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Journal articles on the topic 'Temperature - Mathematics'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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1

Mbonambi, Martin Sipho, and Sarah Bansilal. "Comparing Grade 11 Mathematics and Mathematical Literacy Learners' Algebraic Proficiency in Temperature Conversion Problems." African Journal of Research in Mathematics, Science and Technology Education 18, no. 2 (May 4, 2014): 198–209. http://dx.doi.org/10.1080/10288457.2014.929247.

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2

CIMATTI, GIOVANNI. "The mathematics of varistors." European Journal of Applied Mathematics 28, no. 2 (May 19, 2016): 208–20. http://dx.doi.org/10.1017/s0956792516000218.

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A three-dimensional model of the varistor device is proposed. The thermal and electric conductivity of the material are taken to depend, in addition to the electric potential, on the temperature. Two theorems of existence and uniqueness of solutions for the boundary-value problem which determine the potential and the temperature inside the device are proposed. Levy–Caccioppoli global inversion theorem is used for the proof.

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3

Bucă, Anca M., Mihai Oane, Ion N. Mihăilescu, Muhammad Arif Mahmood, Bogdan A. Sava, and Carmen Ristoscu. "An Analytical Multiple-Temperature Model for Flash Laser Irradiation on Single-Layer Graphene." Nanomaterials 10, no. 7 (July 5, 2020): 1319. http://dx.doi.org/10.3390/nano10071319.

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A Multiple-Temperature Model is proposed to describe the flash laser irradiation of a single layer of graphene. Zhukovsky’s mathematical approach is applied to solve the Fourier heat equations based upon quantum concepts, including heat operators. Easy solutions were inferred with respect to classical mathematics. Thus, simple equations were set for the electrons and phonon temperatures in the case of flash laser treatment of a single layer of graphene. Our method avoids the difficulties and extensive time-consuming nonequilibrium green function method or quantum field theories when applied in a condensed matter. Simple expressions were deduced that could prove useful for researchers.

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4

Zhang, Yaqi, Wenyu Bai, and Gerald J. Diebold. "Mathematics of thermal diffusion in an exponential temperature field." Chemical Physics 505 (April 2018): 1–5. http://dx.doi.org/10.1016/j.chemphys.2018.03.002.

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5

Kharin, Stanislav, and Targyn Nauryz. "ONE-PHASE SPHERICAL STEFAN PROBLEM WITH TEMPERATURE DEPENDENT COEFFICIENTS." Eurasian Mathematical Journal 12, no. 1 (2021): 49–56. http://dx.doi.org/10.32523/2077-9879-2021-12-1-49-56.

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6

Dinh, L. N., T. C. Sun, and W. McLean. "Temperature-Dependent Kinetic Prediction for Reactions Described by Isothermal Mathematics." Journal of Physical Chemistry A 120, no. 39 (September 22, 2016): 7617–23. http://dx.doi.org/10.1021/acs.jpca.6b08219.

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7

Labay, V. Yo, V. Yu Yaroslav, O. M. Dovbush, and A. Ye Tsizda. "Mathematical modeling bringing the operation of air split conditioners heat pumps to the same internal temperature conditions." Mathematical Modeling and Computing 8, no. 3 (2021): 509–14. http://dx.doi.org/10.23939/mmc2021.03.509.

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Nowadays, the use of heat pumps (HP) of air split-conditioners in air conditioning and heating systems of small industrial, public and residential facilities is becoming more common. It is known that the nominal heat capacity of HP of air split-conditioners is given in catalogs or reference literature under standard outdoor temperature conditions, namely: outdoor air temperature +7oС, indoor air temperature +21oС. At the same time, manufacturers of air split-conditioners do not ensure that, regardless of the size of heating capacity, all air split-conditioners have the same internal temperature conditions, namely: the evaporation temperature of the refrigerant and its condensation temperature. In this case, the thermodynamic efficiency, which can be best assessed by the exergetic output-input ratio (OIR) of different heating capacity of HP of air split-conditioners, is different; this, in our opinion, is incorrect. However, today there is a lack of mathematical models of bringing the operation of air split-conditioners HP to the similar internal temperature conditions, which will allow us to obtain the same exergetic OIR for different heating capacity of HP. To create the mathematical model of bringing the operation of HP of air split-conditioners to the equal internal temperature conditions, we have proposed them, namely: the evaporation temperature of the refrigerant +0.7oC and its condensation temperature +40oC. Taking these temperatures on the basis of the heat balances of the HP evaporator and HP condenser of air split-conditioners, we obtained the dependences for calculating air flow rates on the evaporator and condenser, which respectively maintain the proposed temperatures.

