M E 4210 Lecture Notes - Lecture 3: Spherical Coordinate System, Cylindrical Coordinate System, Thermal Conductivity

• School: Wayne State University
• Department: Mechanical Engineering
• Course: M E 4210
• Professor: Bashar S.Abdul Nour

Document Summary

Recall that the heat diffusion equation in rectangular coordinates is given as. For the shown plane wall with heat conduction in the x-direction only, the 1- D ( t/ y = 0, t/ z = 0), steady ( t/ t = 0) heat conduction without heat generation (q = 0), reduces the above equation to. Lecture #03-a where the partial derivative is converted to ordinary derivative since t = In addition, for the case of constant thermal conductivity, we have. The above can be solved for the temperature distribution t(x) by successive integration. T(x) = c1x + c2 or where c1 and c2 are constants of integration. To evaluate c1 and c2, use the boundary conditions. Then, the expression for t becomes which is the equation for the temperature distribution in the wall. It is a straight line with a slope = and y-intercept = ts,1.