18.13
Conduction, Convection and Radiation: Problem Solving
There are three methods by which heat transfer can take place: conduction, convection, and radiation. Each method has unique and interesting character…
A 13 cm thick wall with a 100 m2 area and 1.5 W/mK thermal conductivity separates a room from the outer atmosphere, which is at 3 degrees Celsius.
The outside surface of the wall is at 10 degrees Celsius, and its emissivity is 0.8. If the convective heat transfer coefficient is 15 W/m2K , find the total heat loss rate to the surrounding. Also, calculate the temperature of the inner surface of the wall.
Here, all three mechanisms of heat transfer are involved. Heat is transferred from the inner to the outer surface of the wall through conduction, while heat loss to the surroundings occurs due to convection and radiation.
The rate of heat loss through convection depends on the temperature gradient, surface area, and heat transfer coefficient.
So, total heat loss to the surrounding due to convection and radiation can be calculated as 13.27 x 103 W.
Employing the conservation of energy and substituting the terms in the heat equation, the temperature of the inner surface of the wall can be calculated.
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Q1: How do you identify which heat transfer mechanisms are involved in a problem?
First, examine the situation to determine the type of heat transfer involved. This could be conduction, convection, radiation, or all three of them. For example, in a wall separating a room from the atmosphere, heat transfers through the wall via conduction, while heat loss to surroundings occurs through convection and radiation. Identifying the correct mechanisms ensures you apply the appropriate equations.
Q2: What factors determine the rate of heat loss through convection?
The rate of heat loss through convection depends on three key factors: the temperature gradient between surfaces, the surface area exposed to the fluid, and the heat transfer coefficient. A larger temperature difference, greater surface area, or higher heat transfer coefficient increases convective heat loss. These variables are combined in the convection equation to calculate total heat transfer rate.
Q3: How does emissivity affect radiative heat transfer in a wall problem?
Emissivity is a material property that determines how effectively a surface emits thermal radiation. A surface with higher emissivity radiates more heat at a given temperature. In the wall example, an emissivity of 0.8 means the outer surface radiates 80% of the heat that a perfect black body would emit, significantly contributing to total heat loss alongside convection.
Q4: What is the role of thermal conductivity in calculating conductive heat transfer?
Thermal conductivity measures a material's ability to conduct heat through its thickness. A higher thermal conductivity value means heat flows more easily through the material. In the wall problem, the conductivity of 1.5 W/mK, combined with wall thickness and temperature difference, determines the conductive heat transfer rate from the inner to outer surface.
Q5: Why is conservation of energy important when solving combined heat transfer problems?
Conservation of energy ensures that the heat conducted through the wall equals the total heat lost to surroundings via convection and radiation. By applying this principle, you can set the conduction equation equal to the combined convection and radiation equations, allowing you to solve for unknown temperatures like the inner surface temperature.
Q6: What steps should you follow to solve a heat transfer problem systematically?
First, examine the situation to identify which heat transfer mechanisms are involved. Second, list all unknown quantities and known values given in the problem. Third, select the appropriate equations for each mechanism. Finally, substitute known quantities with their units into the equations and solve numerically to find the desired result.
Q7: How does temperature difference drive all three heat transfer mechanisms?
All three heat transfer mechanisms—conduction, convection, and radiation—transfer heat solely because of a temperature difference. The greater the temperature difference between surfaces or between a surface and its surroundings, the faster the heat transfer occurs through any mechanism. This fundamental principle applies whether heat moves through a solid, fluid, or across empty space.