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8

Nicholas, J. V., and D. R. White. "Traceable Temperatures: An introduction to temperature measurement and calibration, 2nd edn." Measurement Science and Technology 13, no. 10 (September 19, 2002): 1651. http://dx.doi.org/10.1088/0957-0233/13/10/701.

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9

Lan, Hai Peng, Yu Rong Tang, Jin Zhu Zhang, and Yong Mei He. "The Model of the Korla Fragrant Pear Mature Based on Effective Accumulated Temperature." Applied Mechanics and Materials 700 (December 2014): 364–67. http://dx.doi.org/10.4028/www.scientific.net/amm.700.364.

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In order to investigate the mature law of Korla fragrant pear with mathematics method, Korla pears in Aksu area be taken as the study object, and the fruit hardness and soluble solid content (SSC) be selected as the research index. The data of the two indices in the mature process are analyzed with Excel, SigmaPlot and Matlab. To draw the change rule of indices and establish the mathematical mode. The research shows that the effective accumulated temperature reaching up 3000°C to 3843°C is main mature stage of the Korla fragrant pear, and there is an accelerating stage in which. The change rule can be precise description by the established mathematical model that can provide reference for fruit maturity modeling.

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10

Chung, Soon-Yeong. "Positive definite temperature functions and a correspondence to positive temperature functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 127, no. 5 (1997): 947–61. http://dx.doi.org/10.1017/s0308210500026822.

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SynopsisPositive definite temperature functionsu(x, t) in ℝn+1= {(x, t)|x∈ ℝn,t> 0} are characterised bywhere μ is a positive measure satisfying that for every ℰ > 0,is finite. A transformis introduced to give an isomorphism between the class ofall positive definite temperature functions and the class of all possible temperature functions inThen correspondence given bygeneralises the Bochner–Schwartz Theorem for the Schwartz distributions and extends Widder's correspondence characterising some subclass of the positive temperature functions by the Fourier-Stieltjes transform.

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11

Darus, Mukminah, and Che Mohd Imran Che Taib. "Temperature modelling and pricing of temperature index insurance." Japan Journal of Industrial and Applied Mathematics 36, no. 3 (June 15, 2019): 791–808. http://dx.doi.org/10.1007/s13160-019-00372-4.

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12

Pyko, S. M., V. A. Snurnikov, V. G. Kharazov, M. S. Uteshev, and D. A. Gordeev. "Digital temperature regulator." Measurement Techniques 39, no. 11 (November 1996): 1126–30. http://dx.doi.org/10.1007/bf02375390.

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13

Memet, Feiza. "A Research on Satisfaction during Friday Religious Services, Practices Associated with Health and Social Relationships, in Anadolchioi Mosque." European Journal of Theology and Philosophy 1, no. 3 (June 19, 2021): 25–28. http://dx.doi.org/10.24018/theology.2021.1.3.16.

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This paper evaluates the indoor temperature and thermal sensation inside the naturally ventilated small-medium size, historical Anadolchioi Mosque, built in Constanta, in 1870, for the Muslim minority living in Constanta. Are considered Friday prayers (Dhuhr). The methodology used for this assessment is related to the outdoor and indoor temperatures measurements, each Friday, in July, between 10 AM and 4 PM, due to the fact that in Constanta, Friday prayers (in July) starts between 1.20 PM and 1.23 PM (depending on the sun position). The measurements will indicate that, although indoor temperature is slightly higher than the outdoor one, the average indoor temperature, for the considered period, is in the recommended thermal comfort temperature range, according to ASHRAE 2010. Also, the measured indoor air temperatures and predicted temperature for comfortable indoors- given by Humphreys formula, have been compared, in order to have an idea if the building is able to provide pleasant indoor temperatures. On the other hand, the methodology is focusing on ASHRAE seven point scale, when assessing the thermal sensation. In this respect, a survey regarding the thermal sensation of the occupants indicated that a low percent (5.55%) felt uncomfortable during the religious services. The majority of occupants (77.77%) felt comfortable and do not need a cooler environment. The results are in concordance with the participants’ age profiles: older persons preferring higher indoor temperatures.

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14

Maslov, V. P. "On high-temperature superconductivity." Mathematical Notes 66, no. 5 (November 1999): 585–98. http://dx.doi.org/10.1007/bf02674200.

