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.