Q5) For laminar free convection from a heated vertical surface, the local convection coeffi may be expressed as h, = Czx-1/4, where h, is the coefficient at a distance x from the lea edge of the surface and the quantity C, which depends on the fluid properties, is indeper of x. Obtain an expression for the ratio h/hy, where x is the average coefficient betwee Jonding odgo (r O) ond the x loeetion S kotoh the veriotion of h ond b with

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A hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T.

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36 -S 42 2. Metal castings can sometimes develop a gap between the casting and mold as the molten metal hardens. The result can be a substantially altered cooling process. Set up a simple heat-transfer model that would let you look at the effect of the gap on the cooling process. Assume the casting and mold are square in shape, with an air gap of thickness das shown in the figure. The mold sits in some ambient room temperature. State clearly all assumptions and develop a corresponding model of the heat transfer problem. Assuming that the casting is aluminum, the mold is diatomaceous earth and the gap is filled with air, see if you can arrive at and summarize some insight into the effect of the gap and its size on the heat transfer process.

One of the strengths of numerical methods is their ability to handle complex boundary conditions. In the sketch, the boundary condition changes from specified heat flux ′′ qs (into the domain) to convection, at the location of the node (m, n). Write the steady-state, two- dimensional finite difference equation at this node.

Why do vapor bubbles get larger in boiling water as they approach the surface? Type your detailed answer on Canvas using thermal concepts. BIUA A-IEE 33I X x, EE 2 V TT 12pt • Paragraph esc & %23 %$4 4 5 1 S F LE !! e

dT = k(T- Tm), where T(t) is the temperature of the object at The mathematical model for Newton's law of cooling is ot time t and Tm is the constant temperature of the surrounding medium. What is lim T(t) ? t+ 00

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