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15

Hamid, R., D. Sendogdu, and C. Erdogan. "The temperature stabilization and temperature measurement of a Kösters interferometer." Measurement Science and Technology 16, no. 11 (September 28, 2005): 2201–7. http://dx.doi.org/10.1088/0957-0233/16/11/010.

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16

Khlevnoi, B. B., V. R. Gavrilov, D. A. Otryaskin, I. A. Grigor’eva, M. V. Solodilov, M. L. Samoilov, and V. I. Sapritskii. "Measurement of the thermodynamic temperature of high-temperature fixed points." Measurement Techniques 56, no. 4 (July 2013): 433–39. http://dx.doi.org/10.1007/s11018-013-0224-z.

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17

Tag, M. A., and M. E. Mansour. "Automatic computing of the grand potential in finite temperature many-body perturbation theory." International Journal of Modern Physics C 30, no. 11 (November 2019): 1950100. http://dx.doi.org/10.1142/s0129183119501006.

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A new program created in C/C[Formula: see text] language generates automatically the analytic expression of grand potential and prints it in Latex2e format and in textual data. Another code created in Mathematica language can translate the textual data into a mathematical expression and help any interested to evaluate the thermodynamic quantities in analytic or numeric forms.

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18

Arous, Gérard Ben, Eliran Subag, and Ofer Zeitouni. "Geometry and Temperature Chaos in Mixed Spherical Spin Glasses at Low Temperature: The Perturbative Regime." Communications on Pure and Applied Mathematics 73, no. 8 (November 19, 2019): 1732–828. http://dx.doi.org/10.1002/cpa.21875.

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19

Klamkin, M. S. "Point of Minimum Temperature." SIAM Review 33, no. 3 (September 1991): 474. http://dx.doi.org/10.1137/1033107.

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20

Hultmark, Marcus, and Alexander J. Smits. "Temperature corrections for constant temperature and constant current hot-wire anemometers." Measurement Science and Technology 21, no. 10 (August 13, 2010): 105404. http://dx.doi.org/10.1088/0957-0233/21/10/105404.

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21

Avrin, Joel D., and Mokhtar Kirane. "Temperature growth and temperature bounds in special cases of combustion models." Applicable Analysis 50, no. 1-2 (August 1993): 131–44. http://dx.doi.org/10.1080/00036819308840189.

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22

Tokarev, E. F., G. S. Pado, V. I. Ivannikov, I. A. Dan'kov, G. S. Kudryashov, and F. Sh Khattamov. "High-temperature acoustic receivers for the temperature range 20?500�c." Measurement Techniques 35, no. 4 (April 1992): 499–501. http://dx.doi.org/10.1007/bf00978969.

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23

PHILLIPS, P. M., and A. D. REY. "Characterising texture formation in fibre lattices embedded in a nematic liquid crystal matrix." European Journal of Applied Mathematics 23, no. 1 (January 28, 2011): 155–80. http://dx.doi.org/10.1017/s0956792510000331.

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A two-dimensional computational study is performed on the texturing of fibre-filled nematic liquid crystals using the Landau-de Gennes model describing the spatio-temporal evolution of the second moment of the orientation distribution function or quadrupolar tensor order parameter. The investigation is performed on a consistent computational domain comprising a square array of four circular fibres embedded within a unit square containing a uniaxial low molar mass calamitic liquid crystal. Interest is focused on the role of temperature, boundary conditions and their effect on the nucleation and evolution of defect structures. Thermal effects are characterised below and above the temperature at which the nematic state is stable. Simulations in the stable nematic state serves as a scenario for investigating the effect of imposing different external boundary conditions, namely periodic and Dirichlet; the former describes a square lattice array of fibres embedded in a nematic liquid crystal, and the latterdescribes a four-fibre arrangement in an aligned nematic material. In each case, the influence of temperature is characterised, with defect structures forming and either remaining or splitting into lower strength defects. For fibre lattices, splitting transitions of defects at the centre of the domain occur at a critical temperature, but for the four-fibre arrangement, defect transitions occur continuously over a temperature range. The discontinuous defect splitting transition in fibre arrays occurs at lower temperatures than the continuous defect transformation in the four-fibre arrangement. At sufficiently low temperatures, the four-fibre arrangement and the fibre lattice give the same texture consisting of two disclination lines close to each fibre. The evolution of the texture with respect to temperature can be characterised as a change from single-fibre mode at low temperature to a collective mode with a centre-located heterogeneity at higher temperature. At higher temperatures, in the stable isotropic state, it is shown that surface-induced ordering arising from the fibre/liquid crystal interaction propagates into the bulk forming thin disclination lattices around the four-fibre configuration.

