Formulation of Heat Transfer

Having gained some appreciation of the three modes of heat transfer we proceed now to the methodology adopted in this text. We shall return to the three modes of heat transfer in Section 1.5, elaborate on conduction, and make further remarks on convection and radiation. 

In the preceding section we established the place of heat transfer among the engineering disciplines and distinguished the modes of heat transfer—conduction, convection, and radiation. We proceed now to the formulation of heat transfer. 

The formulation of an engineering discipline such as heat transfer is based on definitions of concepts and statements of natural laws in terms of these concepts. The natural laws of heat transfer, like those of other disciplines, can be neither proved nor disproved but are arrived at inductively, on the basis of evidence collected from a wide variety of experiments. As we continue to increase our understanding of the universe, the present statements of natural laws will be refined and generalized. For the time being, however, we shall refer to these statements as the available approximate descriptions of nature and employ them for the solution of current problems of engineering. 

In this text we shall employ two general laws, 

---

Sodium nitrate is also used in formulations of heat-transfer salts for he at-treatment baths for alloys and metals, mbber vulcanization, and petrochemical industries. A mixture of sodium nitrate and potassium nitrate is used to capture solar energy (qv) to transform it into electrical energy. The potential of sodium nitrate in the field of solar salts depends on the commercial development of this process. Other uses of sodium nitrate include water (qv) treatment, ice melting, adhesives (qv), cleaning compounds, pyrotechnics, curing bacons and meats (see Food additives), organics nitration, certain types of pharmaceutical production, refining of some alloys, recovery of lead, and production of uranium. 

Here a steady-state formulation of heat transfer is considered (Pollard, 1978). A hot fluid flows with linear velocity v, through a tube of length L, and diameter D, such that heat is lost via the tube wall to the surrounding atmosphere. It is required to find the steady-state temperature profile along the tube length. 

Formulation of heat transfer (sensible and latent) from various types of surface to the cloud... 

To predict the heat transfer effects, the engineer must have an adequate quantitative description of heat transfer between the tube wall and the fluid phases, heat transfer between the tube wall and the fluid phases, heat transfer between the two phases, the rate of phase change within the system, and the rate of heat transfer resulting from phase change. Unfortunately, present design procedures only provide estimates of the system performance. Many procedures have not been formulated in a systematic manner, and therefore it is difficult to pinpoint areas where the present understanding of the design process is weakest. 

The designer now needs to make some estimates of mass transfer. These properties are generally well known for commercially available adsorbents, so the job is not difficult. We need to re-introduce the adsorber cross-section area and the gas velocity in order to make the required estimates of the external film contribution to the overall mass transfer. For spherical beads or pellets we can generally employ Eq. (7.12) or (7.15) of Ruthven s text to obtain the Sherwood number. That correlation is the mass transfer analog to the Nusselt number formulation in heat transfer ... 

In an extension of simply monitoring and controlling dryers, Morris and colleagues have demonstrated how in situ probes can provide real-time analysis that enables optimization of a drying process.61,62 In these articles, the authors demonstrate how evaporative cooling can be used to expedite drying in formulations where heat transfer... 

The boundary conditions of particle temperature may be obtained from the heat transfer due to the collision of two bodies. Sun and Chen (1988) formulated the heat transfer per impact of two elastic particles by considering the collision of two elastic particles with different temperatures and assuming the heat conduction occurs only in the normal direction. 

The assumed direction of heat transfer at surfaces of a volume element has no effect on the finite difference formulation. 

Or, would it be supposed in Semenov s formulation that the walls of the container were of infinite thickness, of infinite heat content or of infinite thermal conductivity, so that To was kept constant over a long time Such a situation will not be realistic. Besides, it seems that such a supposition that the container wall has a large overall coefficient of heat transfer is inconsistent with the Semenov model that the rate of heat transfer from a self-heating fluid filled in a container and placed in the atmosphere under isothermal conditions, through the whole fluid surface, across the container walls, to the atmosphere is far less than the rate of thermal conduction in the fluid. 

Sirignano WA (1986) The Formulation of Spray Combustion Models Resolution Compared to Droplet Spacing. Journal of Heat Transfer 108 633-639... 

Conjugated eonduetion-convection problems are among the elassieal formulations in heat transfer that still demand exact analytical treatment. Since the pioneering works of Perelman (1961) [14] and Luikov et al. (1971) [15], such class of problems continuously deserved the attention of various researchers towards the development of approximate formulations and/or solutions, either in external or internal flow situations. For instance, the present integral transform approach itself has been applied to obtain hybrid solutions for conjugated conduction-convection problems [16-21], in both steady and transient formulations, by employing a transversally lumped or improved lumped heat conduction equation for the wall temperature. 

The foundations of an engineering discipline may be best understood by considering the place of that discipline in relation to other engineering disciplines. Therefore, our first concern in this chapter will be to determine the place of heat transfer among engineering disciplines. Next, we shall proceed to a review of the general principles needed for heat transfer. Finally, we shall discuss the three modes of heat transfer— conduction, convection, and radiation—and introduce a five-step methodology for an inductive formulation. 

---