Peak Temperature Reached at any Point in Material Solution

STEP 0: Pre-Calculation Summary
Formula Used
Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length)
Tp = ta+(HNet*(Tm-ta))/((Tm-ta)*sqrt(2*pi*e)*ρm*t*Qc*y+HNet)
This formula uses 2 Constants, 1 Functions, 8 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Peak Temperature Reached at a Distance of y - (Measured in Kelvin) - Peak Temperature reached at a distance of y is the temperature reached at a distance of y from the fusion boundary.
Ambient Temperature - (Measured in Kelvin) - Ambient Temperature is the temperature of the surrounding.
Net Heat Supplied per Unit Length - (Measured in Joule per Meter) - Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter.
Melting Temperature of Base Metal - (Measured in Kelvin) - Melting Temperature of Base Metal is the temperature at which its phase changes to liquid to solid.
Density of Metal - (Measured in Kilogram per Cubic Meter) - Density of Metal is the mass per unit volume of the given metal.
Thickness of the Metal - (Measured in Meter) - Thickness of the metal is the thickness of the base metal and is denoted by h symbol.
Specific Heat Capacity - (Measured in Joule per Kilogram per K) - Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount.
Distance from the Fusion Boundary - (Measured in Meter) - Distance from the Fusion Boundary is measured from the fusion boundary during welding.
STEP 1: Convert Input(s) to Base Unit
Ambient Temperature: 37 Celsius --> 310.15 Kelvin (Check conversion here)
Net Heat Supplied per Unit Length: 1000 Joule per Millimeter --> 1000000 Joule per Meter (Check conversion here)
Melting Temperature of Base Metal: 1500 Celsius --> 1773.15 Kelvin (Check conversion here)
Density of Metal: 7850 Kilogram per Cubic Meter --> 7850 Kilogram per Cubic Meter No Conversion Required
Thickness of the Metal: 5 Millimeter --> 0.005 Meter (Check conversion here)
Specific Heat Capacity: 4.184 Kilojoule per Kilogram per K --> 4184 Joule per Kilogram per K (Check conversion here)
Distance from the Fusion Boundary: 100 Millimeter --> 0.1 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
Tp = ta+(HNet*(Tm-ta))/((Tm-ta)*sqrt(2*pi*e)*ρm*t*Qc*y+HNet) --> 310.15+(1000000*(1773.15-310.15))/((1773.15-310.15)*sqrt(2*pi*e)*7850*0.005*4184*0.1+1000000)
Evaluating ... ...
Tp = 324.737452012249
STEP 3: Convert Result to Output's Unit
324.737452012249 Kelvin -->51.5874520122489 Celsius (Check conversion here)
FINAL ANSWER
51.5874520122489 51.58745 Celsius <-- Peak Temperature Reached at a Distance of y
(Calculation completed in 00.020 seconds)

Credits

Created by Rajat Vishwakarma
University Institute of Technology RGPV (UIT - RGPV), Bhopal
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13 Heat Flow in Welded Joints Calculators

Peak Temperature Reached at any Point in Material
Go Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length)
Position of peak temperature from fusion boundary
Go Distance from the Fusion Boundary = ((Melting Temperature of Base Metal-Temperature Reached at a Distance of y)*Net Heat Supplied per Unit Length)/((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal)
Net heat supplied to weld area to raise it to given temperature from fusion boundary
Go Net Heat Supplied per Unit Length = ((Temperature Reached at a Distance of y-Ambient Temperature)*(Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density*Specific Heat Capacity*Thickness of the Metal*Distance from the Fusion Boundary)/(Melting Temperature of Base Metal-Temperature Reached at a Distance of y)
Net heat supplied to achieve given cooling rates for thin plates
Go Net Heat Supplied per Unit Length = Thickness of the Metal/sqrt(Cooling Rate of Thinplate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))
Thickness of base metal for desired cooling rate
Go Thickness = Net Heat Supplied per Unit Length*sqrt(Cooling Rate/(2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)))
Thermal conductivity of base metal using given cooling rate (thin plates)
Go Thermal Conductivity = Cooling Rate of Thinplate/(2*pi*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3))
Cooling rate for relatively thin plates
Go Cooling Rate of Thinplate = 2*pi*Thermal Conductivity*Density*Specific Heat Capacity*((Thickness of the Metal/Net Heat Supplied per Unit Length)^2)*((Temperature to Calculate Cooling Rate-Ambient Temperature)^3)
Relative plate thickness factor
Go Relative Plate Thickness Factor = Thickness of the Metal*sqrt(((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density of Metal*Specific Heat Capacity)/Net Heat Supplied per Unit Length)
Thickness of Base Metal using Relative Thickness Factor
Go Thickness of the Base Metal = Relative Plate Thickness Factor*sqrt(Net Heat Supplied per Unit Length/((Temperature to Calculate Cooling Rate-Ambient Temperature)*Density*Specific Heat Capacity))
Net Heat supplied using Relative Thickness Factor
Go Net Heat Supplied = ((Thickness of the Metal/Relative Plate Thickness Factor)^2)*Density*Specific Heat Capacity*(Temperature to Calculate Cooling Rate-Ambient Temperature)
Thermal conductivity of base metal using given cooling rate (thick plates)
Go Thermal Conductivity = (Cooling Rate*Net Heat Supplied per Unit Length)/(2*pi*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))
Net heat supplied to achieve given cooling rates for thick plates
Go Net Heat Supplied per Unit Length = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Cooling Rate
Cooling Rate for Relatively Thick Plates
Go Cooling Rate = (2*pi*Thermal Conductivity*((Temperature to Calculate Cooling Rate-Ambient Temperature)^2))/Net Heat Supplied per Unit Length