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24

Mar n, Jos M., Bel n. Zalba, Luisa F. Cabeza, and Harald Mehling. "Determination of enthalpy temperature curves of phase change materials with the temperature-history method: improvement to temperature dependent properties." Measurement Science and Technology 14, no. 2 (January 7, 2003): 184–89. http://dx.doi.org/10.1088/0957-0233/14/2/305.

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25

Amendola, Giovambattista, Carlo Banfi, and Mauro Fabrizio. "Entropy equation and absolute temperature." ANNALI DELL'UNIVERSITA' DI FERRARA 56, no. 2 (May 11, 2010): 217–29. http://dx.doi.org/10.1007/s11565-010-0099-8.

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26

Michalski, L., K. Eckersdorf, J. Kucharski, and J. McGhee. "Temperature Measurement, 2nd edn." Measurement Science and Technology 13, no. 10 (September 19, 2002): 1651–52. http://dx.doi.org/10.1088/0957-0233/13/10/702.

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27

Korobtsov, V. G., and V. M. Naumov. "PID-type temperature regulator." Measurement Techniques 31, no. 10 (October 1988): 986–88. http://dx.doi.org/10.1007/bf00864882.

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28

Barkovskii, Yu M., and S. I. Kamalkhodzhaev. "A measuring temperature converter." Measurement Techniques 55, no. 12 (March 2013): 1388–95. http://dx.doi.org/10.1007/s11018-013-0138-9.

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29

Bagmet, O. L., V. V. Sebko, N. N. Sirenko, and Ngo Kuang Eung. "Differential electromagnetic temperature converter." Measurement Techniques 37, no. 7 (July 1994): 804–8. http://dx.doi.org/10.1007/bf00975803.

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30

Yaruntsev, V. K. "Automated low-temperature dilatometer." Measurement Techniques 37, no. 10 (October 1994): 1170–75. http://dx.doi.org/10.1007/bf00978850.

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31

Zhuk, A. Z., V. A. Petukhov, and V. Ya Chekhovskoi. "Laser high-temperature dilatometer." Measurement Techniques 29, no. 10 (October 1986): 947–50. http://dx.doi.org/10.1007/bf00862449.

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32

Onufriev, S. V., V. A. Petukhov, and V. Ya Chekhovskoi. "High-temperature photoelectric dilatometer." Measurement Techniques 29, no. 10 (October 1986): 950–53. http://dx.doi.org/10.1007/bf00862450.

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33

Que, Rui Yi, Rong Zhu, Qing Zhen Wei, and Zhe Cao. "Temperature compensation for thermal anemometers using temperature sensors independent of flow sensors." Measurement Science and Technology 22, no. 8 (July 7, 2011): 085404. http://dx.doi.org/10.1088/0957-0233/22/8/085404.

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34

Mola, S., M. Magini, and C. Malvicino. "Equivalent Temperature Estimator Using Mean Radiant Temperature Sensor." Measurement and Control 34, no. 6 (July 2001): 167–69. http://dx.doi.org/10.1177/002029400103400603.

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Air conditioning in transport vehicles is becoming more and more a standard equipment rather than an optional one. Therefore, to assure better comfort conditions in rather non- homogeneous environments like a car cabin becomes a primary task. Since human thermal comfort is the result of the combined effect of several physical quantities, there is the need for new sensors to evaluate real comfort conditions in cars, so to have reliable feedback for a climate control. The present paper describes an equivalent temperature estimator which makes use of a mean radiant temperature sensor. A prototype car has been set up to perform on road and subjective tests.

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35

Rodriguez-Silva, Rodet, and Ingo Schlupp. "Elevational gradients do not affect thermal tolerance at local scale in populations of livebearing fishes of the genus Limia (Cyprinodontiformes: Poeciliinae)." Novitates Caribaea, no. 18 (July 15, 2021): 46–62. http://dx.doi.org/10.33800/nc.vi18.264.

