Heal generation uniform

Consider a long resistance wire of radius r, = 0.3 cm and thermal conductivity = 18 W/m C in which heat is generated uniformly at a constant rate of = 1.5 W/cm as a result of resistance healing. The wire is embedded in a 0.4-cm-thick layer of plastic whose thermal conductivity is = 1.8 W/m °C. The outer surface of Ihe plastic covet loses heat by convection to the ambient air at T = 25 C with an average combined heat transfer coefficient of A = 14 W/m °C. 

Analysis Heat is generated in the wire and its temperature rises as a result of resistance heating. We assume heal Is generated uniformly throughout the wire and is transferred to the surrounding medium in the radial direction. In steady operation, the rate of heat transfer becomes equal to the heal generated within the wire, which is determined to be... 

S-73 Consider transient heat conduction in a plane wall whose left surface (node 0) i.s maintained at. >0°C while the tiglil surface (node 6) is subjeeted to a solar heal flux of 600 W/m. The wall is initially at a uniform temperature of 50°C. Express the explicit finite difference fomiulalion of the boundary nodes 0 and 6 for the case of no heal generation. Also, obtain die finite difference formulaiioti for the total amount of heat transfer at the left boundary during the first three lime steps. 

Consider transient heat conduction in a plane wall with variable heal generation and constant thermal conductivity. The nodal network of (he medium consists of nodes 0, 1, 2, 3, and 4 with a uniform nodal spacing of A.r. The wall is initially at a specified temperaWre. The temperature at the right bound ary (node 4) is specified. Using the energy balance approach, obtain the explicit finite difference formulation of the boundary... 

Water is to be healed from 10°C to 80°C as it flows through a 2-cm-inleinal-diameter, 13-m-long tubc.Tlie tube is equipped with an electric resistance heater, which provides uniform healing throughout the surface of (he tube. The outer surface of Ihe healer is well insulated, so that in steady operation all the heal generated in the heater is transferred to... 

Heat transfer is one-dimensional since this two-layer heal transfer problem possesses symmetry about the centerline and involves no change in the axial direction, and thus T = Tir). 3 Thermal conductivities are constant. 4 Heat generation in the wire is uniform. 

Consider a small hot metal object of mass m and specific heal c lliat is initially at a temperature of 7j. Now the object is allowed to cool in an environment at T by convection with a heat transfer coefficient of /r. The (emperanire of the metal object is observed to vary uniformly with time during cooling. Writing an energy balance on the entire metal object, derive the differential equation that describes the variation of temperature of the ball with time, T(/). Assume constant thermal conductivity and no heat generation in the object. Do not solve. 

Consider an I8 cm X 18-cm multilayer circuit board dissipating 27 W of heat. The board consists of four layers of 0.2-mm-lhick copper (k — 386 W/m °C) and three layers of 1.5-mm-thick epoxy glas.s (k = 0.26 W/m "C). sandwiched together, as shown in the figure. The circuit board is attached to a heal sink om both ends, and the temperature of the board at those ends is 35°C. Heat is considered to be uniformly generated in the epoxy layers of the board at a rate of 0.5 W per 1-cm X... 

Consider a sltori cylinder of height a and radius r initially at a uniform temperature T,. There is no heat generation in the cylinder. At time t = 0. the cylinder is subjected to convection from all surfaces to a medium at temperature l with a heal transfer coefficieiu h. The temperature within the cylinder will change with a as well as r and time f since heal transfer occurs from Ihe top and bottom of the cylinder as weU as its side surfaces. That is, T = 7 (r,, v, f) and thus this is a two-dimensional transient heal conduction problem. When the properties are assumed to be constant, it can be shown that the solution of this two-dimensional problem can be expressed as... 

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