## Heat Transfer Mechanisms

Heat transfer can occur through three main mechanisms: conduction, convection, and radiation. The rate of heat transfer is often expressed using different formulas for each mechanism. Here are the basic formulas for each:

### Conduction:

The rate of heat transfer (Q) through a material by conduction is given by Fourier's Law:

Q = -kA (ΔT/d)

where:

- Q is the rate of heat transfer,
- k is the thermal conductivity of the material,
- A is the cross-sectional area through which heat is transferred,
- ΔT is the temperature difference across the material,
- d is the thickness of the material.

### Convection:

The rate of heat transfer (Q) by convection is given by Newton's Law of Cooling:

Q = hAΔT

where:

- Q is the rate of heat transfer,
- h is the convective heat transfer coefficient,
- A is the surface area through which heat is transferred,
- ΔT is the temperature difference between the surface and the surrounding fluid.

### Radiation:

The rate of heat transfer (Q) by radiation is given by the Stefan-Boltzmann Law:

Q = σA(T_{1}^{4} - T_{2}^{4})

where:

- Q is the rate of heat transfer,
- σ is the Stefan-Boltzmann constant,
- A is the surface area of the radiating body,
- T
_{1}is the absolute temperature of the radiating body, - T
_{2}is the absolute temperature of the surroundings.

These formulas are basic representations, and more complex scenarios may require additional considerations or modifications. Additionally, units should be consistent when using these formulas. Q is typically measured in watts (W), k in watts per meter-kelvin (W/(m·K)), and h in watts per square meter-kelvin (W/(m²·K)). The Stefan-Boltzmann constant (σ) is approximately 5.67 × 10^{-8} W/(m²·K^{4}).

## Total Heat Gained Calculation

A system weighing 6 Kgs is heated from its initial temperature of 40ᵒC to its final temperature of 70ᵒC. Calculate the total heat gained by the system. (Specific heat of the system = 0.45 kJ/Kg K)

**Formula:**

Q = mcΔT

where:

- Q is the heat gained,
- m is the mass of the system,
- c is the specific heat of the material,
- ΔT is the change in temperature.

**Given:**

- m = 6 kg (mass of the system),
- c = 0.45 kJ/kg K (specific heat of the system),
- ΔT = T
_{final}- T_{initial}= 70ᵒC - 40ᵒC = 30K (converted to Kelvin).

**Calculation:**

Q = (m) × (c) × (ΔT)

Q = (6 kg) × (0.45 kJ/kg K) × (30 K)

Q = 8.1 kJ

Therefore, the total heat gained by the system is 8.1 kJ.

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