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.

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 Development of A Process for Predicting the Overall Heat Transfer Coefficient for Transient Heat Transfer in An Exhaust System using CFD

2019 ◽  
Vol 8 (2) ◽  
pp. 2529-2533
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Gas Flow ◽  
Transient Flow ◽  
Exhaust System ◽  
Outlet Temperature ◽  
Governing Equations ◽  
Overall Heat Transfer Coefficient

The analysis of heat transfer of automotive exhaust system is most important since their prominence in the design and also in the optimization phase of exhaust after treatment system.This paperdeals with the process which can be useful to predict the overall heat transfer coefficient for the transient flow of pipe in the after treatment system. This considers the convection of heat along gas flow, the convection between gas and wall, conduction through wall, radiation and of course convection to the ambient. Governing equations are obtained for the transient flow in a pipe for calculating gas temperature and wall temperature at distance x and time t. Analytical solution will be computed using CFD techniques for these governing equations. From the obtained analytical solution to the transient flow in pipe an excel tool will be developed which can be able to give the outlet temperature of the pipe in transient flow at length x and time t, total heat loss from pipe to the ambient, overall heat transfer coefficient for the pipe

scholarly journals Thermal-Hydraulic Performance of Graphene Nanoribbon and Silicon Carbide Nanoparticles in the Multi-Louvered Radiator for Cooling Diesel Engine

2020 ◽  
Vol 7 (1) ◽  
pp. F22-F29 ◽  
Author(s):  
E. Nogueira
Keyword(s):  
Heat Transfer ◽  
Silicon Carbide ◽  
Heat Transfer Coefficient ◽  
Pressure Drop ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Mass Flow ◽  
Volume Fraction ◽  
Graphene Nanoribbon ◽  
The Heat Transfer Coefficient

Analytical solution for application and comparison of Graphene Nanoribbon and Silicon Carbide for thermal and hydraulic performance in flat tube Multi-Louvered Finned Radiator is presented. The base fluid is composed of pure water and ethylene glycol at a 50% volume fraction. The results were obtained for Nusselt number, convection heat transfer coefficient and pressure drop, for airflow in the radiator core and nanofluids in flat tubes. The main thermal and hydraulic parameters used are the Reynolds number, the mass flow rate, the Colburn Factor, and Friction Factor. In some situations, under analysis, the volume fraction, for Graphene Nanoribbon and Silicon Carbide, were varied. The value of the heat transfer coefficient obtained for Graphene Nanoribbon, for the volume fraction equal 0.05, is higher than twice the amount received by Silicon Carbide. The flow is laminar, for whatever the fraction value by volume of the Graphene nanoparticles when the mass flow of the nanofluid is relatively low. For turbulent flow and relatively small fractions of nanoparticles, the heat transfer coefficient is significantly high for mass flow rates of Graphene Nanoribbon. The pressure drop, for the same volume fraction of nanoparticles, is slightly higher than the pressure drop associated with Silicon Carbide. These high values for the heat transfer coefficient is a favorable result and of great practical importance, since lower values for the fraction in volume can reduce the costs of the compact heat exchanger (radiator). Keywords: analytical solution, nanofluid, compact exchanger, automotive radiator.

Conjugate Heat Transfer Analysis of Circular Microtube Under Time Varying Heat Source

2005 ◽  
Author(s):  
Abdullatif A. Gari ◽  
Muhammad M. Rahman
Keyword(s):  
Magnetic Field ◽  
Heat Transfer ◽  
Magnetic Material ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Transient Heat Conduction ◽  
Heat Transfer Analysis ◽  
Working Fluid ◽  
Heating And Cooling ◽  
The Magnetic Field

When a magnetic field is applied to a magnetic material it releases energy. It has been proven experimentally that this temperature rise could be as high as 20 K when a magnetic field of 10 T is applied. Heat is generated when the magnetic field is applied and cooling is produced when the magnetic field is released. The purpose of this study is to explore transient heat transfer coefficient when a fluid is circulated in the substrate through microchannels. Equations for the conservation of mass, momentum, and energy were solved in the fluid region. In the solid region, the transient heat conduction equation was solved. Gadolinium and water were picked as the magnetic material and working fluid respectively. The results are represented by plotting the variations of heat transfer coefficient and Nusselt number with time at various sections of the tube. The effects of the magnetic field strength, diameter of the microtube in the substrate, and Reynolds number were studied. It was found that the heat transfer coefficient changes with time in a periodic fashion when heating and cooling are generated in the system by repeated introduction and relaxation of the magnetic field. The results of this study will be useful for the development of microtube heat exchangers for a compact magnetic refrigerator.

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