Analytical Solution of Nonequilibrium Heat Conduction in Porous Medium Incorporating a Variable Porosity Model With Heat Generation

2008 ◽  
Vol 131 (1) ◽  
Author(s):  
M. Nazari ◽  
F. Kowsary
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Heat Conduction ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Conductivity Ratio ◽  
Variable Porosity ◽  
Porosity Model

This paper is concerned with the conduction heat transfer between two parallel plates filled with a porous medium with uniform heat generation under a nonequilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields at constant porosity incorporating the effects of thermal conductivity ratio, porosity, and a nondimensional heat transfer coefficient at pore level. The two coupled energy equations for the case of variable porosity condition are transformed into a third order ordinary equation for each phase, which is solved numerically. This transformation is a valuable solution for heat conduction regime for any distribution of porosity in the channel. The effects of the variable porosity on temperature distribution are shown and compared with the constant porosity model. For the case of the exponential decaying porosity distribution, the numerical results lead to a correlation incorporating conductivity ratio and interstitial heat transfer coefficient.

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.

Effect of Heater Configurations on Transient Heat Transfer for Various Gases Flowing Over a Twisted Heater

2009 ◽  
Author(s):  
Makoto Shibahara ◽  
Qiusheng Liu ◽  
Katsuya Fukuda
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Gas Flow ◽  
Generation Rate ◽  
Transient Heat Transfer ◽  
Heat Generation Rate ◽  
Transfer Coefficients ◽  
Heat Transfer Coefficients

Forced convection transient heat transfer coefficients were measured for helium gas and carbon dioxide gas flowing over a twisted heater due to exponentially increasing heat input (Q0exp(t/τ)). The twisted platinum plate with a thickness of 0.1 mm was used as test heater and heated by electric current. The heat generation rate was exponentially increased with a function of Q0exp(t/τ). The gas flow velocities ranged from 1 to 10 m/s, the gas temperatures ranged from 313 to 353 K, and the periods of heat generation rate ranged from 46 ms to 17 s. The surface temperature difference and heat flux increase exponentially as the heat generation rate increases with the exponential function. Transient heat transfer coefficients increase with increasing gas flow velocity. The geometric effect of twisted heater in this study shows an enhancement on the heat transfer coefficient. Empirical correlation for quasi-steady-state heat transfer was obtained based on the experimental data. The data for heat transfer coefficient were compared with those reported in authors’ previous paper.

Non-Intrusive Heat Transfer Coefficient Determination in a Packed Bed of Spheres

2010 ◽  
Author(s):  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Generation ◽  
Packed Bed ◽  
Computational Procedure ◽  
Spherical Particles ◽  
Average Heat Transfer Coefficient ◽  
Heat Generation Rate ◽  
Average Heat

Non-intrusive measurements of the internal average heat transfer coefficient [1] in a randomly packed bed of spherical particles are made. It is desired to establish accurate results for this simple geometry so that the method used can then be extended to determine the heat transfer characteristics in any porous medium, such as a compact heat exchanger. Under steady, one-dimensional flow the spherical particles are subjected to a step change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The average heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory with the experimental results. More specifically, the average heat transfer coefficient is adjusted within the computational procedure until the predicted values of the fluid outlet temperature match the experimental values. The only information needed is the basic material properties, the flow rate, and the experimental data. The computational procedure alleviates the need for solid and fluid phase temperature measurements, which are difficult to make and can disturb the solid-fluid interaction. Moreover, a simple analysis allows us to proceed without knowledge of the heat generation rate, which is difficult to determine due to challenges associated with calibrating an inductively-coupled, sample specific, heat generation system. The average heat transfer coefficient was determined, and expressed in terms of the Nusselt number, over a Reynolds number range of 20–600. The results compared favorably to the work of Whitaker [2] and Kays and London [3]. The success of this method, in determining the average heat transfer coefficient in a randomly packed bed of spheres, suggests that it can be used to determine the average heat transfer coefficient in other porous media.

Finned Metal Foam Heat Sinks for Electronics Cooling in Forced Convection

2002 ◽  
Vol 124 (3) ◽  
pp. 155-163 ◽  
Author(s):  
A. Bhattacharya ◽  
R. L. Mahajan
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Forced Convection ◽  
Metal Foam ◽  
Experimental Results ◽  
Heat Sinks ◽  
The Heat Transfer Coefficient

In this paper, we present recent experimental results on forced convective heat transfer in novel finned metal foam heat sinks. Experiments were conducted on aluminum foams of 90 percent porosity and pore size corresponding to 5 PPI (200 PPM) and 20 PPI (800 PPM) with one, two, four and six fins, where PPI (PPM) stands for pores per inch (pores per meter) and is a measure of the pore density of the porous medium. All of these heat sinks were fabricated in-house. The forced convection results show that heat transfer is significantly enhanced when fins are incorporated in metal foam. The heat transfer coefficient increases with increase in the number of fins until adding more fins retards heat transfer due to interference of thermal boundary layers. For the 20 PPI samples, this maximum was reached for four fins. For the 5 PPI heat sinks, the trends were found to be similar to those for the 20 PPI heat sinks. However, due to larger pore sizes, the pressure drop encountered is much lower at a particular air velocity. As a result, for a given pressure drop, the heat transfer coefficient is higher compared to the 20 PPI heat sink. For example, at a Δp of 105 Pa, the heat transfer coefficients were found to be 1169W/m2-K and 995W/m2-K for the 5 PPI and 20 PPI 4-finned heat sinks, respectively. The finned metal foam heat sinks outperform the longitudinal finned and normal metal foam heat sinks by a factor between 1.5 and 2, respectively. Finally, an analytical expression is formulated based on flow through an open channel and incorporating the effects of thermal dispersion and interfacial heat transfer between the solid and fluid phases of the porous medium. The agreement of the proposed relation with the experimental results is promising.

Sign in / Sign up

Export Citation Format

Share Document