scholarly journals Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Te-Wen Tu ◽  
Sen-Yung Lee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Time Dependent ◽  
Physical Parameters ◽  
Expansion Theorem ◽  
Present Solution ◽  
Hollow Cylinders

An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

Heat Transfer Coefficient in Rapid Solidification of a Liquid Layer on a Substrate

2000 ◽  
Vol 122 (4) ◽  
pp. 792-800 ◽  
Author(s):  
P. S. Wei ◽  
F. B. Yeh
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Biot Number ◽  
Equilibrium Phase ◽  
Density Ratio ◽  
Solid Substrate ◽  
Time Dependent ◽  
Bottom Surface ◽  
Melting Front

The heat transfer coefficient at the bottom surface of a splat rapidly solidified on a cold substrate is self-consistently and quantitatively investigated. Provided that the boundary condition at the bottom surface of the splat is specified by introducing the obtained heat transfer coefficient, solutions of the splat can be conveniently obtained without solving the substrate. In this work, the solidification front in the splat is governed by nonequilibrium kinetics while the melting front in the substrate undergoes equilibrium phase change. By solving one-dimensional unsteady heat conduction equations and accounting for distinct properties between phases and splat and substrate, the results show that the time-dependent heat transfer coefficient or Biot number can be divided into five regimes: liquid splat-solid substrate, liquid splat-liquid substrate, nucleation of splat, solid splat-solid substrate, and solid splat-liquid substrate. The Biot number at the bottom surface of the splat during liquid splat cooling increases and nucleation time decreases with increasing contact Biot number, density ratio, and solid conductivity of the substrate, and decreasing specific heat ratio. Decreases in melting temperature and liquid conductivity of the substrate and increase in latent heat ratio further decrease the Biot number at the bottom surface of the splat after the substrate becomes molten. Time-dependent Biot number at the bottom surface of the splat is obtained from a scale analysis. [S0022-1481(00)01004-5]

Numerical investigation of laminar forced convection for a non-Newtonian nanofluids flowing inside an elliptical duct under convective boundary condition

2019 ◽  
Vol 29 (1) ◽  
pp. 334-364 ◽  
Author(s):  
Haroun Ragueb ◽  
Kacem Mansouri
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Fluid Flow ◽  
Transfer Coefficient ◽  
Convective Boundary Condition ◽  
Bulk Temperature ◽  
Convective Boundary ◽  
Content Type ◽  
The Heat Transfer Coefficient

PurposeThe purpose of this study is to investigate the thermal response of the laminar non-Newtonian fluid flow in elliptical duct subjected to a third-kind boundary condition with a particular interest to a non-Newtonian nanofluid case. The effects of Biot number, aspect ratio and fluid flow behavior index on the heat transfer have been examined carefully.Design/methodology/approachFirst, the mathematical problem has been formulated in dimensionless form, and then the curvilinear elliptical coordinates transform is applied to transform the original elliptical shape of the duct to an equivalent rectangular numerical domain. This transformation has been adopted to overcome the inherent mathematical deficiency due to the dependence of the ellipsis contour on the variables x and y. The yielded problem has been successfully solved using the dynamic alternating direction implicit method. With the available temperature field, several parameters have been computed for the analysis purpose such as bulk temperature, Nusselt number and heat transfer coefficient.FindingsThe results showed that the use of elliptical duct enhances significantly the heat transfer coefficient and reduces the duct’s length needed to achieve the thermal equilibrium. For some cases, the reduction in the duct’s length can reach almost 50 per cent compared to the circular pipe. In addition, the analysis of the non-Newtonian nanofluid case showed that the addition of nanoparticles to the base fluid improves the heat transfer coefficient up to 25 per cent. The combination of using an elliptical duct and the addition of nanoparticles has a spectacular effect on the overall heat transfer coefficient with an enhancement of 50-70 per cent. From the engineering applications view, the results demonstrate the potential of elliptical duct in building light-weighted compact shell-and-tube heat exchangers.Originality/valueA complete investigation of the heat transfer of a fully developed laminar flow of power law fluids in elliptical ducts subject to the convective boundary condition with application to non-Newtonian nanofluids is addressed.

An Investigation of Local Heat Transfer during Grinding Process—Effects of Porosity of Grinding Wheel

1979 ◽  
Vol 101 (2) ◽  
pp. 97-103 ◽  
Author(s):  
Y. Saito ◽  
N. Nishiwaki ◽  
Y. Ito
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Thermal Boundary Condition ◽  
Grinding Wheel ◽  
Grinding Process ◽  
Workpiece Surface

The thermal boundary condition around the workpiece surface is one of important factors to analyze the thermal deformation of a workpiece, which is in close relation to the machining, accuracy of grinding. The heat dissipation from the workpiece surface which is influenced by the flow pattern, may govern this thermal boundary condition. In consequence, it is necessary to clarify the convection heat transfer coefficient and the flow pattern of air and/or grinding fluid around surroundings of a rotating grinding wheel and of a workpiece. Here experiments were carried out in a surface grinding process to measure the flow velocity, wall pressure and local heat transfer by changing the porosity of the grinding wheel. The air blowing out from the grinding wheel which is effected by the porosity may be considered to have large influences on the local heat transfer coefficient, which is found to be neither symmetric nor uniform over the workpiece surface.

