THERMAL RESISTANCES CLASS NOTES FOR MECHANICAL ENGINEERING

 THERMAL RESISTANCES  CLASS NOTES

FOR MECHANICAL ENGINEERING

 

1.      THERMAL RESISTANCES IN CONDUCTION

(i)    For a single wall of thickness x

         Thermal resistance Rth=x/kA                                K/W

(ii)  For a composite wall of thicknesses x1, x2 and x3 with thermal conductivities k1, k2 and k3 respectively.

        Thermal resistance  Rth= x1/k1A + x2/k2A + x3/k3A       K/W

(iii) For a single cylindrical surface

         Rth = ln(ro/ri) /2 π k L

(iv) For a multi-wall (three layers) cylindrical surface

         Rth = ln(r2/r1) /2π k1L + ln(r3/r2) /2 π k2L + ln(r4/r3) /2 π k3L

(v) For a single spherical surface

       Rth = (ro –ri) /4 πkrori

(vi) For a multi-wall (three layers) spherical surface

          Rth = (r2 –r1) /4π k1rori + (r3 –r2) /4π k2rori + (r4 –r3) /4 π k3rori

(vii) Contact resistance due to surface roughness and void space

          Area available will be less. Due to surface roughness, contact won’t be perfect, the reduced area and             or presence of voids, there is a large resistance called the surface contact resistance. It causes                       temperature drop, ΔT, between the two surfaces.

         (Rth)contact = ΔT/ (Q. / A)

Units of thermal resistance is oC/W

2. THERMAL RESISTANCES IN CONVECTION

     Rth = 1/hA

     Based on inside conditions          Rth i = 1/hiAi

     Based on outside conditions       Rth o = 1/hoAo

In case cylindrical and spherical bodies A o will be greater than Ai, therefore ho will be smaller than hi.

3. THERMAL RESISTANCES IN RADITION

     Rth = 1/σAF12 (T12 + T22)( T1 + T2)

    Surface resistance in radiation in a real body

   Rth sur  = (1 – Є) / AЄ

   Surface resistance of a black body = 0

   Space resistance in radiation (there is space between two radiating surfaces)

   Rth space = 1/A1 F12

 Thermal resistances help a lot in solving problems of heat transfer.