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)

**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

- 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)

**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)

- 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.