_{Sr. No.}

_{Item or quantity}

_Definition

_Symbol

_Formula

_Units

_1.

_{Thermal conductivity}

_{Rate of heat transfer per unit area per unit temperature difference and per unit wall thickness.}

_{k=q.  For A= 1m2 , dt=10c and dx=1m}

_k

_{Q=-kA∂t/∂x}

_W/m0C

_2.

_{Thermal diffusivity}

_{Ratio of thermal conductivity to heat capacity per unit volume}

_α

_{Α =k/ρcp}

_m2/s

_3.

_{Temperature gradient}

_{Change of temperature with respect to x,}

_{it is NEGATIVE because as x increases t decreases.}

_∂t/∂x,.

_∂t/∂x,.

_0C/m

_4.

_{Fourier equation}

_{Gives rate of heat transfer in conduction.}

_{q. = -k A dt/dx}

_{q. = -k A dt /dx}

_WATTS

_5.

_{Fourier Law}

_{(i)                 q.    A}

_{(ii)               q.   dt}

_{(iii)             q.    A dt}

_{(iv)              q.   =h A dt}

_{q.   =h A dt}

_{q.   =h A dt}

_W

_6.

_CONDUCTION

_CONVECTION

_RADIATION

_{Fourier equation is conduction equation.}

_{Newton’s Law of cooling is convection equation.}

_{Stephen’s Boltzmann Law is radiation equation.}

_7.

_{CRITICAL RADIUS OF INSULATION}

_{It is a radius of insulation at which the rate of heat transfer is maximum}

_rcr

_{For a cylinder}

_{rcr = k/h0}

_{For a sphere}

_{rcr =2 k/h0}

_mm

_8.

_{Biot number}

_{internal resistance/external resistance}

_{=Conductive resistance/Convective resistance}

_Bi

_{Bi =hx/ksolid}

_{No units}

_9.

_{Steady state}

_{Temperature does change with time. Human body}

_{∂t/∂time=0}

_{∂t/∂time=0}

_0C/s

_10.

_{Unsteady state}

_{Temperature changes with time. Atmospheric temp}

_∂t/∂time

_∂t/∂time

_0C/s

_11.

_{FREE OR NATURAL CONVECTION}

When bulk motion of the fluid is caused by the density difference or Buoyancy force, it is called Free or Natural convection. It is governed by the product of Grashoff’s number and Prandtl number. All the convection processes in nature are of free convection.

CRITICAL REYNOLD NUMBER

Reynolds number where the laminar region ends.

(a)Its value is 5 x 10⁵for a flat horizontal plate.

(b)            It is 2100 for flow through a pipe.

q^. _actual = m_h c_ph dt_h = m_c c_pc dt_c

q^._max = C_min(t_{hot in} – t_{cold in})

q^._max  is rate of HT with same base temperature t_b all along the fin length

Є_f=(kP/hA_c)^1/2  

Theorem

Total no. of dimensions = m

Number of