Heat transfers Unidirectional

A large block of material of thermal diffusivity Du — 0.0042 cm2/s is initially at a uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained at that temperature. Calculate the time taken for the material at a depth of 0.45 m to reach a temperature of 475 K on the assumption of unidirectional heat transfer and that the material can be considered to be infinite in extent in the direction of transfer. 

Also, the pyrolyser construction plays an important role in the rate of attaining the Teq temperature. This construction may determine the way in which heat is transferred to the sample. This transfer process can be understood by evaluating the heat transfer mechanisms, which are conduction, convection, and radiation. The heat transfer rate q in J/s = W (watts) by unidirectional conduction for a small element of a material having the area A and thickness dx is given by Fourier s law ... 

Abstract. This chapter introduces crystallization process of multicrystalline silicon by using a directional solidification method. Numerical analysis, which includes convective, conductive, and radiative heat transfers in the furnace is also introduced. Moreover, a model of impurity segregation is included in this chapter. A new model for three-dimensional (3D) global simulation of heat transfer in a unidirectional solidification furnace with square crucibles was also introduced. 

Conductive heat transfer in all solid components, radiative heat exchange between all diffusive surfaces in the unidirectional solidification furnace, and the Navier-Stokes equations for the melt flow in the crucible are coupled. 

There have been many papers concerning the computational studies of unidirectional solidification for solar cells, in which the growth system was imposed to be axisymmetric. However, the actual crystal shape is square, calculation of square-shaped crystals is necessary. When square crucibles are used, the configuration of the furnace becomes asymmetric, and heat transfer in the furnace consequently becomes three-dimensional. Three-dimensional (3D) global modeling is, therefore, necessary for the investigation of m-c interface shape with square crucibles [20],... 

The three bodies — plate, very long cylinder and sphere — shall have a constant initial temperature d0 at time t = 0. For t > 0 the surface of the body is brought into contact with a fluid whose temperature ds d0 is constant with time. Heat is then transferred between the body and the fluid. If s < i90, the body is cooled and if i9s > -i90 it is heated. This transient heat conduction process runs until the body assumes the temperature i9s of the fluid. This is the steady end-state. The heat transfer coefficient a is assumed to be equal on both sides of the plate, and for the cylinder or sphere it is constant over the whole of the surface in contact with the fluid. It is independent of time for all three cases. If only half of the plate is considered, the heat conduction problem corresponds to the unidirectional heating or cooling of a plate whose other surface is insulated (adiabatic). 

Chapter 3 Unidirectional and One-Dimensional Flow and Heat Transfer Problems... 

For all of the flows that can be classified as unidirectional, the analysis of Section A shows that the governing equations reduce to solving a single heat equation for the magnitude of the scalar velocity component in the flow direction. For heat transfer applications, mathematically analogous problems involve heat transport by pure conduction. As noted earlier, there are excellent comprehensive books devoted exclusively to the solution of this class of problems.4 Here, we consider a related problem, which is chosen because it addresses the physically important coupling of heat transfer in the presence of phase change and also because it is another ID problem that exhibits a self-similar solution. 

In this section, we instead consider two well-known examples of heat transfer in the fully developed, laminar, and unidirectional flow of a Newtonian fluid in a straight circular tube. We begin with a problem in which there is a prescribed heat flux into the fluid at the walls of the tube, so that there is a steady-state temperature distribution in the tube. At the end of the section, we consider the transient evolution of the temperature distribution beginning with an initially sharp temperature jump within the fluid at a fixed position (say z = 0), which illustrates an important phenomenon that is known as Taylor dispersion. 

---