Extension of the Maximum Slope Method to Arbitrary Upstream Fluid Temperature Changes

1968 ◽  
Vol 90 (1) ◽  
pp. 130-134 ◽  
Author(s):  
G. F. Kohlmayr
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Transfer Test ◽  
Step Change ◽  
Fluid Temperature ◽  
Critical Number ◽  
Maximum Slope ◽  
Temperature Changes ◽  
Slope Method ◽  
Maximum Slope Method

Locke’s maximum slope method for the reduction of transient heat transfer test data is extended to include arbitrary upstream fluid temperature changes. The analytical solution of the single-blow problem is used to evaluate maximum slopes which are shown to depend, in general, nonmonotonically on the number of transfer units, Ntu. It is shown that there is a critical number of transfer units, (Ntu)crit, such that, for Ntu > (Ntu)crit, the maximum slope method remains applicable. In illustration of the analysis, maximum slopes and maximum slope errors are presented for various upstream temperature changes deviating from the step change.

scholarly journals Determination Of Heat Transfer Characteristics Employing Modified Maximum Slope Method For Porous Media Heat Exchanger Using Al2O3–Water Nanofluids

2019 ◽  
Vol 128 ◽  
pp. 04011
Author(s):  
Dijin J S ◽  
Rajkumar M R ◽  
Anjan R Nair
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Engineering System ◽  
Fluid Temperature ◽  
Heat Transfer Characteristics ◽  
Maximum Slope ◽  
Slope Method ◽  
Transfer Characteristics ◽  
Maximum Slope Method

It has been well documented in many literature that porous media and nanofluid can augment heat transfer in many engineering system. However the combined usage of these two media has not been given much attention in literature. The objective of the present work is to experimentally investigate porous media heat exchanger using Al2O3/water nanofluids. The heat transfer characteristics is determined using transient testing method wherein, only one fluid stream flows steadily throughthe test core, then a transient perturbation in the inlet fluid temperature is induced and the outletfluid temperature variation is measured continuously. The measured data is evaluated using the maximum slope method to obtain the heat transfer characteristics. The results show an increase in Nusselt number values with the use of nanofluids in porous media heat exchanger compared to water

scholarly journals The Single-Blow Problem Including the Effects of Longitudinal Conduction

1964 ◽  
Author(s):  
C. P. Howard
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Conduction ◽  
Transient Behavior ◽  
Step Change ◽  
Graphical Form ◽  
Compact Heat Exchanger ◽  
Fluid Temperature ◽  
Transfer Data ◽  
Method Of Calculation

The results are presented from a numerical finite-difference method of calculation for the transient behavior of porous media when subjected to a step change in fluid temperature considering the case where the longitudinal thermal heat conduction cannot be neglected. These results, given in tabular and graphical form, provide a useful means for evaluating the heat-transfer data obtained from the transient testing of compact heat-exchanger surfaces.

Thermal Effects in Cryogenic Liquid Annular Seals—Part I: Theory and Approximate Solution

1993 ◽  
Vol 115 (2) ◽  
pp. 267-276 ◽  
Author(s):  
Zhou Yang ◽  
Luis San Andres ◽  
Dara W. Childs
Keyword(s):  
Heat Transfer ◽  
Analytical Solution ◽  
Thermal Effects ◽  
Approximate Analytical Solution ◽  
Cryogenic Liquid ◽  
Bulk Flow ◽  
Absolute Pressure ◽  
Fluid Temperature ◽  
Numerical Predictions ◽  
Annular Seals

A thermohydrodynamic (THD) analysis is introduced for calculation of the performance characteristics of cryogenic liquid annular seals in the turbulent flow regime. A full-inertial bulk-flow model is advanced for momentum conservation and energy transport. The liquid material properties depend on the local absolute pressure and temperature. Heat flow to the rotor and stator is modeled by bulk-flow heat transfer coefficients. An approximate analytical solution is obtained to the governing equations when the seal operates at a steady-state and concentric condition. The temperature-rise in the fluid film of a cryogenic liquid seal is found to be composed of four sources due to viscous dissipation, pressure extrusion work, surface heat transfer and kinetic energy variation. For incompressible adiabatic flows, the fluid temperature rises linearly along the axial direction. The approximate analytical solution provides a useful tool for preliminary design and a better understanding of seal performance. Full numerical predictions of load, leakage, temperature, and rotordynamic coefficients for a high speed liquid oxygen seal are given in Part II to show the importance of thermal effects on seal performance. The accuracy of the approximate concentric seal analysis is then demonstrated by comparison to the results from the full numerical solution.

