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Steady-State Conduction in One Dimension
Published in William S. Janna, Engineering Heat Transfer, 2018
Let us consider a one-dimensional coordinate system, as shown in Figure 2.1. The system consists of a plane wall on which we impose the T versus x axes. A slice of the material dx thick is selected for study. The fact that energy can be generated within the material is taken into account by a term denoted as q”’. Typically, internal heat generation within a solid can be from chemical reactions, as the result of an electric current passing through the material (a wire for example), or by a nuclear reaction. Some of the energy passing through the control volume may be stored, thus increasing the internal energy of the material, which is sensed physically as an increase in the temperature of the material. This is the case for an unsteady problem.
Applications
Published in Raj P. Chhabra, CRC Handbook of Thermal Engineering Second Edition, 2017
Joshua D. Ramsey, Ken Bell, Ramesh K. Shah, Bengt Sundén, Zan Wu, Clement Kleinstreuer, Zelin Xu, D. Ian Wilson, Graham T. Polley, John A. Pearce, Kenneth R. Diller, Jonathan W. Valvano, David W. Yarbrough, Moncef Krarti, John Zhai, Jan Kośny, Christian K. Bach, Ian H. Bell, Craig R. Bradshaw, Eckhard A. Groll, Abhinav Krishna, Orkan Kurtulus, Margaret M. Mathison, Bryce Shaffer, Bin Yang, Xinye Zhang, Davide Ziviani, Robert F. Boehm, Anthony F. Mills, Santanu Bandyopadhyay, Shankar Narasimhan, Donald L. Fenton, Raj M. Manglik, Sameer Khandekar, Mario F. Trujillo, Rolf D. Reitz, Milind A. Jog, Prabhat Kumar, K.P. Sandeep, Sanjiv Sinha, Krishna Valavala, Jun Ma, Pradeep Lall, Harold R. Jacobs, Mangesh Chaudhari, Amit Agrawal, Robert J. Moffat, Tadhg O’Donovan, Jungho Kim, S.A. Sherif, Alan T. McDonald, Arturo Pacheco-Vega, Gerardo Diaz, Mihir Sen, K.T. Yang, Martine Rueff, Evelyne Mauret, Pawel Wawrzyniak, Ireneusz Zbicinski, Mariia Sobulska, P.S. Ghoshdastidar, Naveen Tiwari, Rajappa Tadepalli, Raj Ganesh S. Pala, Desh Bandhu Singh, G. N. Tiwari
Passive cooling methods are predominantly used in outdoor enclosures on account of their simplicity and lack of maintenance. The most common cooling method used today in the OSP is relatively simple. The enclosure is unventilated to protect the internal equipment from the rain, dust, and contaminants in the outside air. The internal heat is transferred primarily by convection to the inside surfaces of the enclosure, by conduction through the walls of the enclosure, and then by convection and radiation to the external heat sinks. Other passive methods include natural (free) convection in conjunction with phase change materials (PCMs) and solar reflectors. PCMs are substances that change phase, most often from solid to liquid, as they absorb heat. PCMs are selected for the temperature at which they change phase and for the latent heat associated with phase change. PCMs are sometimes used in conjunction with thermosiphons. Typical PCMs for high-temperature applications include waxes, salts, and paraffins. Water (ice) is used for low-temperature applications. The PCM is kept inside or attached to the enclosure in appropriately designed and sealed reservoirs (Figure 4.22.51). PCMs take advantage of thermal inertia and phase change effects. For example, an enclosure with PCMs during daylight hours will absorb heat through the cabinet walls and protect the electronics within the enclosure from overheating. The heat absorbed during the day will then be released to the outside world at night when it is cooler.
Fundamentals of Heat Transfer in Food Processing
Published in Mohammed M. Farid, Mathematical Modeling of Food Processing, 2010
Volumetric heating effect of high pressure can be modeled with internal heat generation theory. For this purpose, internal heat generation value (W/m3) can be obtained using the equation given by Rasanayagam et al. [47] to determine rise in temperature due to compression during high pressure processing: ∂T∂P=β⋅Tρ⋅cp
Double diffusive convection of CuO + MWCNT hybrid nanofluid in an inclined open cavity with internal heat generation/absorption
Published in International Journal of Ambient Energy, 2023
P. Gokulavani, M. Muthtamilselvan, Qasem Al-Mdallal
Internal heat generation/absorption takes an important part in energy-based engineering problems. Khanafer and Chamkha (1998) numerically analysed the free convection in an inclined closed enclosure with hydromagnetic and heat generation. Again, the above-said problem with the opposing thermal and computational buoyancy force is inspected by Chamkha and Al-Naser (2002). They also studied these effects in the porous medium filled with a tall closed enclosure (Chamkha 2002). From their study, they found that the mass and heat transfer was highly influenced by the heat generation/absorption factor. The rate of heat transfer was enhanced with a heat sink while it decreased in the presence of a heat source. Later, Chamkha and Al-Mudhaf (2008) tested double-diffusive convection in an inclined porous-filled cavity along with the presence of a heat source/sink. They analysed the problem in the binary fluid-filled closed cavity with various aspect ratios. The results were discussed for the alternative parametric condition. The numerical examination of internal heat generation in a closed square enclosure containing an isothermal obstacle fastened in the bottom wall is conducted by Oztop and Bilgen (2006). Their results indicate that the external Rayleigh number is improving the function of the heat transfer.