Tham khảo tài liệu 'computational fluid mechanics and heat transfer third edition_6', kỹ thuật - công nghệ, điện - điện tử phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 184 Chapter 4 Analysis of heat conduction and some steady one-dimensional problems the dimensionless functional equation for the local velocity cf. Section . A steam preheater consists of a thick electrically conducting cylindrical shell insulated on the outside with wet stream flowing down the middle. The inside heat transfer coefficient is highly variable depending on the velocity quality and so on but the flow temperature is constant. Heat is released at q J m3s within the cylinder wall. Evaluate the temperature within the cylinder as a function of position. Plot 0 against p where 0 is an appropriate dimensionless temperature and p r ro. Use pi 2 3 and note that Bi will be the parameter of a family of solutions. On the basis of this plot recommend criteria in terms of Bi for a replacing the convective boundary condition on the inside with a constant temperature condition b neglecting temperature variations within the cylinder. Steam condenses on the inside of a small pipe keeping it at a specified temperature Ti. The pipe is heated by electrical resistance at a rate q W m3. The outside temperature is Tn and there is a natural convection heat transfer coefficient h around the outside. a Derive an expression for the dimensionless expression temperature distribution 0 T - Tn Ti - Tn as a function of the radius ratios p r ro and pi ri ro a heat generation number r qr2 k Ti - Tn and the Biot number. b Plot this result for the case pi 2 3 Bi 1 and for several values of r. c Discuss any interesting aspects of your result. Solve Problem if you have not already done so putting it in dimensionless form before you begin. Then let the Biot numbers approach infinity in the solution. You should get the same solution we got in Example using . s of the first kind. Do you Complete the algebra that is missing between eqns. and eqn. and eqn. . Complete the algebra that is missing between eqns. and eqn. and eqn. .