scholarly journals Thermal Load and Heat Transfer in Dental Titanium Implants: an Exact Analytical Solution to the ‘Heat Equation’

2021 ◽  
Author(s):  
Ziyad S. Haidar
Keyword(s):  
Heat Transfer ◽  
Thermal Stress ◽  
Analytical Solution ◽  
Heat Equation ◽  
Exposure Time ◽  
Thermal Load ◽  
Exact Analytical Solution ◽  
Titanium Implants ◽  
Surrounding Tissue ◽  
Temperature Changes

Introduction: Heat is a kinetic process whereby energy flows from between two systems; hot-to-cold objects. In oro-dental implantology, conductive heat transfer/(or thermal stress) is a complex physical phenomenon to analyze and consider in treatment planning. Hence, ample research has attempted to measure heat-production to avoid over-heating during bone-cutting and -drilling for titanium (Ti) implant-site preparation and insertion, thereby preventing/minimizing early (as well as delayed) implant-related complications and failure. Objective: Given the low bone-thermal conductivity whereby heat generated by osteotomies is not effectively dissipated and tends to remain within the surrounding tissue (peri-implant), increasing the possibility of thermal-injury; this work attempts to obtain an exact analytical solution of the heat equation under exponential thermal-stress, modeling transient heat transfer and temperature changes in Ti implants upon hot-liquid intake. Materials and Methods: We investigate the impact of the material, the location point along implant length, and the exposure time of the thermal load on temperature changes. Results: Despite its simplicity, the presented solution contains all the physics and reproduces the key features obtained in previous numerical analyses studies. To the best of knowledge, this is the first introduction of the intrinsic time, a “proper” time that characterizes the geometry of the dental implant, where we show, mathematically and graphically, how the interplay between “proper” time and exposure time influences temperature changes in Ti implants, under the suitable initial and boundary conditions. Conclusions: This work aspires to accurately complement the overall clinical diagnostic and treatment plan for enhanced bone-implant interface, implant stability and success rates, whether for immediate or delayed loading strategies.

scholarly journals Thermal-Boundary-Layer Response to Convected Far-Field Fluid Temperature Changes

2008 ◽  
Vol 130 (10) ◽  
Author(s):  
Hongwei Li ◽  
M. Razi Nalim
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Thermal Boundary Layer ◽  
Steady State Solution ◽  
Step Change ◽  
Far Field ◽  
Fluid Temperature ◽  
Constant Wall Temperature

Fluid flows of varying temperature occur in heat exchangers, nuclear reactors, nonsteady-flow devices, and combustion engines, among other applications with heat transfer processes that influence energy conversion efficiency. A general numerical method was developed with the capability to predict the transient laminar thermal-boundary-layer response for similar or nonsimilar flow and thermal behaviors. The method was tested for the step change in the far-field flow temperature of a two-dimensional semi-infinite flat plate with steady hydrodynamic boundary layer and constant wall temperature assumptions. Changes in the magnitude and sign of the fluid-wall temperature difference were considered, including flow with no initial temperature difference and built-up thermal boundary layer. The equations for momentum and energy were solved based on the Keller-box finite-difference method. The accuracy of the method was verified by comparing with related transient solutions, the steady-state solution, and by grid independence tests. The existence of a similarity solution is shown for a step change in the far-field temperature and is verified by the computed general solution. Transient heat transfer correlations are presented, which indicate that both magnitude and direction of heat transfer can be significantly different from predictions by quasisteady models commonly used. The deviation is greater and lasts longer for large Prandtl number fluids.

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