Chapter 2 Heat Conduction Equation2-86A long resistance heater wire is subjected to convection at its outer surface. The surface temperature of the wire is to be determined using the applicable relations directly and by solving the applicable differential equation. Assumptions 1Heat transfer is steady since there is no indication of any change with time. 2 Heat transfer is one-dimensional since there is thermal symmetry about the center line and no change in the axial direction.3 Thermal conductivity is constant.4 Heat generation in the wire is uniform. PropertiesThe thermal conductivity is given to be k= 15.1 W/m⋅°C. T∞h r k g T∞h ro0 Analysis(a) The heat generation per unit volume of the wire is &&&(..gQVQrLgengeno====×wire23Wm) (6 m)W/mπ2820000 0011061 10The surface temperature of the wire is then (Eq. 2-68) TTgrhso=+=°+×°=°∞&)(2301061 100 0012 1408Cm)W/m . C)32409 C(b) The mathematical formulation of this problem can be expressed as 01=+⎟⎠⎞⎜⎝⎛kgdrdTrdr
This is the end of the preview. Sign up
access the rest of the document.