MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.051 Introduction to Heat Transfer Equation Sheet (Fall 2015) Mode of Heat Transfer Equation Conduction q  kT Fourier’s Law Newton’s law of cooling Convection   5.67 108 W/(m2 K 4 ) where   emissivity of object (1) Radiation 1 Radiation heat transfer from a small grey object (1) to a large isothermal environment (2) STEADY HEAT TRANSFER: Mode of Heat Transfer Conduction Resistance [K/W] Slab Rcond = L / (kA) Cylindrical (radial direction) Rcond  Spherical (radial direction) Rcond  ln(rout / rin ) 2 kL  1 rin  rout1   4 k  Convection Rconv = 1/ (hA) Radiation Rrad = 1/ (hr A) where hr  41 Tavg 3 when T1  T2 Steady state heat equation with energy generation:   T    T    T  k k  k  x  x  y  y     z  z Planar coordinate Cylindrical coordinate    qgen  0  1   T  1   T    T  k  k  kr    qgen  0 r r  r  r 2     z  z  Equation Sheet (Quiz 1) Page 1 of 1

2.051 Introduction to Heat Transfer: Quiz 1 Equation Sheet

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