Since the sun is at it's brightest around noon, does that mean that a tree should be planted towards the south side of the house? If so then what if your front lawn also sits towards the south. Would i need to shift all my vegetables and flowering plants towards the east? What kind of tree would do best and what kind of shadow would you get from the tree around noon?
Around noon, you will only get shade directly beneath the tree - as the sun moves west, then the east side will start to get shade,which will increase as the afternoon wears on. The closer the tree to whatever is growing nearby, the more shade, but it will extend in length as the hours tick on. But you can't plant a large tree too close to your vegetables - it will compete for moisture and nutrients to the detriment of your vegetable garden,so it needs to be a distance away, and the larger/taller the mature height of the tree, the farther away it needs to be. Also bear in mind that a tree with a broad crown will cast more shade sideways as well as in length than,say, a cone shaped conifer will. Whether its deciduous or not may not matter - depends how strong the sun is likely to be during the winter months, and what you'll be growing at that time of year - if the uv levels are significantly lower during the winter months, then having a deciduous tree will be fine.
I'm a bit confused, because at one point I thought you mentioned shading a pergola rather than your vegetable garden...
I thought I'd add a few more thoughts, Hamid. Make sure you plant this tree far enough away from the house that allows for proper root growth and height. I'd make a scale mock up. Use a book for your house, a wine bottle with flowers for the tree and a light bulb as the sun. Keep the 'tree' and a 'side' of your home in scale.
Deciduous tree would be best for the most shade. And if you had winters it would allow for the sun to warm your house. Windows should have awnings for the best protection from the sun's direct heat.
Here is another idea that could provide shade for your house right away. Make a lattice of 2X2s, lapjointed, , attach it to the side of your home with a block to have the panel stand out away from your siding 10". Frame the panels (s) with 2X4s with metal like the use on trusses to strengthen the corners (back side of panels). On one side or both sides depending on the size of the panel (s), install hinges to be able to maintain your siding, paint, cleaning. Grow vines. Best to chose just one species. Paint the lattice either the color of your house or allow to dove grey using a UV enhancing wood stain. Or make it look the same as your pergola. Make as many as you like to look all the same. Or have a good carpenter make them for you. 6 to 8" grid squares/rectangles.
While your vines and trees are growing the lattice still provides shade, the shade pattern of the lattice looks wonderful giving your home more...interest. Also a hinged lattice makes it easy to clean and maintain whatever vine you chose. These panels could become a shutter system over your windows instead of awnings or they would look nice in conjunction with awnings.
My suggestion would be hops, Golden Hops. Fastest growing vine I know. I have no idea where you live. But this is a lighter vine that is gorgeous with huge bright green to yellow gold leaves. Also easy to chop down to the ground, pull out all the debris and start over. Just an idea. This vine would cover your panels the first season you plant them. You would have to prune them to keep them from covering the entire wall or your entire house. Just an idea. Leaves are 6 to 8" wide! But this might be too fast growing? Hops flowers are like little Japanese rice paper lanterns, beautiful.
If the heat is too intense for plants, young plants, your trees, cover them with white Reemay, a light fabric like material, white to reflect the heat allowing light to get to the leaves.