Heat transfer coefficient components

The heat-transfer coefficient of most interest is that between the bed and a wall or tube. This heat-transfer coefficient, is made up of three components. To obtain the overall dense bed-to-boiling water heat-transfer coefficient, the additional resistances of the tube wall and inside-tube-waH-to-boiling-water must be added. Generally, the conductive heat transfer from particles to the surface, the convective heat transfer... 

Likewise, the microscopic heat-transfer term takes accepted empirical correlations for pure-component pool boiling and adds corrections for mass-transfer and convection effects on the driving forces present in pool boiling. In addition to dependence on the usual physical properties, the extent of superheat, the saturation pressure change related to the superheat, and a suppression factor relating mixture behavior to equivalent pure-component heat-transfer coefficients are correlating functions. 

N,n = Minimum theoretical stages at total reflux Q = Heat transferred, Btu/hr U - Overall heat transfer coefficient, Btu/hrfP"F u = Vapor velocity, ft/sec U d = Velocity under downcomer, ft/sec VD(js = Downcomer design velocity, GPM/fL Vioad = Column vapor load factor W = Condensate rate, Ibs/hr Xhk = Mol fraction of heavy key component Xlk = Mol fraction of the light key component a, = Relative volatility of component i versus the heavy key component... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Example 10-8. Calculation of Overall Heat Transfer Coefficient from Individual Components... 

By using the simple Reynolds Analogy, obtain the relation between the heat transfer coefficient and the mass transfer coefficient for the gas phase for the absorption of a soluble component from a mixture of gases. If the heat transfer coefficient is 100 W/m2 K, what will the mass transfer coefficient be for a gas of specific heat capacity Cp of 1.5 kJ/kg K and density 1.5 kg/m- The concentration of the gas is sufficiently low for hulk flow effects to be negligible. 

In the model equations, A represents the cross sectional area of reactor, a is the mole fraction of combustor fuel gas, C is the molar concentration of component gas, Cp the heat capacity of insulation and F is the molar flow rate of feed. The AH denotes the heat of reaction, L is the reactor length, P is the reactor pressure, R is the gas constant, T represents the temperature of gas, U is the overall heat transfer coefficient, v represents velocity of gas, W is the reactor width, and z denotes the reactor distance from the inlet. The Greek letters, e is the void fraction of catalyst bed, p the molar density of gas, and rj is the stoichiometric coefficient of reaction. The subscript, c, cat, r, b and a represent the combustor, catalyst, reformer, the insulation, and ambient, respectively. The obtained PDE model is solved using Finite Difference Method (FDM). 

In model equations, Uf denotes the linear velocity in the positive direction of z, z is the distance in flow direction with total length zr, C is concentration of fuel, s represents the void volume per unit volume of canister, and t is time. In addition to that, A, is the overall mass transfer coefficient, a, denotes the interfacial area for mass transfer ifom the fluid to the solid phase, ah denotes the interfacial area for heat transfer, p is density of each phase, Cp is heat capacity for a unit mass, hs is heat transfer coefficient, T is temperature, P is pressure, and AHi represents heat of adsorption. The subscript d refers bulk phase, s is solid phase of adsorbent, i is the component index. The superscript represents the equilibrium concentration. 

In forced-convective boiling the effective heat-transfer coefficient hcb can be considered to be made up of convective and nucleate boiling components h fc and h nb. 

The effect of pressure on the heat transfer coefficient is influenced primarily by hgc (Botterill and Desai, 1972 Xavier etal., 1980). This component of h transfers heat from the interstitial gas flow in the dense phase of the fluidized bed to the heat transfer surface. For Group A and small Group B particles, the interstitial gas flow in the dense phase can be assumed to be approximately equal to Um ed. 6/i s extremely small for... 

Further experimental work has been carried out on the rates of melting of a solid in a liquid, using a single component system, and Hixson and Baum express their results for the heat transfer coefficient as ... 

In the following analysis, both p-z-n and junction barrier Schottky diodes will be evaluated for use in a 3-kV, 30A SiC bridge rectifier module. Four of these modules will replace the 10 Si diode bridge rectifiers and will reduce system volume and increase efficiency. To optimize the design of the module, we will evaluate the power density at the die level as a function of the number of paralleled diodes in each rectifier leg. A typical value of the heat-transfer coefficient of conventional, power components is 100 W/cm In the present analysis, we have a design limit of 200 W/cm and will determine the number of JBS and p-z -n diode needed to meet this goal. 

The particle convective component hpc may be calculated from Eq. (12.39). The heat transfer coefficients of film can be calculated from Eq. (12.48)... 

The reactor is modeled by three partial differential equations component balances on A and B [Eqs. (6.1) and (6.2)] and an energy balance [Eq. (6.3) for an adiabatic reactor or Eq. (6.4) for a cooled reactor]. The overall heat transfer coefficient U in the cooled reactor in Eq. (6.4) is calculated by Eq. (6.5) and is a function of Reynolds number Re, Eq. (6.6). Equation (6.7) is used for pressure drop in the reactor using the friction factor /given in Eq. (6.8). The dynamics of the momentum balance in the reactor are neglected because they are much faster than the composition and temperature dynamics. A constant... 

In order to capture the fast component of the dynamics, we define the stretched time scale r = t/e and consider the limit s — 0 (i.e., an infinitely high heat-transfer coefficient between Bi and B2). We thus obtain a description of the fast dynamics as... 

Condensation of mixed vapors of immiscible liquids is not well understood. The conservative approach is to assume that two condensate films are present and all the heat must be transferred through both films in series. Another approach is to use a mass fraction average thermal conductivity and calculate the heat-transfer coefficient using the viscosity of the film-forming component (the organic component for water-organic mixtures). 

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