Heat transfer dimensionless

Zh Ratio of sensible heat removed from vapor to total heat transferred Dimensionless Dimensionless... 

Equation (4.36) provides a simple method for estimating an important heat transfer dimensionless group called the Prandtl number. Recall from general chemistry and thermodynamics that there are two types of molar heat capacities, C , and the constant pressure heat capacity, Cp. For an ideal gas, C = 3Cpl5. The Prandtl number is... 

Dimensionless group Dimensionless group Dimensionless concentration Peclet number for mass transfer Peclet number for heat transfer Dimensionless temperature Dimensionless length Activation energy group Dimensionless time... 

StH Stanton number for heat transfer dimensionless. t tray spacing m. 

Convection Heat Transfer. Convective heat transfer occurs when heat is transferred from a soHd surface to a moving fluid owing to the temperature difference between the soHd and fluid. Convective heat transfer depends on several factors, such as temperature difference between soHd and fluid, fluid velocity, fluid thermal conductivity, turbulence level of the moving fluid, surface roughness of the soHd surface, etc. Owing to the complex nature of convective heat transfer, experimental tests are often needed to determine the convective heat-transfer performance of a given system. Such experimental data are often presented in the form of dimensionless correlations. 

Dimensionless Mumbers used in Convection Heat-Transfer Analysis. 

Example Buckingham Pi Method—Heat-Transfer Film Coefficient It is desired to determine a complete set of dimensionless groups with which to correlate experimental data on the film coefficient of heat transfer between the walls of a straight conduit with circular cross section and a fluid flowing in that conduit. The variables and the dimensional constant believed to be involved and their dimensions in the engineering system are given below ... 

J Ordinate, Colburn j factor, equals f/2 for heat transfer for inner wall of annulus /h2 for outer wall of annulus jy for heat transfer for ideal tube bank Dimensionless Dimensionless... 

Since each ratio is dimensionless, any consistent units may be employed in any ratio. The significance of the symbols is as follows t = temperature of the surroundings tb = initial uniform temperature of the body t = temperature at a given point in the body at the time 0 measured from the start of the heating or coohng operations k = uniform thermal conductivity of the body p = uniform density of the boc c = specific heat of the body hf = coefficient of total heat transfer between the surroundings and the surface of the body expressed as heat transferred per unit time per unit area of the surface per unit difference in temperature between surroundings and surface r = distance, in the direction of heat conduction, from the midpoint or midplane of the body to the point under consideration / = radius of... 

Representation of Heat-Transfer Film Coefficients There are two general methods of expressing film coefficients (1) dimensionless relations and (2) dimensional equations. 

The dimensionless relations are usually indicated in either of two forms, each yielding identical resiilts. The preferred form is that suggested by Colburn ran.s. Am. In.st. Chem. Eng., 29, 174—210 (1933)]. It relates, primarily, three dimensionless groups the Stanton number h/cQ, the Prandtl number c Jk, and the Reynolds number DG/[L. For more accurate correlation of data (at Reynolds number <10,000), two additional dimensionless groups are used ratio of length to diameter L/D and ratio of viscosity at wall (or surface) temperature to viscosity at bulk temperature. Colburn showed that the product of the Stanton number and the two-thirds power of the Prandtl number (and, in addition, power functions of L/D and for Reynolds number <10,000) is approximately equal to half of the Fanning friction fac tor//2. This produc t is called the Colburn j factor. Since the Colburn type of equation relates heat transfer and fluid friction, it has greater utility than other expressions for the heat-transfer coefficient. 

Jh /m Chilton-Colbum factor for heat transfer See /D Dimensionless Dimensionless... 

Heat Exchangers Since most cryogens, with the exception of helium 11 behave as classical fluids, weU-estabhshed principles of mechanics and thermodynamics at ambient temperature also apply for ctyogens. Thus, similar conventional heat transfer correlations have been formulated for simple low-temperature heat exchangers. These correlations are described in terms of well-known dimensionless quantities such as the Nusselt, Reynolds, Prandtl, and Grashof numbers. 

Heat Transfer In general, the fluid mechanics of the film on the mixer side of the heat transfer surface is a function of what happens at that surface rather than the fluid mechanics going on around the impeller zone. The impeller largely provides flow across and adjacent to the heat-transfer surface and that is the major consideration of the heat-transfer result obtained. Many of the correlations are in terms of traditional dimensionless groups in heat transfer, while the impeller performance is often expressed as the impeller Reynolds number. 

The value of tire heat transfer coefficient of die gas is dependent on die rate of flow of the gas, and on whether the gas is in streamline or turbulent flow. This factor depends on the flow rate of tire gas and on physical properties of the gas, namely the density and viscosity. In the application of models of chemical reactors in which gas-solid reactions are caiTied out, it is useful to define a dimensionless number criterion which can be used to determine the state of flow of the gas no matter what the physical dimensions of the reactor and its solid content. Such a criterion which is used is the Reynolds number of the gas. For example, the characteristic length in tire definition of this number when a gas is flowing along a mbe is the diameter of the tube. The value of the Reynolds number when the gas is in streamline, or linear flow, is less than about 2000, and above this number the gas is in mrbulent flow. For the flow... 

From the slope and intereept of the heat absorption line, it is possible to manipulate Equation 6-117 by ehanging operating variables sueh as u, Tq, and T or design variables sueh as the dimensionless heat transfer group UA/puCp. It is also possible to alter the magnitude of the reaetion exotherm by ehanging the inlet reaetant eoneentrations. Any of tliese manipulations ean be used to vary tlie number of loeations of the possible steady states. 

This chapter reviews the various types of impellers, die flow patterns generated by diese agitators, correlation of die dimensionless parameters (i.e., Reynolds number, Froude number, and Power number), scale-up of mixers, heat transfer coefficients of jacketed agitated vessels, and die time required for heating or cooling diese vessels. 

Empirieal dimensionless group eorrelations have been used in the seale-up proeess. In partieular, the eorrelation for the inside film heat transfer eoeffieient for agitated, jaeketed vessels has been employed for the seale-up to a larger vessel. Reaetion ealorimeters are often used to give some indieation of heat transfer eoeffieients eompared to water in the same unit. Conelation for plant heat transfer is of the general form... 

The dimensionless quantity Sh is called the Sherwood number. The heat transfer factor a is defined bv... 

Impeller speed of rotation, rpm Power number, dimensionless Prandl number (heat transfer)... 

Useful dimensionless groups for heat transfer calculation are ... 

Sc = Schmidt number, dimensionless Pr = Prandtl number, dimensionless Cg = gas specific heat, Btu/lb-°F a = interfacial area, fti/fti Q, = sensible heat transfer duty, Btu/hr Qj. = total heat transfer duty, Btu/hr... 

F = MTD correction factor, dimensionless FA = face area, fF FV = standard air face velocity, sfm G = mass velocity, lb/ (sec) (fF) h = individual heat transfer coefficient,... 

LMTD = log mean temperature difference, °F M = mass flow rate, Ib/hr Ntu = number of heat transfer units, dimensionless N = number tubes/row in direction of air flow n = number tubes/row, per ft of exchanger width, 1 /ft Q = total exchanger heat load (duty), Btu/hr R = = heat capacity ratio, dimensionless... 

Forced convection heat transfer has been measured under widely differing conditions, and using the dimensionless groups makes correlation of the experimental... 

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