Basic Heat Transfer Calculations: Conduction, Convection and Radiation

The following are the basic heat transfer calculation formulas for conduction, convection, and radiation:

Conduction Heat Transfer

Conduction is the transfer of heat through a material due to a temperature gradient within the material itself.

Fourier Law of Conduction

  • The rate of heat transfer through conduction is given by Fourier’s Law:

                  Q =  KA (T1 -T2)/ΔX

  • Q is the rate of  heat transferred  through the surface (W or J/S)
  • K is the thermal conductivity of the material (W/m-K)
  • A is an area of the surface (m^2) normal to heat transfer direction
  • T2  is the temperature of the hot surface (K)
  • T1 is the temperature of the cold surface (K)
  • Δx  is the thickness of the material (m)
conduction heat Transfer types
Conduction heat Transfer Calculations

Determination of Conduction Rate

  •  For multilayer conduction heat transfer
  • Thermal resistance, R = Δx/KA
  • The total thermal resistance (RTotal) of a multilayer system is the sum of the individual thermal resistances. For a series arrangement of layers, the formula is:

                    Rtotal = R1 + R2 + R3 + ….. + Rn

  • Where R1, R2, and R3 are the thermal resistances of the individual layers. Each layer’s thermal resistance (Ri)) can be calculated using the formula
  • Determine the overall heat transfer rate (Q) through the multilayer system using:

Q  = Overall Temperature Difference/Total thermal resistance

                      Q =  ΔT /Rtotal

  • Where ΔT  is the overall Temperature difference across the multilayer system.
  • Please note that this method assumes
    • steady-state conditions
    • and uniform material properties
    • One-dimensional heat transfer through the layers.
  • Real-world applications may involve more complex geometries and material properties that might require more sophisticated models or numerical methods for accurate analysis.

Convection Heat Transfer 

  • Convection is the transfer of heat between a surface and a fluid (liquid or gas) flowing over it.
  • The convective heat transfer rate is commonly calculated using Newton’s Law of Cooling
convective Heat transfer formula
Convective Heat Transfer Formula
  • Q  is the convective rate of  heat transfer (J/S)
  • h  is the heat transfer coefficient (W/m^2-K)
  • C  is the specific heat capacity of the fluid (J/kg-K)
  • A is  area of the surface (m^2)
  • Ts  is the surface temperature of the hot surface (K)
  • Tf  is the  temperature of the flowing fluid (K)
Forced convection heat transfer
Forced convection heat transfer

Calculation of Total Heat Transfer from Composite Wall

  • Input Data
    • Surface Area, A (m2)
    • Thermal conductivities of materials, K (w/m-k)
    • Heat Transfer coefficients of fluid on both sides of composite walls
    • Temperature of fluids
  • Calculate overall thermal resistance, Rth
  • Calculate overall heat transfer coefficients, U (w/m2-k)
Calculation of Heat Transfer from composite walls
Calculation of Heat Transfer from composite walls
  • Calculate heat transfer per unit area, heat flux  (q,w/m2)
  • Calculate total heat
  • Refer to the following spread for calculations

Radiation Heat Transfer

  • Radiation is the transfer of heat through electromagnetic waves.
  • The rate of heat transfer through radiation between two surfaces is given by the Stefan-Boltzmann Law:

          Q = σ A (T2^4     –  T1^4)

where

  • Q is the radiative  heat transferred (W or J/S)
  • σ is the constant of Stefan-Boltzmann  (5.67 x 10^-8 W/m^2-K^4)
  • A is  area of the surface (m^2)
  • T2 is the  temperature of the hot surface (K)
  • T1 is the  temperature of the cold surface (K)

These formulas can be used to calculate the heat transfer rate between two surfaces or to calculate the temperature of a surface after a certain amount of time.

radiative heat transfer law
Radiative heat transfer law