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One of the main assumptions of Janzen’s mountain passes hypothesis is that due the low overlap in temperature regimes between low and high elevations in the tropics, organisms living in high-altitude evolve narrow tolerance for colder temperatures while low-altitude species develop narrow tolerance for warmer temperatures. Some studies have questioned the generality of the assumptions and predictions of this hypothesis suggesting that other factors different to temperature gradients between low and high elevations may explain altitudinal distribution of species in the tropics. In this study we test some predictions of the Janzen’s hypothesis at local scales through the analysis of the individual thermal niche breadth in populations of livebearing fishes of the genus Limia and its relationship with their altitudinal distribution in some islands of the Greater Antilles. We assessed variation in tolerance to extreme temperatures (measured as critical thermal minimum (CTmin) and maximum (CTmax) and compared thermal breadth for populations of eight species of Limia occurring in three Caribbean islands and that occupy different altitudinal distribution. Our results showed that species analyzed had significant differences in thermal limits and ranges. Generally, species distributed in high and low elevations did not differ in thermal limits and showed a wider range of thermal tolerance. However, species living in mid-elevations had narrower range of temperature tolerance. We found no significant effect of phylogeny on CTmin, CTmax and thermal ranges among species. This study did not provide evidence supporting Janzen’s hypothesis at a local scale since thermal tolerance and altitudinal distribution of Limia species were not related to temperature gradients expected in nature. Phylogeny also did not explain the patterns we observed. We suggest that biotic factors such as species interactions, diet specializations, and others should be considered when interpreting current distribution patterns of Limia species.

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36

Feuerman, Martin. "Standard deviation of a temperature coefficient." International Journal of Mathematical Education in Science and Technology 21, no. 6 (November 1990): 963–66. http://dx.doi.org/10.1080/0020739900210614.

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37

GURUNG, D. B., and V. P. SAXENA. "TRANSIENT TEMPERATURE DISTRIBUTION IN HUMAN DERMAL PART WITH PROTECTIVE LAYER AT LOW ATMOSPHERIC TEMPERATURE." International Journal of Biomathematics 03, no. 04 (December 2010): 439–51. http://dx.doi.org/10.1142/s1793524510001070.

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A mathematical model of temperature distribution in human dermal part under cooling is discussed in this paper. The skin is assumed to be covered by artificial protective layer which absorbs sweat. The metabolic heat generation rate in subcutaneous part is assumed to be decreasing exponentially. Also the quantitative behavior of blood flow rate due to cooling is considered in this part. Finite element approach based on calculus of variations has been employed to solve the model equations with appropriate considerations regarding parameters.

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38

Halas, S., A. Kaminski, and T. Durakiewicz. "A bridge-based temperature controller with a resistor as temperature sensor and heater." Measurement Science and Technology 4, no. 11 (November 1, 1993): 1208–12. http://dx.doi.org/10.1088/0957-0233/4/11/004.

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39

McDaid, Chloe, and Yang Zhang. "Wall temperature measurements using a thermal imaging camera with temperature-dependent emissivity corrections." Measurement Science and Technology 22, no. 12 (November 8, 2011): 125503. http://dx.doi.org/10.1088/0957-0233/22/12/125503.

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40

Savostenko, P. I. "A method of making a constant-temperature thermoanemometer independent of the environmental temperature." Measurement Techniques 34, no. 5 (May 1991): 474–79. http://dx.doi.org/10.1007/bf00975265.

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41

Cheng, Yao Nan, Zhen Jia Li, Yi Zhi Liu, Hui Ping Zhang, and Xian Zhou Wang. "Experiment Study on Disrepair Principle for the Waved-Edge Milling Insert with Complex 3D Grooves." Advanced Materials Research 311-313 (August 2011): 722–25. http://dx.doi.org/10.4028/www.scientific.net/amr.311-313.722.

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The impact disrepair and adhering disrepair of milling insert are the important factors that affect the normally running of the automated processing system. Based on machining the 45 steel, find out the difference of the impact disrepair invalidation types between the waved-edge milling insert and flat rake milling insert, build the impact disrepair life cumulating distribution function mathematic models by the mathematics statistic method and have contrast analysis of the impact disrepair average lives between them. Based on the experiments on milling the 3Cr-1Mo-1/4Vsteel, find out the difference of the adhering disrepair invalidation types between them, build the quantitative mathematic relation between milling temperature and maximal adhering disrepair depth on rake face, and analyze the rule that the milling temperature affects the adhering disrepair. All these studies provide the theoretic and experimental bases for the groove optimization.

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42

Deswita, Leli. "Pemodelan Matematika Perpindahan Panas Konveksi Campuran (Mixed Convection) pada Pelat Horizontal." Jurnal Matematika "MANTIK" 3, no. 2 (October 28, 2017): 96–100. http://dx.doi.org/10.15642/mantik.2017.3.2.96-100.