scholarly journals An Analytical Solution for Transient Heat Conduction in a Composite Slab with Time-Dependent Heat Transfer Coefficient

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Ryoichi Chiba
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Differential Equations ◽  
Transfer Coefficient ◽  
Transient Heat Conduction ◽  
External Boundary ◽  
Composite Slab ◽  
Composite Slabs

An analytical solution is derived for one-dimensional transient heat conduction in a composite slab consisting of n layers, whose heat transfer coefficient on an external boundary is an arbitrary function of time. The composite slab, which has thermal contact resistance at n-1 interfaces, as well as an arbitrary initial temperature distribution and internal heat generation, convectively exchanges heat at the external boundaries with two different time-varying surroundings. To obtain the analytical solution, the shifting function method is first used, which yields new partial differential equations under conventional types of external boundary conditions. The solution for the derived differential equations is then obtained by means of an orthogonal expansion technique. Numerical calculations are performed for two composite slabs, whose heat transfer coefficient on the heated surface is either an exponential or a trigonometric function of time. The numerical results demonstrate the effects of temporal variations in the heat transfer coefficient on the transient temperature field of composite slabs.

Nodal Topology in Compact Thermal Models

2007 ◽  
Author(s):  
D. H. Greisen ◽  
V. P. Manno
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Heat Transfer Coefficient ◽  
Boundary Conditions ◽  
Transfer Coefficient ◽  
Area Ratio ◽  
System Level ◽  
Thermal Models ◽  
Single Boundary

Compact Thermal Models (CTMs) utilize a few connected thermal nodes to represent the thermal characteristics of electronic packages. These models are preferable to highly discretized models in preliminary design and system level analysis because of their computational efficiency. Surface heat flux non-uniformities often make it necessary to subdivide the package surfaces into multiple CTM nodes. This division is often quantified as the surface area ratio. This work assesses CTM performance sensitivity to area ratio changes and variation in heat transfer coefficient boundary conditions. CTMs for benchmark TQFP and BGA packages are developed using an admittance matrix approach. While optimum area ratios are identified, a direct correlation between these optimal values and the heat flux distributions computed from fully-discretized models was not obtained. CTM performance was found to be sensitive to changes in the heat transfer coefficient used to generate the CTM parameter values. A critical generating heat transfer coefficient was determined such that the resulting CTM, when optimized for a single boundary condition, was relatively accurate over the whole set of boundary conditions considered. This single boundary condition also provided an upper bound for error. This finding could be significant in future CTM development procedures.

Heat transfer coefficients for quenching process simulation

2004 ◽  
Vol 120 ◽  
pp. 269-276
Author(s):  
M. Maniruzzaman ◽  
R. D. Sisson
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Process Simulation ◽  
Nucleate Boiling ◽  
Film Boiling ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients ◽  
Quenching Process

Quenching heat treatment in a liquid medium is a very complex heat transfer process. Heat extraction from the part surface occurs through several different heat transfer mechanisms in distinct temperature ranges, namely, film boiling, partial film boiling (i.e. transition), nucleate boiling and convection. The maximum heat transfer occurs during the nucleate boiling stage. Experimental study shows that, the effective surface heat transfer coefficient varies more than two orders of magnitude with the temperature during the quenching. For quenching process simulation, accurate prediction of the time-temperature history and microstructure evolution within the part largely depends on the accuracy of the boundary condition supplied. The heat transfer coefficient is the most important boundary condition for process simulation. This study focuses on creating a database of heat transfer coefficients for various liquid quenchant-metallic alloy combinations through experimentation using three different quench probes. This database is a web-based tool for use in quench process simulation. It provides at-a-glance information for quick and easy analysis and sets the stage for a Decision Support System (DSS) and Data Mining for heat-treating process.

Lower Entropy Generation in Microchannels With Laminar Single Phase Flow

2010 ◽  
Author(s):  
E. Galvis ◽  
J. R. Culham
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Entropy Generation ◽  
Entropy Generation Rate ◽  
Channel Geometry ◽  
Micro Channels ◽  
Optimum Channel

In this study the entropy generation minimization method is used to find the optimum channel dimensions in micro heat exchangers with a uniform heat flux. With this approach, pressure drop and heat transfer in the micro channels are considered simultaneously during the optimization analysis. A computational model is developed to find the optimum channel depth knowing other channel geometry dimensions and coolant inlet properties. The flow is assumed laminar and both hydrodynamically and thermally fully developed and incompressible. However, to take into account the effect of the developing length in the friction losses, the Hagenbach’s factor is introduced. The micro channels are assumed to have an isothermal or isoflux boundary condition, non-slip flow, and fluid properties have dependency on temperature accordingly. For these particular case studies, the pressure drop and heat transfer coefficient for the isoflux boundary condition is higher than the isothermal case. Higher heat transfer coefficient and pressure drop were found when the channel size decreased. The optimum channel geometry that minimizes the entropy generation rate tends to be a deep, narrow channel.

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