Abstract
The present paper comprises the quasi-stationary, non-homogeneous thermoelastic problem with a second kind boundary condition in two-dimensional rod of isotropic material. The unidirectional rod is examined with the condition that ambient and initial temperature is zero. The rod has been observed under the activity of moving heat source located at \( x^{{\prime }} \) moving with constant velocity along x-axis. Heat conduction equation is evaluated by using integral transform technique. The three materials, viz. aluminum, copper, and brass, have been studied, and the same are analyzed numerically and graphically for their respective thermal stresses. For aluminum, the change is observed from maximum to minimum stress. The response of copper to change in temperature is linear. The curve of copper shows constant value of stress because of its larger coefficient of thermal expansion. Tensile stress is reduced in copper. Minimum stress is observed in brass that indicates the hardness and tensile strength of brass.
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References
Nowinski JL (1978) Theory of thermoelasticity with application. Sijth of Noordhoff, Alphen Aan Den Rijn, The Netherlands, 407
Nowacki W (1957) The state of stresses in a thick circular plate due to temperature field. Bull Acad Polon Sci Scl Tech 5:227
Boley BA, Weiner JH (1960) Theory of thermal stresses. Wiley, New York
Roy Choudhary SK (1972) A note of quasi static stress in a thin circular plate due to transient temperature applied along the circumference of a circle over the upper face. Bull Acad Polon Sci Ser Sci Math, 20–21
Khobragade NW, Wankhede PC (2003) An inverse unsteady state thermoelastic problem of a thin rectangular plate. J. Indian Acad Math 25(2)
Gaikwad KR, Ghadle KP (2010) Quasi static thermoelastic problem of an infinitely long circular cylinder. J Korea Soc Indus Appl Math 14(3):141–149
Gaikwad KR, Ghadle KP (2012) Non-homogeneous heat conduction problem and its thermal deflection due to internal heat generation in a thin hollow circular disk. J Thermal Stress 35(6):485–498 (Taylor & Francis)
Patil VB, Ahirrao BR, Khobragade NW (2013) Thermal stresses of semi infinite rectangular slab with internal heat source. IOSR J Math 8(6):57–61
Solanke DT, Durge MH (2014) Quasi static thermal stresses in thin rectangular plate with internal moving line heat source. Sci Park Res J 1(44)
Thakare MS, Sutar CS, Khobragade NW (2015) Thermal stresses of a thin rectangular plate with internal moving heat source. IJEIT 4(9)
Solanke DT, Durge MH (2015) Quasi-stationary thermo elastic problem with moving heat source in unidirectional Robin’s rod. Eng Sci Int J (ESIJ) 2(3)
Gaikwad KR (2016) Two dimensional steady state temperature distribution of a thin circular plate due to uniform internal energy generation. Cogent Math 3:1135720
Ahire YM, Ghadle KP (2016) Three-dimensional unsteady state temperature distribution of thin rectangular plate with moving point heat source. Indian J Mater Sci 2016:7, Article ID 7563215 (Hindawi Publishing Corporation)
Ozisik NM (1968) Boundary value problem of heat conduction, Dover Publication INC., Mineola, New York
Noda N, Hetnarski RB, Tanigawa Y (2002) Thermal stresses, 2nd edn
Sneddon IN (1972) The use of integral transform. McGraw Hill, New York, pp 235–238
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Ahire, Y.M., Ghadle, K.P. (2021). Distribution of Temperature and Thermal Stresses in Unidirectional Rod with Moving Point Heat Source. In: Rushi Kumar, B., Sivaraj, R., Prakash, J. (eds) Advances in Fluid Dynamics. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-4308-1_37
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DOI: https://doi.org/10.1007/978-981-15-4308-1_37
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