HEAT TRANSFER SYMBOLS AND FORMULAS-1

 

https://www.mesubjects.net/wp-admin/post.php?post=7462&action=edit  Dimensionless num HT

https://www.mesubjects.net/wp-admin/post.php?post=7420&action=edit        HT Symbols-2

https://www.mesubjects.net/wp-admin/post.php?post=7368&action=edit          MCQ HT-1

https://www.mesubjects.net/wp-admin/post.php?post=7340&action=edit           MCQ HT-2

https://www.mesubjects.net/wp-admin/post.php?post=6732&action=edit       PTU HT Paper Sol B

https://www.mesubjects.net/wp-admin/post.php?post=6434&action=edit      PTU HT Paper Sol A

https://www.mesubjects.net/wp-admin/post.php?post=6261&action=edit            Fin HT

HEAT TRANSFER SYMBOLS AND FORMULAS-1

Heat transfer symbols and formula are very helpful in understanding the topic in great depth with lot of ease.

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.

 

q. = h A dt q. = h A dt
12. FORCED CONVECTION Motion of liquid is caused by a pump and the motion of gas is caused by a blower over the heated surface——–Car radiator. It is governed by the Reynolds number and Prandtl number. q. = h A dt q. = h A dt
13  

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.

 

Re Re = ρVD/μ
14 Nusselt number It is used to find ‘h’ Nu Nu= hl/kfluid
15 OVERALL HEAT TRANSFER COEFFICIENT It accounts for convection+conduction+convection U
16 LMTD It is a mean temperature DIFFERENCE for a heat exchanger LMTD LMTD = (θmax—θmin)/ ln(θmax/θmin)
17 NTU It is number of transfer units. It represents area. NTU NTU= U A/ Cmin

 

18. Effectiveness of a HEX Ratio of actual RATE of heat transfer to RATE of maximum heat transfer.

q. actual = mh cph dth = mc cpc dtc

q.max = Cmin(thot in – tcold in)

 

Є Є = q.actual /q.max
19. FIN FIN IS AN EXTENDED SURFACE WHICH INCREASES SIGNIFICANTLY THE SURFACE AREA AS WELL AS THE RATE OF HEAT TRANSFER MOST ECONOMICALLY.
20.  FIN EFFICIENCY ηf = actual q.fin/ q.max

q.max  is rate of HT with same base temperature tb all along the fin length

 

ηf ηf = (Pk/hAc)1/2
21. FIN EFFECTIVENESS    Ratio of rate of heat transfer with fin to rate of heat transfer without fin. Єf Єf = q.with fin/ q.without fin

 

Єf=(kP/hAc)1/2  

22. Dimensional analysis It is a process to develop an equation between dimensionless numbers based on dimensional homogenity
23 Bukingham

Theorem

Let total number of variables =n

Total no. of dimensions = m

Number of

24. Planck’s Law Gives emissive power of a black body FOR A SINGLE WAVELENGTH Eλ = C1λ—5/(ec2/λT –1) Eλ = C1λ—5/(ec2/λT –1)