Carslaw and Jaeger, Conduction of Heat in Solids ()(ISBN ) - Ebook download as PDF File .pdf), Text File .txt) or read book online. Carslaw and Jaeger Conduction of Heat in Solids ISBN medical-site.infotion Heat medical-site.info medical-site.info Carslaw and Jaeger, Conduction of Heat in Solids ()(ISBN ). Temperature distributions recorded by thermocouples in a solid body (slab) subject to surface heating are used in a mathematical model of 2-D heat conduction.
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In the literature, there are six kinds of thermal condition is applied at the boundary of the adjacent boundary conditions derived for the parabolic, diffusion, domain and takes into account all thermal effects of the energy equation Beck et al. These effects are the thermal capacity, enth- ; Ozisik, Three of these boundary conditions alpy flow, thermal diffusion, viscous dissipation and include the thermal effects of the thin layer and its in- other aspects of thermal interaction between the thin teraction with both the adjacent domain and the sur- layer and both its surroundings and adjacent domain.
The first modified boundary The generalized thermal boundary condition is modified condition is the fourth kind or Carslaw boundary to describe situations in which the thermal contact be- condition. This boundary condition takes into account tween the thin layer and its adjacent domain is imper- the thermal capacity of the thin layer and its capability fect.
An example is given to demonstrate the importance to store thermal energy. The second modified boundary of the introduced generalized thermal boundary condi- 70 condition is of the fifth kind or Jaeger boundary tion. The effects of different geometrical and thermo- condition. The fifth kind boundary takes into account physical properties on the validity of the generalized the thermal capacity of the thin layer and permits heat thermal boundary condition are investigated.
It is worth mentioning that the above referenced mod- 2 ified boundary conditions assume perfect thermal con- Analysis tact between the thin layer and its adjacent domain.
The Consider a thin layer that is in perfect thermal contact with third modified boundary condition is the generalized, or an adjacent domain as shown in Fig. The thin layer may the sixth, boundary condition Al-Nimr and Alkam, be a stationary, a moving solid-skin or a fluid-film. The , which takes into account the following effects. The enthalpy flow within the thin layer. This effect the temperature distribution in the transverse direction of appears when the thin layer is in the form of a moving the layer is assumed to be lumped.
Applying the balance of solid-skin or a moving fluid-film. Multi-dimensional thermal diffusion effects. Viscous dissipa- to different forms of heat fluxes imposed on the outer tion may be very important in applications involve thin surface of the thin layer.
The enthalpy flow term fluid layer moving at very high velocity. In these applica- accounts for the energy carried due to the thin layer tions, high velocity gradients enhance the generated movement. The constitution law which relates the energy by viscous dissipation. Situations in which the thermal contact between the thin layer and its adjacent domain is imperfect. The above mentioned six kinds of boundary conditions are derived for parabolic, diffusion, energy equation. In this classical energy equation, heat flux is postulated to be directly proportional to the temperature gradient.
How- ever, in situations dealing with transient heat flow in extremely short periods of time or at very low tempera- tures approaching absolute zero, the classical heat diffu- sion theory breaks down, because the wave nature of heat propagation becomes dominant.
Cattaneo and Vernotte are the earliest investigators to formulate, independently, the hyperbolic wave energy equation and Peshkov is the earliest investigator to detect experimentally the existence of thermal waves using superfluid liquid helium near absolute zero. Since then, the wave nature of heat propagation has been the subject of numerous investigations Kim et al.
The aim of the present work is to derive a generalized thermal boundary condition for a given domain, which is in thermal contact with an adjacent thin layer.
The thermal behavior of both domains is described by the Fig. Schematic diagram of the thin layer and its adjacent hyperbolic energy equation.
This reduces Eq. Also, Eq. This boundary condition represents a prescribed heat flux Six boundary conditions may be considered as special qi imposed on the boundary. To obtain these cases, rewrite Eq.
The fourth or Carslaw boundary condition depending on the particular case. The boundary condition for imperfect effect of the thin layer is taken into consideration. A contact situations is obtained by applying the balance of physical example of this kind is heat transfer into a large thermal energy on a differential element of the thin layer, ceramic object with a thin metal coating on the surface.
This boundary Also, condition can also describe a surface film composed of a well-stirred fluid with heat capacity Dyq2 c2. In the limit of zero thermal in 0 x a and the second layer thin in a x b, relaxation time, Eq. Transfer of heat within a fluid is by convection. Strictly speaking, in fluids the transfer of energy through Brownian motion is called diffusion. Let's talk about heat — solids, liquids, and gases are made up of molecules.
Transfer of heat in solids is by conduction.
Convection; that is, the transfer of heat from one place to another through the movement of fluids or gases. Conduction Firefighter Conduction. The governing equation for heat transfer by conduction is: Conduction Equation.
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