Publisher Summary Heating or cooling of large surface area products is often carried out in devices consisting of arrays of round or slot nozzles, through which air impinges vertically upon the product surface. This chapter presents a comprehensive survey emphasizing the engineering applications and empirical equations, presented for the prediction of heat and mass transfer coefficients within a large and technologically important range of variables. The local variations of the transfer coefficients are based on the experimental data for single round nozzles (SRN), arrays of round nozzles (ARN), single slot nozzles (SSN), and arrays of slot nozzles (ASN). The variation of local transfer coefficients is graphically represented. It also explores how to apply these equations in heat exchanger and dryer design as well as in optimization. The flow field of impinging flow is diagrammatically represented. External variables influencing heat and mass transfer in impinging flow depends on mass flow rate, kind and state of the gas and on the shape, size, and position of the nozzles relative to each other and to the solid surface. The design of high-performance arrays of nozzles is also discussed.

Heat and Mass Transfer between Impinging Gas Jets and Solid Surfaces

Study of the time dependence of physical properties in the transformation range of glass is complicated by the “memory effect” and the inherent nonlinearity which are characteristic of structural relaxation. A multiparameter model of structural relaxation is presented that differs from earlier models in that it takes account of both these effects. This model fits available experimental data well; these data were obtained for the most part by observing the evolution of properties (such as density or refractive index) following a step change in temperature. The present model also permits prediction of the physical properties of glass subjected to arbitrary and more complex temperature-time histories. It should, therefore, also be useful in the rational design of heat treating processes such as annealing.

A Model of Structural Relaxation in Glass

The field of enthalpy relaxation is reviewed. Current phenomenologies for dealing with the non-linear and non-exponential character of enthalpy relaxation are presented, and their successes and shortcomings are discussed. Qualitative experimental data and quantitative parameterizations are summarized, and some directions for future research are suggested.

Enthalpy relaxation and recovery in amorphous materials

A review of heat transfer data for single circular jet impingement

Heat transfer to impinging isothermal gas and flame jets

The role of turbulence in determining the heat-transfer characteristics of impinging jets

Heat Transfer Characteristics of Impinging Two-Dimensional Air Jets

Laboratory simulation of the industrial process of annealing sheet glass has yielded data on the genesis of stresses in initially stress-free glass. The experimental results differed from expectations based on classical annealing theory in that stresses began to develop in the annealing range even when the glass was being cooled at a constant rate, i.e. even in the absence of any changes of temperature gradients within the glass. Typically, these stresses account for 40% of the total residual stress in glass annealed according to a linear schedule. The remaining 60% are the well-known thermoelastic stresses that arise later in the annealing process from the decay of temperature gradients in the glass. The stresses observed to arise in glass as it is being cooled at a constant rate are attributed to volume relaxation effects which, in parts of the annealing range, generate stresses rapidly enough that they are not dissipated by stress relaxation. A mathematical model of annealing is proposed that takes account of both stress and structural relaxation. The model fits the experimentally observed evolution of stresses during linear cooling. It also suggests that (with the activation energies of stress and structural relaxation about the same) the actual rate, at any given temperature, of structural relaxation is about 4 times lower than that of stress relaxation.

Stress and Volume Relaxation in Annealing Flat Glass

Thermal Tempering of Glass

Lee, Rogers, and Woo presented a theory for calculating the stresses produced in glass by tempering. Unlike earlier treatments, theirs takes account of the viscoelastic properties of glass. The purpose of this paper is to evaluate this theory by comparison with experimental data. Discrepancies were found to exist between calculated and observed stress distributions. For cases in which glass is quenched from initial temperatures well above the strain point, these discrepancies result from the numerical formulation of the theory, not from any shortcomings of the theory itself. A modification of this formulation brought calculated and observed stresses into good agreement. For quenching from lower initial temperatures, the present theory could not be brought into agreement with experimental data. The reasons for this are briefly considered in the context of the structural heterogeneity of tempered glass and its possible effects on residual stresses.

Robert Gardon

Papers

The role of turbulence in determining the heat-transfer characteristics of impinging jets

Heat Transfer Characteristics of Impinging Two-Dimensional Air Jets

Stress and Volume Relaxation in Annealing Flat Glass

Thermal Tempering of Glass

Calculation of Residual Stresses in Glass