Peak Temperature Reached at any Point in Material Formula

Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length)
Tp = ta+(HNet*(Tm-ta))/((Tm-ta)*sqrt(2*pi*e)*ρm*t*Qc*y+HNet)

Why peak temperature reached in Heat Affected Zone is important to calculate ?

The peak temperature reached at any point in the material is another important parameter that needs to be calculated. This would help in identifying what type of metallurgical transformations are likely to takes place in the heat affected zone (HAZ).

How to Calculate Peak Temperature Reached at any Point in Material?

Peak Temperature Reached at any Point in Material calculator uses Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length) to calculate the Peak Temperature Reached at a Distance of y, The Peak Temperature reached at any point in material formula is defined as the temperature reached during welding in the heat affected zone. Peak Temperature Reached at a Distance of y is denoted by Tp symbol.

How to calculate Peak Temperature Reached at any Point in Material using this online calculator? To use this online calculator for Peak Temperature Reached at any Point in Material, enter Ambient Temperature (ta), Net Heat Supplied per Unit Length (HNet), Melting Temperature of Base Metal (Tm), Density of Metal m), Thickness of the Metal (t), Specific Heat Capacity (Qc) & Distance from the Fusion Boundary (y) and hit the calculate button. Here is how the Peak Temperature Reached at any Point in Material calculation can be explained with given input values -> -221.562548 = 310.15+(1000000*(1773.15-310.15))/((1773.15-310.15)*sqrt(2*pi*e)*7850*0.005*4184*0.1+1000000).

FAQ

What is Peak Temperature Reached at any Point in Material?
The Peak Temperature reached at any point in material formula is defined as the temperature reached during welding in the heat affected zone and is represented as Tp = ta+(HNet*(Tm-ta))/((Tm-ta)*sqrt(2*pi*e)*ρm*t*Qc*y+HNet) or Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length). Ambient Temperature is the temperature of the surrounding, Net heat supplied per unit length can also be converted to newton since energy is newton multiplied meter, Melting Temperature of Base Metal is the temperature at which its phase changes to liquid to solid, Density of Metal is the mass per unit volume of the given metal, Thickness of the metal is the thickness of the base metal and is denoted by h symbol, Specific Heat Capacity is the heat required to raise the temperature of the unit mass of a given substance by a given amount & Distance from the Fusion Boundary is measured from the fusion boundary during welding.
How to calculate Peak Temperature Reached at any Point in Material?
The Peak Temperature reached at any point in material formula is defined as the temperature reached during welding in the heat affected zone is calculated using Peak Temperature Reached at a Distance of y = Ambient Temperature+(Net Heat Supplied per Unit Length*(Melting Temperature of Base Metal-Ambient Temperature))/((Melting Temperature of Base Metal-Ambient Temperature)*sqrt(2*pi*e)*Density of Metal*Thickness of the Metal*Specific Heat Capacity*Distance from the Fusion Boundary+Net Heat Supplied per Unit Length). To calculate Peak Temperature Reached at any Point in Material, you need Ambient Temperature (ta), Net Heat Supplied per Unit Length (HNet), Melting Temperature of Base Metal (Tm), Density of Metal m), Thickness of the Metal (t), Specific Heat Capacity (Qc) & Distance from the Fusion Boundary (y). With our tool, you need to enter the respective value for Ambient Temperature, Net Heat Supplied per Unit Length, Melting Temperature of Base Metal, Density of Metal, Thickness of the Metal, Specific Heat Capacity & Distance from the Fusion Boundary and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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