
Circular Pipes ◽  
The Heat Transfer Coefficient

An analytical method for the numerical calculation of the heat transfer coefficient in arbitrarily shaped ducts with constant wall temperature at the boundary is presented. The flow is considered to be laminar and fully developed, both thermally and hydrodynamically. The method presented herein makes use of Galerkin-type functions for computation of the Nusselt number. This method is applied to circular pipes and ducts with rectangular, isosceles triangular, and right triangular cross sections. A three-term or even a two-term solution yields accurate solutions for circular ducts. The situation is similar for right triangular ducts with two equal sides. However, for narrower ducts, a larger number of terms must be used.

Convective Heat Transfer in a Circular Annulus With Various Wall Heat Flux Distributions and Heat Generation

1985 ◽  
Vol 107 (2) ◽  
pp. 334-337 ◽  
Author(s):  
O. A. Arnas ◽  
M. A. Ebadian
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Heat Generation ◽  
Navier Stokes ◽  
Circular Pipes ◽  
Negative Effect ◽  
Energy Equations ◽  
Steady Laminar

Convective heat transfer for steady laminar flow between two concentric circular pipes with walls heated and/or cooled independently and subjected to uniform heat generation is presented in analytical closed form utilizing the linearized Navier-Stokes and energy equations. The flow field is hydrodynamically and thermally fully developed. The effect of heat generation is depicted in Fig. 1 where the ratio of the Nusselt number with heat generation to without heat generation is plotted against the radius ratio, the core size ω. It is seen that heat generation may have positive as well as negative effect on the Nusselt number.

Conjugate Thermal Transport in Gas Flow in Long Rectangular Microchannel

2011 ◽  
Vol 133 (2) ◽  
Author(s):  
Zhanyu Sun ◽  
Yogesh Jaluria
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Conjugate Heat Transfer ◽  
Fused Silica ◽  
Maximum Temperature ◽  
Bulk Temperature ◽  
Uniform Heat Flux ◽  
Substrate Thickness ◽  
Variable Properties ◽  
Axial Conduction

This paper is directed at the numerical simulation of pressure-driven nitrogen slip flow in long microchannels, focusing on conjugate heat transfer under uniform heat flux wall boundary condition. This problem has not been studied in detail despite its importance in many practical circumstances such as those related to the cooling of electronic devices and localized heat input in materials processing systems. For the gas phase, the two-dimensional momentum and energy equations are solved, considering variable properties, rarefaction, which involves velocity slip, thermal creep and temperature jump, compressibility, and viscous dissipation. For the solid, the energy equation is solved with variable properties. Four different substrate materials are studied, including commercial bronze, silicon nitride, pyroceram, and fused silica. The effects of substrate axial conduction, material thermal conductivity and substrate thickness are investigated in detail. It is found that substrate axial conduction leads to a flatter bulk temperature profile along the channel, lower maximum temperature, and lower Nusselt number. The effect of substrate thickness on the conjugate heat transfer is very similar to that of the substrate thermal conductivity. That is, in terms of axial thermal resistance, the increase in substrate thickness has the same impact as that caused by an increase in its thermal conductivity. By comparing the results from constant and variable property models, it is found that the effects of variation in substrate material properties are negligible.

Unsteady Laminar Forced-Convective Tube Flow Under Dynamic Time-Dependent Heat Flux

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
M. Fakoor-Pakdaman ◽  
Mehdi Andisheh-Tadbir ◽  
Majid Bahrami
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Analytical Model ◽  
Time Dependent ◽  
Bulk Temperature ◽  
Fluid Temperature ◽  
Tube Flow ◽  
Flux Boundary Condition ◽  
Arbitrary Time

A new all-time model is developed to predict transient laminar forced convection heat transfer inside a circular tube under arbitrary time-dependent heat flux. Slug flow (SF) condition is assumed for the velocity profile inside the tube. The solution to the time-dependent energy equation for a step heat flux boundary condition is generalized for arbitrary time variations in surface heat flux using a Duhamel's integral technique. A cyclic time-dependent heat flux is considered and new compact closed-form relationships are proposed to predict (i) fluid temperature distribution inside the tube, (ii) fluid bulk temperature and (iii) the Nusselt number. A new definition, cyclic fully developed Nusselt number, is introduced and it is shown that in the thermally fully developed region the Nusselt number is not a function of axial location, but it varies with time and the angular frequency of the imposed heat flux. Optimum conditions are found which maximize the heat transfer rate of the unsteady laminar forced-convective tube flow. We also performed an independent numerical simulation using ansys fluent to validate the present analytical model. The comparison between the numerical and the present analytical model shows great agreement; a maximum relative difference less than 5.3%.

Experimental and numerical analysis of heat transfer in the helically coiled heat exchanger

2019 ◽  
Vol 30 (6) ◽  
pp. 2935-2951 ◽  
Author(s):  
Tomasz Sobota
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Heat Transfer Coefficient ◽  
Heat Exchanger ◽  
Transfer Coefficient ◽  
Least Squares Method ◽  
Thermal Design ◽  
Content Type ◽  
Tube Heat Exchanger

Purpose The knowledge of the heat transfer coefficient is important for the proper design of heat exchangers as well as for the determination of the working medium outlet temperatures. This paper aims to present a method of simultaneous determination of coefficients in correlation formulas for the Nusselt number on both sides of the heat transfer surface. Design/methodology/approach The idea of the developed method is based on determining such a values of the coefficients in Nusselt number correlations that fulfill the condition of equality between the measured and calculated temperature at the outlet of heat exchanger in terms of least squares method. To test the proposed method, a special experimental installation was built. The heat transfer in helically coiled tube-in-tube heat exchanger was examined for the wide range of temperature changes and volumetric flow rates of working fluid. Findings The simulation results were validated with an experimental data. The results show that the heat transfer coefficient of the counter-current is higher than the co-current flow in helically coiled heat exchanger. This phenomenon can be beneficial particularly in the laminar flow regime. Research limitations/implications The correlation for the Nusselt number as a function of the Reynolds and Prandtl numbers for hot and cold liquid was obtained with the least squares method for the experimental data. Practical implications The presented method allows for the simultaneous determination of heat transfer coefficient on both sides of the wall without the necessity of indirect calculation of the overall heat transfer coefficient. The presented method can be used in the thermal design of various type heat exchangers. Originality/value This work presents the new methodology of determination correlations for the helically coiled tube-in-tube heat exchanger for co-current and counter-current arrangement, which can be used in thermal design.

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