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trasferencia de calor
Magaly rosada
Diego Bermdez
Johanna Vargas
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One approach to parameter estimation was applied tocharacterize
the heat transfer in scraped surface heatexchangers (SSHEs)
specifically designed for the foodindustry. It is difficult to
apply the data available in theliterature for SSHEs, due to the
specificity of eachproduct, heat treatment and
geometricalconfiguration, causing the thermal design of
thesedevices is critical.
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There are generally two to four blades, which can bedisposed
longitudinally in the wall of the rotor
along the entire length of the heat exchanger.Alternatively,
short blades can be arranged in pairsand offset by 180 with respect
to the rotor axis, inthe presence or absence of a certain degree
ofoverlap. These two configurations are called directand
alternating leaves, respectively
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Although SSHEs are frequently used in industrialapplications
such as in the dairy and food industry, the scientificliterature
on this topic contains some gaps, includingthermal design of these
devices
although the numerical approach has led to some critical
results Most SSHEs studies are based on
experimentalinvestigations of the forms of single-phase heat
transferand two phase.
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This is done assuming that the external resistanceis smaller q
internal
Heat transfer to the correlation of the internal side,in a
manner monomial is generally adopted by thedependence of the
Nusselt number to the Reynoldsnumber of rotation and the
Prandtl
while the dependence of the axial Reynoldsnumber is generally
disregarded.
Uncertainty analyzes, provides information aboutboth the problem
by allowing an assessment of thequality and robustness of the
correlations resultingheat transfer.
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For any heat exchanger of parallel flow, the transfercoefficient
Ai internal surface area can be obtainedfrom the equation:
where T is the logarithmic mean temperature difference and Qis
the heat flow rate.
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where kW is the thermal conductivity of the wallmaterial and L
is the length of the heat exchanger.
The thermal resistance Rw of the wall can beassumed to be known
and constant for a given heatexchanger under running
conditions.
Using bore exchanger tube as the characteristiclength, inner
side Nusselt number is expressed inthe following straightforward
manner:
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where k is the product (fluid in the inner side)
thermalconductivity.
Regarding SSHEs, under the hypothesis of a singlephase flow, the
heat transfer coefficient of the productside can be assumed to be
correlated in terms of the
Nusselt number as follows:
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where the Reynolds number is defined as rotation Rerfollows:
In Eq. (7), N is the rotational speed of viscosity anddensity
dynamics respectively.
This implies that the following function must be
minimized by using the least squares approach habitual :
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where M is the number of measurements made for a massflow rate
of the f luid by varying RrandPr, with resultant
UCalcexpressed as follows:
Then, the parameter estimation method applied to the
heattransfer SSHEs characterization results from the minimization
of
the equation given by S function. (8) assumingRer and Pras
theindependent variables; C, , , and Ho as the unknown
variables,and all other quantities and geometrical properties as
known.
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The coefficients are defined with respect to the
genericparameter Pi in a dimensionless form as:
where Pi represents the unknown variables, C, , , and Ho, and
Uisthe overall heat transfer coefficient expressed as a function of
theindependent variables and PR Rer. Following this approach, once
thebest-fit curve P parameters are determined, the standard errors
ofparameters RPare given by:
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where J is the Jacobian matrix of the target variable is
theUCalcfunction.
And 2U is the residual variance:
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whereMis the number of measurements and zis the number
ofparameters to be fitted.
In order to express the reliability of the parameter
estimates
and compare the relative accuracy of the various estimates of
theparameters
confidence interval of 95%, the coefficient of variation,
CVis generally used with respect to the parameter Pi, defined as
follows:
The sensitivity and uncertainty analysis applied to both
synthetic
and experimental data for a coaxial SSHE.It must be stressed
that the approach presented here is based on theassumption that the
heat transfer coefficient on the outside varieswith the mass flow
rate of secondary fluid is optimized for apparatusin which a
convection one phase is present in the secondary side
fluid.
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The convective heat transfer coefficient of the fluidstream
flowing in the jacket side, namely h, was firstvaried over the
range 1000- 4000 W/m2K, which isrepresentative of SSHEs in which
the secondary fluidflows under the turbulent regime, as often
happenswhen water is used as the service fluid.
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The aim of the present investigation was to enable therobust
estimation of the heat transfer correlation for theproduct side
Nusselt number in an SSHE by assuming thatthe values of the
external side heat transfer coefficient areunknown, as well. The
estimation procedure presented
here did not require any hypothesis about the
functionaldependence of the external side heat transfer
coefficient, asis generally assumed in modified Wilson plot
approaches.
The procedure was validated through its application toboth
synthetic and experimental data acquired from a
coaxial alternate blade SSHE pilot plant planned to treathighly
viscous fluid foods. The parameter estimationprocedure was
optimized for sensitivity and uncertaintyanalysis, which provided
considerable insight into theproblem.
