Heat Transfer Analysis: Conduction, Convection, Radiation

Fundamental Laws of Heat Transfer

Transfer of heat energy takes place in accordance with the Laws of Thermodynamics.

The assumption in the Fourier Law Q = –kA(dT/dx) is that the heat flow is steady and one-dimensional.

The temperature difference between two sides of a wall can be increased by increasing the heat flow rate or increasing the thermal resistance.

Conduction and Thermal Resistance

A slab 50 cm thick is made of fire brick (k = 1.5 W/m·K). For the same heat transfer and same temperature drop, what will be the wall thickness of a material having a thermal conductivity of 0.75?

Arrange the thermal conductivity of materials in ascending order: Brick, Steel, Aluminium, and Copper.

The thermal conductivity of a material varies with temperature and pressure.

For the same thickness, the temperature drop in an insulation material is significantly higher than in a conductor.

A thin flat plate is hanging freely in air at 27°C. Solar radiation falls on one of its sides at the rate of 500 W/m². For maintaining the temperature of the plate constant at 32°C, what is the value of the heat transfer coefficient?

The radiation heat transfer rate per unit area between two black bodies at temperatures 900 K and 40 K (in kW/m²) is calculated using the Stefan-Boltzmann Law.

Transient Heat Conduction and Diffusivity

The thermal conductivity k, the density ρ, and specific heat C of an aluminium plate are 160 W/m·K, 2790 kg/m³, and 0.88 kJ/kg·K respectively. Calculate the thermal diffusivity of the material.

Thermal resistance for a hollow sphere is expressed as (r₂ - r₁) / (4πk r₁ r₂).

Thermal resistance due to a stagnant air gap is equal to the reciprocal of the heat transfer coefficient.

If the total thermal resistance for this arrangement is 0.53282 K/W, the total heat transfer rate is equal to the temperature difference divided by the resistance.

Thermal resistance due to a single glass sheet of 10 mm thickness will be L/kA.

Dimensionless Numbers in Heat Transfer

The characteristic length of the steel ball L_c is the ratio of volume to surface area.

The Biot number is the ratio of internal conductive resistance to external convective resistance.

The time taken by the center to reach a temperature of 150°C is determined using transient heat flow analysis.

One end of a long rod 3 cm in diameter is subjected to heat; calculate the thermal conductivity of the rod material.

Convection Principles

During forced convection, fluid is forced to flow using external power (such as a pump or fan).

During natural (free) convection, fluid flows due to density differences caused by temperature gradients.

The ratio of buoyancy forces to viscous forces is called the Grashof number.

The ratio of inertia forces to viscous forces is called the Reynolds number.

The ratio of convection heat flux to conduction heat flux is called the Nusselt number.

The critical value of the Reynolds number for transition from laminar to turbulent flow when flow is over a flat plate is 5 × 10⁵.

The critical value of the Reynolds number for transition from laminar to turbulent flow when flow is inside tubes is 2300.

The product of the Grashof number and Prandtl number is called the Rayleigh number.

The characteristic length of a vertical cylinder during convection heat transfer is equal to its height.

The characteristic length of a horizontal cylinder during convection heat transfer is equal to its diameter.

Heat Exchanger Performance

In the case of a parallel flow heat exchanger, both fluids move in the same direction.

In a heat exchanger, if the tube wall thickness is very small and thermal conductivity of the material is very high, then the conductive resistance is negligible.

Which of the following is true for a counter-flow heat exchanger? (It generally provides higher effectiveness than parallel flow).

Which of the following is true for a parallel flow heat exchanger? (The exit temperature of the cold fluid cannot exceed the exit temperature of the hot fluid).

A heat exchanger is required to cool 55,000 kg/h of alcohol from 66°C to 40°C using 40,000 kg/h of water entering at 5°C. Calculate the exit temperature of water, if C_p (alcohol) = 3760 J/kg·K and C_p (water) = 4180 J/kg·K.

Steam enters a counter-flow heat exchanger. Neglect the thermal resistance offered by metallic tubes. Use the following data: For steam T_sat = 180°C (at 10 bar), C_ps = 2.71 kJ/kg·K, h_i = 600 W/m²·K. For gas C_pg = 1 kJ/kg·K, h_o = 250 W/m²·K. Calculate the overall heat transfer coefficient U.

The ratio of the actual heat transfer rate by a heat exchanger to the maximum possible heat transfer rate is called Effectiveness.

The ratio of the heat capacity rate of the heat exchanger to the heat capacity rate of the fluid is called the Capacity Ratio.

The ratio of minimum heat capacity rate to maximum heat capacity rate is called the Capacity Rate Ratio.

The higher the value of NTU (Number of Transfer Units) of a heat exchanger, the higher its effectiveness.

Radiation Laws and Properties

The emissivity of real surfaces is always less than 1.0.

The minimum temperature for the beginning of radiation heat transfer is Absolute Zero (0 K).

Which of the following is true for a white body? (Reflectivity is equal to 1).

Wien’s Displacement Law gives us the relationship between the temperature of a body and the wavelength corresponding to maximum monochromatic radiation.

Planck’s Law gives us the variation of monochromatic radiation heat transfer at a particular temperature.