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This study examines and analyzes mathematical model of mixed convection in horizontal plate. The heat transfer uses the model of a two dimensional nonlinear partial differential equations system. Then, this equation is derived first into the dimensionless equation form, and then it is changed into system of nonlinear ordinary differential equations form using similarity transformation. This system of nonlinear ordinary differential equations is solved by using the finite-difference scheme method, also with the mathematics program with software Matlab. The results obtained form this program is to determine skin friction coefficient , wall temperature velocity profiles and temperature profiles

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43

Marin, M., R. P. Agarwal, and S. R. Mahmoud. "Modeling a Microstretch Thermoelastic Body with Two Temperatures." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/583464.

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We consider a theory of thermoelasticity constructed by taking into account the heat conduction in deformable bodies which depends on two temperatures. The first one is the conductive temperature, the second is the thermodynamic temperature, and the difference between them is proportional to the heat supply.

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44

Et.al, DalievKhojiakbarSultanovich. "Increasing the Thermostability of Optoelectronic Devices on Semiconductor Radiators." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 3 (April 10, 2021): 3112–19. http://dx.doi.org/10.17762/turcomat.v12i3.1535.

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The article proposes a scheme for thermal stabilization of the radiation flux of mid-IR LEDs in the temperature range + 20 ° C + 80 ° C. It is shown that the relevance of mid-IR LEDs for solving problems of gas analysis, environmental monitoring, moisture measurement and medical diagnostics. It was revealed that the guarantee of the measurement accuracy and sensitivity of optoelectronic devices is the correct spectral matching of the photodetector, LED and absorption of the investigated substance. The disadvantages of emitting diodes associated with time and temperature instability during operation are considered. A study of the spectral characteristics of mid-IR LEDs at various temperatures showed that the wavelength at the maximum the emission spectrum increases almost linearly with increasing temperature, which leads to additional errors and lowers the measurement accuracy of optoelectronic devices. A schematic diagram is proposed for stabilizing the radiation flux of mid-IR LEDs in the temperature range + 20 ° C + 80 ° C..

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45

Pang, Kun, Yao Yong Duan, and Xiu Lin Li. "The Study on the Improvement for Mathematical Model and the Affected Actors of Gas Storage Vessel Leakage." Advanced Materials Research 753-755 (August 2013): 2742–46. http://dx.doi.org/10.4028/www.scientific.net/amr.753-755.2742.

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Based on the method of mathematics and physics, the mathematical model of gas storage vessel leakage is improved. The improved mathematical model can better simulate the leakage at anytime, And we gets some results that (1) the function of leakage of quantity, intensity and gas pressure with the variable t, (2) the more correct the mathematical model for the gas storage vessel leakage, and (3) on the analysis of the affected actors of gas storage vessel leakage, the risk order of the factors is the area of the leakage hole, gas initial temperature, and pressure storage vessel.

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46

Yariv, Ehud. "Thermophoresis Due to Strong Temperature Gradients." SIAM Journal on Applied Mathematics 69, no. 2 (January 2008): 453–72. http://dx.doi.org/10.1137/070711219.

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47

Youssef, H. M. "Theory of two-temperature-generalized thermoelasticity." IMA Journal of Applied Mathematics 71, no. 3 (June 1, 2006): 383–90. http://dx.doi.org/10.1093/imamat/hxh101.

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48

Yih, Chia-Shun, and Jinsong Shi. "Stability of time-periodic temperature fields." Quarterly of Applied Mathematics 45, no. 1 (April 1, 1987): 39–50. http://dx.doi.org/10.1090/qam/885166.

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49

Milićević, Miroslav. "Contribution to new calculations of preheating and differentiation temperatures using Lagrange interpolation." Zavarivanje i zavarene konstrukcije 65, no. 4 (2020): 149–57. http://dx.doi.org/10.5937/zzk2004149m.

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This paper presents a chronology of how the critical cooling time and preheating temperature in welding have been determined so far. The author of this paper introduces a new approach in calculating preheating temperature using prior art experience as well as his long-term research results in the field of welding. Earlier solutions were based on Rosenthal's 2D and 3D model for calculating the critical cooling time and the corresponding preheating temperature and the improved expressions used by the British Standard. This paper uses the necessary experience in thermal and the corresponding disciplines of mathematics. Problems that occur and prevent efficient obtaining of solvable expressions in a simple and elementary way, the author of this paper solves it in a completely new and inventive way.

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Denny, J. K., and C. A. Yackel. "Temperature Models for Ware Hall." College Mathematics Journal 35, no. 3 (May 2004): 162. http://dx.doi.org/10.2307/4146891.

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